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Is there a statistically significant correlation between religious faith and total family income in the US?

Introduction and Aim of the Study

The main target of this study (which is available here in pdf) is to investigate any possible relation between religion and financial income in the US in the last decade. More precisely I decided to focus on Protestants, Catholics and the ones who claimed to belong to no religious community at all (identified as None). These three categories, according to the data, have been the most common ones in the United States in the period 2000-2012.
Therefore the target of the investigation may be summarized by the following question: “Is there a relationship between the religious faith of a US citizen (Protestant, Catholic or None) and his/her total family income?”
My personal interest derives from a general conviction that there could be some religious communities wealthier than others, due to historical, social or political reasons and the exploration of this kind of aspects may lead to underline some specific features going on behind the scenes. More generally I thing that digging this matters may enlighten some subtle pattern hiding behind the data, such as religious discrimination at work resulting in people belonging to a specific community getting higher, more qualified and more paid jobs. Highlighting this kind of aspects is a starting point for a broader research about social and financial conditions among and within different religious communities.

General Discussion about the Data of Interest

The research project was based on the data collected in the online-available database of the General Social Survey, 1972-2012 (Citation: Smith, Tom W., Michael Hout, and Peter V. Marsden. General Social Survey, 1972-2012 [Cumulative File]. ICPSR34802-v1. Storrs, CT: Roper Center for Public Opinion Research, University of Connecticut /Ann Arbor, MI: Inter-university Consortium for Political and Social Research [distributors], 2013-09-11. doi:10.3886/ICPSR34802.v1) (GSS), which since 1972 has been monitoring societal change and studying the growing complexity of American society. The GSS aims to gather data on contemporary American society in order to monitor and explain trends and constants in attitudes, behaviors, and attributes; to examine the structure and functioning of society in general as well as the role played by relevant subgroups; to compare the United States to other societies in order to place American society in comparative perspective and develop cross-national models of human society.

The dataset is composed by 57061 cases corresponding to an equal number of interviewed citizens. Each person may be considered as a single case, as there are several pieces of information (variables) which were recorded for each case. In particular, cases are single individuals respecting the following characteristics: all non institutionalized, English and Spanish speaking persons 18 years of age or older, living in the United States. As just mentioned each candidate was asked several questions about a number of aspects of his own life, his family, his community, the society he lives in.
The data were collected by three main methods:

  • computer-assisted personal interview (CAPI). Data are inserted directly into an electronic sheet over a PC and the interviewer and the respondent are both present at the moment of the survey, in front of the computer. The difference with CASI is that in the latter the interviewed is left alone in order to answer the questions more privately.
  • face-to-face interview.
  • telephone interview.

The two variables I took into account from the data set are the following:

  • income06: categorical variable. The interviewed was asked which of the proposed groups he/she thought his/her total-tax-less-family income of the previous year would fall. There are 25 possible interval varying from a minimum of less than 1000$ to a maximum of more than 150.000$, plus a category named “Refused”, including all the cases who did not accept to reveal their financial condition.
  • relig: categorical variable. The interviewed was asked by which of the proposed communities his/her religious faith would better be identified. A more proper description of the variable is going to be provided during the exploratory data analysis.

The study is observational because researchers recorded data “in a way that does not directly interfere with how the data arise”. The structure of the survey and the data collection methods are clearly not typical of an experimental setup. In the latter case, in fact, researchers would have sampled individuals and divided them into groups organizing an experiment in order to investigate the possibility of a causal connection between two or more variables.
From the point of view of the generalizability of the study it is crucial to focus on the population of interest, whic,h in this very case, includes all non institutionalized, English and Spanish speaking persons 18 years of age or older, living in the United States. According to 2011 American Community Survey Data on Language Use 79.2205% of american families speak English at home, while the 20.7794% speak Spanish which added up result in a global 99.9999%.

This means that we can reasonably generalize the results to the totality of US population 18 years of age or older. Furthermore the used data collection methods compensate each other in terms of any potential source of sampling bias. For instance, CAPI is mainly addressed to computer friendly persons. This bias may be prevented by phone interviews which enable researchers to reach and convince less “technology-friendly” people. The last but not the least is the face-to-face survey which compensates the unavoidable bias introduced by a phone call. The latter gives for granted the connection to a phone line which may not always be respected. In addition to that it is necessary to consider that generally children, youngsters or more generally minors do not have a clear financial overview over the family. Despite their belonging to a particular religious community they may have great insights into the total family income, which means that their contribution to the survey, at least on this very aspect, would have been pointless.

All this considerations lead us to the conclusion that the results of the study may be generalized to all US families. However, since the survey is observational, the findings do not imply causal relationships.

Exploratory Data Analysis

In the present section a brief exploratory data analysis is performed. The relevant statistics is provided together with the associated R code.

The first two used functions R are summary and str, which help to get a broader and in the mean time synthetic view over the data. As ir is clear the gss.after.subsetting data set is composed by only two variables , Income and Religion. Both are factors consisting respectively in 26 (actually 25 as I did not take into account the Refused category) and 13 levels. In particular Religion mantains all the original 13 levels despite only three of them have been selected (Protestant, Catholic and None).

In order to visualize the data in a cleaner way a plot is provided too. The whole data set has been converted into a contingency table, which has been properly plotted in the figure below.

The figure below shows pretty clearly the distribution of incomes among and within the three investigated communities. Nevertheless it is quite hard to identify any particular pattern hiding behind the data. It is necessary to proceed with a more complete and rigorous analysis in order to draw any conclusion concerning a possible correlation between religious community and family financial income. For further details about the data see the Appendix at the end of the report.



As stated at the end of the previous section in order to end up with a proper conclusion and answer the original question at the base of the study it is necessary to perform a rigorous statistic test on the data set. First a purpose of clearness, first of all we recap the main target of the project which is to answer the following question: “Is there a relationship between the religious faith of a US citizen (Protestant, Catholic or None) and his/her total family income?”

As we are dealing with two categorical variables (Income and Religion), both of which with more than two levels (respectively 25 and 3), only an hypothesis test is admittable. In particular, as no defined parameter of interest can be highlighted, I have performed a theroretical Chi-square test for independence, which is allowed by the fact that each particular scenario (i.e. cell count) has at least 5 expected cases. The proof of this condition being met is provided in the following table, which summarizes the whole dataset with each case joined by its expected value. As you can see all scenarios have expected value well above 5.

Income Protestant Catholic None
(x$1000) Real Expected Real Expected Real Expected
Below-1 67.00 65.90 23.00 30.80 30.00 23.20
1-2.999 62.00 56.60 22.00 26.50 19.00 19.90
3-3.999 40.00 41.80 17.00 19.50 19.00 14.70
4-4.999 26.00 28.00 11.00 13.10 14.00 9.90
5-5.999 36.00 42.30 22.00 19.80 19.00 14.90
6-6.999 48.00 51.10 21.00 23.90 24.00 18.00
7-7.999 63.00 59.90 27.00 28.00 19.00 21.10
8-9.999 98.00 94.00 33.00 43.90 40.00 33.10
10-12.499 181.00 179.70 72.00 84.00 74.00 63.30
12.5-14.999 172.00 160.50 70.00 75.00 50.00 56.50
15-17.499 156.00 156.10 70.00 73.00 58.00 55.00
17.5-19.999 118.00 114.80 47.00 53.70 44.00 40.40
20-22.499 174.00 173.60 81.00 81.20 61.00 61.10
22.5-24.999 166.00 169.80 83.00 79.40 60.00 59.80
25-29.999 256.00 241.80 109.00 113.10 75.00 85.10
30-34.999 252.00 263.20 133.00 123.10 94.00 92.70
35-39.999 270.00 250.00 109.00 116.90 76.00 88.00
40-49.999 440.00 417.10 199.00 195.00 120.00 146.90
50-59.999 369.00 370.40 175.00 173.20 130.00 130.40
60-74.999 471.00 453.90 206.00 212.30 149.00 159.80
75-89.999 349.00 345.10 176.00 161.40 103.00 121.50
90-109.999 279.00 284.10 142.00 132.90 96.00 100.00
110-129.999 185.00 185.70 87.00 86.90 66.00 65.40
130-149.999 100.00 116.50 64.00 54.50 48.00 41.00
150-Over 228.00 284.10 155.00 132.90 134.00 100.00

The total number of degrees of freedom is df = (R-1) X (C-1) which is equal to df = (25-1) X (3-1) = 48, well above the minimum allowed of 2.
As for the independence issue, the GSS sampling has been randomic and in any case the number of cases in each scenario as well as the total amount of cases is below the 10% of the population of the US.

Given that, we can state our hypothesis:

  • H0 : (nothing going on): Religion and Total Family Income are independent, meaning that the amount of money earned by a US family per year does not vary by belonging to either the Protestant or the Catholic community, or no religious community at all.
  • HA : Religion and Total Family Income are dependent, meaning that the amount of money earned by a US family per year does vary by belonging to either the Protestant or the Catholic community, or no religious community at all.

Let’s recall that applying the Chi-square test for independence means that we are to evaluate whether there is convincing evidence that a set of observed counts O11, O12, O13… ORC in RC categories are unusually different from what might be expected under a null hypothesis. Call the expected counts that are based on the null hypothesis, E11, E12, E13 … ERC computed as

$$E_{row \hspace{1mm} i,\hspace{1mm} col \hspace{1mm} j} = \frac{(row \hspace{1mm} i \hspace{1mm} total) \times (column \hspace{1mm} j \hspace{1mm} total)}{table \hspace{1mm} total}$$

If certain conditions are met, then the test statistic below follows a chi-square distribution with (R-1)X(C-1) degrees of freedom:

$$ \chi^2 = \frac{(O_{11}-E_{11})^2}{E_{11}} + \frac{(O_{12}-E_{12})^2}{E_{12}} + \cdots + \frac{(O_{RC}-E_{RC})^2}{E_{RC}} $$

The p-value for this test statistic is found by looking at the upper tail of this Chi-square distribution. We consider the upper tail because larger values of chi squared would provide greater evidence against the null hypothesis.

The result of the Chi-square test for independence over the data set of interest is the following:

Because we typically test at a significance level of α = 0.05 and the p-value is less than 0.05, the null hypothesis is rejected. That is, the data provide convincing evidence that there is some association between the amount of money earned by a US family per year and belonging to either the Protestant or the Catholic community, or no religious community at all.


The aim of the research project was to investigate whether there could be any association between the total tax-free income of an American family and their belonging to the Protestant, Catholic or none religious community at all. The dataset was taken from the General Social Survey 1972-2012 (GSS), which since 1972 has been monitoring societal change and studying the growing complexity of American society. the original database was subset in order to take into account only the two variables of interest, Income and Religion; the latter has been subset itself to select only three inner levels, Protestant, Catholic and None. Due to the tipology of the investigated data, only a hypothesis test based on the Chi-square test for independence can be performed.

The result of the statistical analysis leads us to reject the null hypothesis and then to state that there is some association between the amount of money earned by a US family per year and belonging to either the Protestant or the Catholic community, or no religious community at all.

This could be only the beginning of a wider study about correlation between religion and financial condition in the US. Deeper insights must be get into the matter and more complex statistical tools and techniques must be used in order to infer complete and satisfying conclusions.

APPENDIX – Attached Dataset

by Francesco Pochetti

What is the gambler’s fallacy?

gamblerImagine you are in a casino at a roulette table waiting to gamble. You have been following the game for a while and you’ve noticed that the last six outcomes were black. Well, it is quite remarkable, isn’t it? The probability to get six outcomes of the same color at the roulette is 1/64, approximately 1,6%. The chance to get seven consecutive blacks is the half, 1/128 or better 0,8%. Figures never lie! You must be very unlucky to obtain seven black shots. Therefore you put all your paycheck on red. But… wait a second. Is that right?

Obviously not! What you are missing is something fundamental which is the fact that consecutive outcomes at the roulette table are independent events which means that knowing the outcome of one provides no useful information about the outcome of the other. This involves that the probability to get seven consecutive blacks is truly 1/128 but the probability to obtain a seventh black after the first six ones is no more that 1/2, as there is nothing preventing the ball to stop either on a red or a black spot.

Unsuspecting gamblers may convince themselves that the odds are in their favor whilstroulette1 they are not! So, be careful!

That’s the gambler’s fallacy.  That’s it! Cool, isn’t it?


by Francesco Pochetti

Endocrine Disruptors: how we are poisoned by everyday chemicals

How many chemicals do we get in touch with every day? Are they safe? In which doses? What kinds of chemicals are they?

If you have ever tried to find an answer to the previous questions probably this is the right place to check it out. In order to be as rigorous as possible I report the transcript of the first part of a very interesting and together frightening video I found on the net on Earth Focus web page, which you can find here and which I embed hereafter. Therefore I limited myself to simply watching the video and carefully writing down what I heard.


The topic dealt is crucial and is about Endocrine Disruptors (ED), a class of compounds, well known to science, which tend to interfere with the biological processes at the base of hormonal control. Basically,  ED have a molecular structure which resembles very closely the one of the most important human hormones (testosterone, progesterone, estrogens…) ; this feature gives them the ability to deceive cellular receptors which cannot recognize the real hormones from the fake ones. The result is that even at very tiny doses these chemicals might be very dangerous, altering irreversibly the most basic physiological human processes.

The above video (which I highly recommend) has been built gluing together pieces of interviews from the highest world experts in this field, whom I list below, before pasting the transcript, and whom I report within the transcript itself in order to clarify the respective contributes.

  • Andy Igrejas (National Campaign Director/ Safer Chemicals, Healthy Families)
  • Theo Colborn, Phd (President & Founder, The Endocrine Disrupting Exchange)
  • Erin Switalski (Executive Director, Women’s voices for the Earth)
  • Cecil Corbin-Mark (Deputy Director, WE ACT)
  • Sean G. Palfrey, MD (Clinical Professor of Pediatrics & Public Health/ Boston University School of Medicine, MA)
  • Heather White (Executive Director, Environmental Working Group)
  • Judith Robinson (Executive Director, Coming Clean)
  • Mia Davis (Vice President of Health & Safety, Beauty Counter)
  • Johanna Congleton, Phd (Senior Scientist,  Environmental Working Group)
  • Linda S. Birnbaum, Phd (Director, National Inst of Environmental Health Sciences/ National Toxicology Program, NH)
  • Julia Brody, Phd (Executive Director, Silent Spring Institute)
  • Tracey Woodruff, Phd, MPH (Director, Program on Reproductive Health in the Environment/ University of California, San Francisco)




“They are everywhere in our environment, in the air we breath, the water we drink, the food we eat, they are in everyday products we use for personal care and cleaning, they are in our furniture, our children toys and the products we use in gardening and agriculture and almost all of us have them inside our bodies.

Andy Igrejas “Chemicals right now according to the best evidence we have are contributing to the chronic disease burden in this country in ways that are substantial.”

Sean G. Palfrey “We are seeing increases clearly in certain kinds of illnesses, asthma is one, autism in another, ADHD (Attention Deficit Hyperactivity Disorder) is a third”

endo5Theo Colborn “One out of every third child born today is going to have diabetes and if you are a minority it’s one out of two”

Andy Igrejas “Chemicals contribute to the incidents of leukemia”

Mia Davis “breast cancer, infertility”

Theo Colborn “alzhaimer’s and parkinson’s”

Tracey Woodruff “People are more obese […] than they were up to 20 years ago”

Judith Robinson “Child’s cancers are going on”

Linda S. Birnbaum “We’re seeing effects on sperm count in men […]”

Andy Igrejas “They are more of these bizarre heart effects particularly around male reproductive development”

Theo Colborn “If I were a parent I would be very concerned”

endo2They were meant to make life easier and they do. Chemicals fight diseases […] and support manufacturing. They’re big business, a key stone of the us economy from consumer goods to high technology almost all aspects of modern life depend on the chemical industry. Chemical production in the US has grown 25 fold since World War II. It sales above 763 billion dollars in 2011. The chemical industry supports over 3 million US jobs and invest billions in the research and development. Our bodies take in […] chemicals every day and this exposure has consequences for out health, our safety and our future.

Andy Igrejas “There are 84 thousand chemicals that are legal for commercing in the US and could be used to make all kinds of things, going to the products we bring into our homes, our workplaces and they are basically unregulated”

Theo Colborn “And of course every year new chemicals are coming on the line that have not been fully tested”

Erin Switalski “There are almost 13000 chemicals that are used in cosmetics and just about 10% of them have actually been evaluated for their safety. We found lead in lipsticks, there is mercury out there in skin lightening creams. We have found phormaldeid in products”

Cecil Corbin-Mark “[…] products that people apply to their faces and their skin daily”

pestSean G. Palfrey “Pesticides are clearly poisonous and it should be obvious to us that if they kill insects they are going to have the possibility of hurting us”

Judith Robinson “In our kitchen cabinet. If you open up the doors and you count up all the tin cans in there, all of them are going to be lined with Bisphenol A unless they are labeled that say they are not”

Sean G. Palfrey PCBs (Polychlorinated Biphenyls) might be in plastics, might be in cups, might be in containers we put in our microwaves, might be perfectly safe when they are first put on the shelf but quite dangerous once they start to break down”

Heather White “All we have is chemical companies that have created products that have contaminated literally every living thing on the planet”

Judith Robinson “I think that the corporations who are profiting from this really have run away with our system”

Heather White “Industrial chemical pollution begins in the womb”

Erin Switalski “Everything that we are bringing into our bodies if we choose to have children, we actually pass our rate on through to a developing child”

Mia Davis “Some of the chemicals we know can cross the placenta and enter the womb and have effects at incredibly tiny tiny doses”

Sean G. Palfrey “About ten years ago a seminal study was done on ten newborns cord blood. The cord blood as the baby was born contained several hundred toxic elements which terrified all of us”

endo3Heather White “Chemicals like Bishenol A, many different classes of flame retardants, we found DDT and PCBs, […] chemicals that we interact with every day from consumer products”

We now know that along with the nutrients and oxygen that the mother supplies to the baby comes a […] toxic chemicals.

Sean G. Palfrey “We know that chemicals will affect younger children, fetuses, new born babies and young children in general more than older children and adults and the reason for that is that younger children and fetuses are developing much more rapidly, their organ systems are much more sensitive”

Erin Switalski “What science is starting to show now is that early exposure to toxic chemicals at critical points when a child is in the womb has effects later in life”

Endocrine disruptors are chemicals of growing concern, fetuses and children exposed to even minute amounts may develop a wide range of health conditions from diminished intelligence to cancers. Our endocrine glands produce hormones that regulate the basic processes of our body like metabolism, growth reproduction and development. Endocrine disruptors disturb how these processes work.

baby1Johanna Congleton “Endocrine disrupting chemicals interfere with hormones signaling. Proper hormone signaling is very important for fetal development and for childhood development as well as sexual maturation. Therefore compounds that interfere with these processes could have very profound effects”

Linda S. Birnbaum “Many of these and other chemicals appear to be associated with lower IQs and/or behavioral problems in children”

Theo Colborn “If you look at what these chemicals can do to the brain we know now these chemicals are also interfering with how we process information”

Sean G. Palfrey “They affect our genetic outcome, they increase the possibility that we lose a baby, they change the activity of our hormones, our sex hormones in a variety of different ways”

Linda S. Birnbaum “We’re seeing children starting puberty at younger ages. So there are many little girls that have, for example, breast at the age of seven in the african american community and eight in the white community. This is too young for our children”

980 endocrine disrupting chemicals have now been identified. Among the most ubiquitous are a class of compounds called Phthalates, Bishpenol-A and flame retardants including PBDEs, chemicals so common that almost all of us have them inside our bodies.


ftalaJudith Robinson “So you may have vinyl floors, you may have vinyl shower curtains, you may have vinyl toys that your kids are using, […] leaching Phthalates which are known to be toxic into the environment where you get exposed”

Phthalates are in many common products, including food packaging, building materials and pharmaceuticals; they’re in our cars and even in new cars’ smell. They’re used in cosmetics to hold fragrance and health products to more effectively penetrate and moisturize the skin.

Julia Brody “We’re concerned about their effects on males, on baby boys…”

Johanna Congleton “We see problems with testicular development, problems with sperm development. They can be associated with a decrease in testosterone levels.”

Tracey Woodruff “So if you interfere with the testosterone levels they don’t quite go up all the way. In animal studies it has been shown to be linked to cryptorchidism, so undescended testicles and hypospadias, which is incomplete formation of the male reproductive organ”

babyPhthalates may also be feminizing boys; scientists found that Phthalates may be associated with a shorter anogenital distance, the distance between the genitals and anus, a subtle marker of feminization in boys. The American Chemistry Council which represents chemical manufacturers says Phthalates are among the most thoroughly studied family compounds in the world and have a history of safe use. But Phthalates are banned from children toys in more than 10 countries and the European Union. In the US 3 Phthlates were permanently banned from children toys […] in 2008 because of their potential to leach frel plastic if chewed or sucked.

Johanna Congleton “The worst actors have been taken out of children’s toys but they are still widely used in many other types of consumer products and a monitoring study showed that these chemicals are still showing up in people”



Tracey Woodruff “BPA is of concern because it looks like an estrogen and it has been shown to have a weak estrogenic effect and so if you are exposed to a chemical that might interfere with your hormone levels, in this case estrogen, it can have effects particularly during development.”

Linda S. Birnbaum “And there are preliminary data that say that it may infact […] directly increase the risk of breast cancer in animal”

BPA1Julia Brody “If they are chemicals that affect the development of the breast even before birth, if they are chemicals that cause breast thumors in animals, these are chemicals that we want to be worried about and start thinking about reducing exposure”

In addition to breast cancer BPA may be associated with genetic damage and a wide variety of reproductive, methabolic, behavioral and developmental problems. It’s one of the top industrial chemicals in the world. About 6 billion punds of BPA are produced globally each year, earning manufacturers a profit of some 8 billion dollars.

Johanna Congleton “We’ve made some progress with eliminating BPA from infant productsBPA2 including infant formula packaging, baby bottles and plastic drinking cups.”

But BPA remains widely used in many consumer products from electronic to medial equipmentsand it’s in the resin of cans […] and in plastic bottles where it can leach into the food or liquid contents inside. The Food And Drug Administration, which has jurisdiction over food packagings says BPA is safe at the low doses that occur in food but many research and health organisations remain concerned about BPA’s impact on human health at current levels of exposure.


PBDEOver 1,5 million tons of flame retardants are used worldwide each year. They’re added to consumer products to meet flamability standards, though their effect remains questionable.

Judith Robinson “Any furniture that you have that has polyurethane in it, that is most of our furniture, may contain toxic flame retardants and those flame retardants don’t stay put in the foam, they leach out and they end up in the dust in our house where we are all exposed, in particular kids who are on the ground, low, picking things up with their hands in their mouth. They are exposed to that dust which is gonna have flame retardants chemicals in it”

There are many different kinds of flame retardants. Among the most studied are PolyBrominated Diphenyl Ethers (PBDEs). Scientists have linked PBDEs to a wide range of conditions from delayed development to learning problems and diminished intelligence. […] Two PBDEs, pentaBDE and octaBDE were taken out the US market voluntarily in 2004 because of growing health concerns. Production of PBDEs deca is in the process of of being terminated.

flameLinda S. Birnbaum “The problem with all PBDEs is that they are very persistent in the environment”

Johanna Congleton “The issue with PBDEs is that they’ve been replaced with other types of chemicals that may have very similar concerns and perhaps even the same mechanism action in terms of their ability to disrupt the endocrine system”

The flame retardants Clorinated Tris and Fire Master 550, which may be linked to DNA damage, cancer or neurological defects continue to be widely used in polyurethane foam and in a number of children’s products.

Linda S. Birnbaum “So I think that the whole issue of flame retardants is one for which there is some concern and I think the real question we should ask, and maybe we need to ask this more broadly about other kinds of chemicals as well, is do we really need them?




by Francesco Pochetti

Why does an airbag inflate?

For years, seat belts have represented the unique real safety device in our cars. Despite its not being immediately accepted, eventually the seat belt demonstrated all its efficiency.

The same happened to the airbag, whose concept has been around for many years. Its invention goes back to 1952, by John W. Hetrick who submitted the patent the following year. The first use is remembered at the end of the sixties, together with the big improvements to the other components necessary to its proper functioning. After all the prototypes introduced and tested by practically all the biggest car companies, the first vehicle carrying this kind of innovation was the Oldsmobile Toronado in 1973, followed by other models produced by Buick and Cadillac. In Europe it was Mercedes Benz the first one to offer the accessory on its top cars in 1980. After a first period of indifference and skepticism the airbag briefly took over at industrial level, turning into one of the strongest safety devices on a vehicle. The National Highway Traffic Safety Administration estimates that the combination of an airbag plus a lap/shoulder belt reduces the risk of serious head injury by 85 percent compared with a 60 percentage reduction for belts alone.

But how does an airbag work? Why does it inflate? Well you can believe it or not but chemistry saves our lives!

airTiming is absolutely crucial for the airbag to save a life. An airbag must be able to inflate and work properly in a few milliseconds after the first collision. Meanwhile, it has to be projected in order to be restrained from deploying when the accident is negligible. Therefore, the primary component of the system is a well calibrated sensor able to reveal front strokes and to generate an immediate inflation of the device. One of the simplest mechanism studied for the collision sensor is a steel little sphere which is free to slide inside a smooth pipe. The ball is controlled by a magnet or by a rigid spring, which reduces the movements of the sphere when encountering bumps or potholes. Nevertheless, when the car decelerates rapidly, as for example during a crash, the sphere moves fast to the front triggering an electric circuit.

When the sensor switches on the circuit, a tiny mass of sodium azide (NaN3) starts burning in a very fast reaction, developing nitrogen (N2). This gas fills a nylon or polyamide envelope, which inflates completely after only 40 milliseconds. Ideally the body of the driver should not hit the airbag during the phase of inflation but just after, when it is beginning to lose pression. Otherwise the surface of the envelope would be too hard and may hurt the driver.

imagesInside the airbag there is a gas generator containing a mixture of NaN3, KNO3, and SiO2. When the car undergoes a collision, a series of three chemical reactions occur inside the gas generator. These reactions produce gas (N2) to fill the airbag and convert NaN3, a highly toxic substance, to harmless sodium and potassium silicate, a major ingredient of glass. Sodium azide (NaN3) can decompose at 300oC to produce sodium metal (Na) and nitrogen gas (N2). The signal from the deceleration sensor ignites the gas-generator mixture by an electrical impulse, creating the high-temperature condition necessary for NaN3 to decompose. The nitrogen gas that is generated then fills the airbag. The purpose of the KNO3 and SiO2 is to remove the sodium metal (which is highly reactive and potentially explosive) by converting it to a harmless material.


First, the sodium reacts with potassium nitrate (KNO3) to produce potassium oxide (K2O), sodium oxide (Na2O), and additional N2 gas. The N2 generated in this second reaction also fills the airbag, and the metal oxides react with silicon dioxide (SiO2) in a final reaction to produce silicate, which is harmless and stable. (First-period metal oxides, such as Na2O and K2O, are highly reactive, so it would be unsafe to allow them to be the end product of the airbag detonation.)

Well… as I said chemistry saves lives!

That’s it! Cool, isn’t it?

(Some information summarized from “Gas Laws Saves Lives: The Chemistry Behind Airbags”)


by Francesco Pochetti

Why does Aurora Borealis occur?

One of the most spectacular phenomena in nature is without doubt the amazing games of light, shades and colors called Aurora Borealis and Australis, depending on which of the two poles it is perceived at.

Those who live at the extreme north and south of Earth might at times experience this colored spectacular lights shimmering across the night sky. But what makes these lights  appear?

Well, it may sound weird but everything begins from the sun.

The temperature above its surface is millions of degrees Celsius. At this temperature, collisions between gas molecules are frequent and explosive. Free electrons and protons are thrown from the sun’s atmosphere by its rotation and escape through holes in the magnetic field. Blown towards the earth by the solar wind, the charged particles get in contact first of all with our planet’s magnetic field which may be thought as been generated by a giant rectangular calamite positioned at the centre of the Earth. The structure of a rectangular calamite’s magnetic field is well known and is based on closed field lines getting out of the south pole and entering the north one. Exactly the same happens on Earth where we have to imagine a giant magnetic shield protecting the whole planet surface, except for the source (south pole) and the pit (north pole) of the field lines which are necessariauroraly more exposed.

The charged particles scattered all around by solar wind are largely deflected by the earth’s magnetic field. In particular these charges are trapped by the force of the magnetic field and they start following the force lines being channeled either towards the south or the north pole.  Therefore some particles enter the earth’s atmosphere and collide with gas atoms or molecules at various heights. These collisions  excite gas particles causing them to light up. Sounds something similar to phosphorescence… 

What does it mean for an atom to be excited? Atoms consist of a central nucleus and a surrounding cloud of electrons encircling the nucleus at increasing distances from the centre. When charged particles from the sun strike atoms in Earth’s atmosphere, electrons move to higher-energy orbits, further away from the nucleus. Then when an electron moves back to a lower-energy orbit, in order to lose the amount of energy it has gained, it releases a particle of light or photon. The color of emitted light depends on the atom and on the size of the inner electron’s jump, but the result is absolutely amazing as it involves billions and billions of particles emitting light at the same time.

aurora3What happens in an aurora is similar to what occurs in the neon lights we see on many business signs. Electricity is used to excite the atoms in the neon gas within the glass tubes of a neon sign. That’s why these signs give off their brilliant colors. The aurora works on the same principle – but at a far more vast scale.

The aurora often appears as curtains of lights, but they can also be arcs or spirals, often following lines of force in Earth’s magnetic field. Most are green in color but sometimes you’ll see a hint of pink, and strong displays might also have red, violet and white colors. The lights typically are seen in the far north – the nations bordering the Arctic Ocean – Canada and Alaska, Scandinavian countries, Iceland, Greenland and Russia. And of course, the lights have a counterpart at Earth’s south polar regions.

The most common auroral color, a pale yellowish-green, is produced by oxygen molecules located about 60 miles above the earth. Rare, all-red auroras are produced by high-altitude oxygen, at heights of up to 200 miles. Nitrogen produces blue or purplish-red aurora.

Several fascinating  myths and legends are connected to the phenomenon of auroras.

aurora2In Finnish, the name for the aurora borealis is “Revontulet”, which literally translated means “Fox Fires.” The name comes from an ancient Finnish myth, a beast fable, in which the lights were caused by a magical fox sweeping his tail across the snow spraying it up into the sky. The Lapps, or the Saami, a people who are a close relative ‘race’ of the Finns, who live in Lapland — that is, north of the Arctic Circle, in what officially are Northern Finland, Sweden, and Norway — traditionally believed that the lights were the energies of the souls of the departed. In Norwegian folklore, the lights were the spirits of old maids dancing in the sky and waving.  Several of the Eskimo tribes also connected the lights with dancing. Eskimos in Eastern Greenland attributed the northern lights to the spirits of children who died at birth.


That’s it! Cool, isn’t it?


by Francesco Pochetti

Why do we slide on ice?



Have you ever wondered why we are able to slide on ice? For example why can we sky or skate? Why do we slide on ice and not on other smooth surfaces?

Well, the reason is quite simple and it is completely contained in the above image representing the so called water’s phase diagram.

icewaterPhase diagrams show the preferred physical states of matter at different Temperatures (abscissa – °C) and Pressure (ordinate – bar). Within each phase, the material is uniform with respect to its chemical composition and physical state. At typical temperatures and pressures on Earth water is a liquid, but it becomes solid (ice) if its temperature is lowered below 0°C and gaseous ( water vapor) if its temperature is raised above 100°C, at the same pressure. Each line (phase line) on a phase diagram represents a phase boundary and gives the conditions when two phases may stably coexist in any relative proportions. Here, a slight change in temperature or pressure may cause the phases to abruptly change from one physical state to the other. Where three phase lines join, there is a ‘triple point’, when three phases stably coexist, but may abruptly and totally change into each other given a slight change in temperature or pressure. Under the singular conditions of temperature and pressure where liquid water, gaseous water and hexagonal ice stably coexist, there is a ‘triple point’ where both the boiling point of water and melting point of ice are equal.  A ‘critical point’ occurs at the end of a phase line where the properties of the two phases become indistinguishable from each other, for example when, under singular conditions of temperature and pressure, liquid water is hot enough and gaseous water is under sufficient pressure that their densities are identical. Critical points are usually found at the high temperature end of the liquid-gas phase line.

Analyzing a phase diagram it is generally possible to predict the thermodynamic behavior of the considered substance.

Water is a scientifically fundamental example of this kind of analysis. So, let’s think about what may happen on a skating rink. The temperature is obviously under 0°C. At this temperature and at the pressure of 1 bar the thermodynamically water stable phase is the solid one. There’s no doubt that there would be ice.

skierBut exactly when an hypothetical skater puts the blade of its runner over the surface of ice the situation changes. Or better the pressure conditions change. This pressure variation involves only the ice surface below the blade of the runner. Actually, the skater applies a pressure on the ground with its weight, determining a global pressure increase over the considered ice area.

Looking at the above water’s phase diagram, it is clear that if we increase the pressure the temperature of water solidification (temperature at which water is converted to ice) decreases under 0°C. The natural consequence is that the skater’s weight makes ice melt under the runner’s blade, as in that conditions of pressure and temperature the thermodynamically water stable phase is the liquid one. This means that, actually, the skater is not sliding over ice but over a thin layer of water between the blade and the below ice! That’s exactly what happens with a skier!

Cool isn’t it?


by Francesco Pochetti

Why does phosphorescence occur?

Ever wondered why the little stars glued on our rooms’ ceilings go on glowing after we’ve switched off the light? What about funny shirts or glasses which are visible at night despite darkness? Why does all this stuff happen?

Well the phenomenon which is behind this cool events is called phosphorescence and we’are about to get a little bit of insight on it!

To better understand what goes on behind the scenes when this phenomenon occurs we have to ask ourselves a simple but fundamental question. What does it happen when a material is exposed to light? Which, in a more basic form, could be reasked in the following way:  what does  happen when a molecule is exposed to light?

Nice one!

fosfo1Without getting into a too detailed analysis of the events we could simply answer the question in this way: the considered molecule absorbs the incident light. Or better, considering that a light beam consists in “little energetic packages” called photons, we should say that when a beam of photons bombs a material’s surface, the inner molecules absorb light in the form of “energetic particles”. The primary consequence of this absorption is that the molecules which were hit increase their internal energy. This energy, however, cannot be kept forever by the molecular system. In general it is quite immediately released by the molecule. This phenomenon is extremely fast and we could never appreciate it to the naked eye!

But let’s see a little bit more in detail what happens inside the molecule right after a photon absorption. There is a huge amount of extremely complex phenomena which are triggered by the absorption of light; all of them can only be explained using quantum mechanics.

fosfo3Nevertheless it is still possible to have an idea of what’s going on in the following way. We first have to accept that each molecule has only well defined accessible energy levels, which means that everything hitting the system won’t automatically be absorbed. We can imagine the reachable energy levels of a molecular system as a building’s several floors. We have also to imagine that these floors are connected one to the other by an internal lift, which lets us reach them from the bottom to the top, and that, in the meantime, we can only use the stairs to go down. That’s it? Absolutely not! There’s another complication. While going down we cannot necessarily access to each floors, as if we had a direct access from the fourth floor to the first one but in order to pass from the third to the second we found a closed keyless door. Forbidden transition there!

Our molecule can be compared to a young man living on the ground floor of this imaginary building and our absorbed photon as a sort of nutritional supplement giving the weak young man some energy to stand up and climb the building to higher floors!

Ok.. So, what does happen after a molecule has absorbed (the right amount of) energy?

Our young man can now stand up and, completely revitalized, takes the lift till the floor allowed by the amount of acquired energy. That’s exactly (more or less!) what happens to a molecular system. It absorbs a photon whose energy excites the molecule to defined level. And what about the energy release?

Our young man has to descend back to the ground floor in order to lose all he has acquired. That’s not easy at all because there is the probability for him to find a forbidden path from a floor to an other. A closed door. What then? Theoretically he should stop and stay there, hopeless. Practically he could, for instance, force the door and access the forbidden transition. Obviously it would not be so fast at all. He would need time to open a passage and finally crash the door. Probably plenty of time. But finally he would succeed and he’d be able to go back to where he began. The ground floor!

After this awesome little story we are able to answer the first real question. Ever wondered why the little stars glued on our rooms’ ceilings go on glowing after we’ve switched off the light?

fosfo2Here’s the answer: when we turn the light on, the stars begin absorbing energy. Or better the molecules inside the material start absorbing photons and get excited to a well defined molecular energy level. Immediately after they try to release this energy but it may happen that the system, attempting to go back to the ground floor, finds itself stuck at a particular energy level. Quantum mechanics reads that, in theory, there are some forbidden transitions. No way to pass! In practice, however, the molecule succeeds in forcing its passage to a lower molecular energetic level. Generally, this operation requires plenty of time, which means that our little star on the ceiling goes on glowing for minutes or hours after its first absorption.

When we switch off the room’s light we will be able to clearly see the phosphorescent star which is slowly releasing the absorbed energy  in the form of light! Phosphorescence! That’s it!

Cool isn’t it?


by Francesco Pochetti

Why does a microwave oven heat so quickly?

Have you ever wondered why we are able to cook food so fast in a microwave oven?
Why is it so convenient in terms of time to use it instead of a classic oven?

To discover what lies in the backend of a microwave oven let’s start from its main components. This kind of oven contains three most important devices: a vacuum tube called a magnetron, which generates the energy that heats food, a waveguide hidden in the wall, to direct energy to the food and a chamber that holds the food and safely contains the radiation. The real cool stuff which is behind this revolutionary device is exactly this last one: the microwave radiation! After having been generated by the magnetron it is channeled by the waveguide and finally scattered into the main chamber of the oven.

fieldFrom a physical point of view, as all the radiations, microwaves are nothing less than an oscillating electromagnetic field, the same as light, or radiowaves.

In principle a microwave does not heat differently than any other type of heat device; at a molecular level we are dealing about an energy transfer that results in an increased motion of the molecules and eventually in a rise in temperature. Its unique feature comes as follows: in a traditional oven we heat food by placing the it inside a radiated chamber with hot walls which cause the outside of the meal to raise in temperature. The inside of the food cooks by the heat transfer taking place from the hot surface to the inside. In contrast, energy from the magnetron penetrates into the food which means that all its mass can cook simultaneously. But how does he do this?


Well our food is generally filled with water which is a funny molecule positively charged at one end and negatively charged at the opposite one. To give this molecule an energy we expose it to the electromagnetic wave generated from the magnetron; this radiation stimulates simultaneously all the water molecules it encounters on its path. The typical microwave electromagnetic field oscillates 2.450.000.000 times per second. Water will try to allign with the oscillating radiation of the electric field, whose very fast variations rock the molecule back and forth rapidly. Well, imagine for a second a water molecule trying desperately to find a stable position in space being punched 2.450.000.000 times per second! That’s a big deal! The natural consequence is that the molecular friction creates heat and the frentic motion destroyes hydrogen bonds which bind molecules to its neighborhood. All this incredibly fast stuff is eventually translated into a progressive, rapid and homogeneous cooking of our food!

Cool, isn’t it?


by Francesco Pochetti

Why is rum and Cola called Cuba Libre?


According to IBA (International Bartenders Association) the classic Cuba Libre must be built adding in a highball the following ingredients with the following doses:

  • 5cl of White Rum
  • 12cl Cola
  • 1cl Fresh lime juice

There are several hypothesis over the origin of the name of this incredibly famous cocktail.

At the moment the most accepted version of the facts is the following one.

downloadThe world’s second most popular drink was born in a collision between the United States and Spain. It happened during the Spanish-American War at the turn of the century when Teddy Roosevelt, the Rough Riders, and Americans in large numbers arrived in Cuba. One afternoon, a group of off-duty soldiers from the U.S. Signal Corps were gathered in a bar in Old Havana. Fausto Rodriguez, a young messenger, later recalled that Captain Russell came in and ordered Bacardi (Gold) rum and Coca-Cola on ice with a wedge of lime. The captain drank the concoction with such pleasure that it sparked the interest of the soldiers around him. They had the bartender prepare a round of the captain’s drink for them. The Bacardi rum and Coke was an instant hit. As it does to this day, the drink united the crowd in a spirit of fun and good fellowship. When they ordered another round, one soldier suggested that they toast ¡Por Cuba Libre! in celebration of the newly freed Cuba. The captain raised his glass and sang out the battle cry that had inspired Cuba’s victorious soldiers in the War of Independence.

That’s it! Cool, isn’t it?


by Francesco Pochetti

Why do we get glued to ice when we touch it with tongue or fingers?


Ever wondered why when we pick up an ice cube between two fingers we tend to get glued to that? And what about the horrible sensation of feeling our tongue stuck on an ice lolly during the summer?

Well, this awful effect is essentially due to the moisture over our skin, which, getting in contact with a surface below zero degrees Celsius, instantly freezes. The result is that the two frozen regions melt together giving us the sensation of being glued to ice.

It is obvious that the effect is highly increased with the tongue which is naturally humid and so much more affected by instantaneous freezing!


by Francesco Pochetti