Airbag Post Lab. Experiment 9. Making an Airbag with Gas Laws.

Experiment 9. Making an Airbag with Gas Laws
Terms:
• Absolute zero
• Avogadro’s Law
• Barotraumas
• Boyle’s Law
• Charles’ Law
• Direct relationship
• Gas constant (R)
• Ideal Gas Equation
• Indirect or inverse relationship
• Kelvin scale
• Pascal
• Pressure
Introduction
You may not feel it but at this very moment millions of O2 and N2 gas molecules arebouncing off your head. In gases, the molecules are very far apart from one another, movingvery fast, and quite literally bouncing off the walls and each other. Pressure measures the forcewhich these bouncing gas molecules have per unit area. While the official scientific unit forpressure is the Pascal, other units are used too – atmospheres (atm), mm mercury (mm Hg),and Torricelli (torr). Normal atmospheric pressure is ~101.3 kilopascals, or ~1 atm or ~760 mmHg or 760 torr.
The Ideal Gas Equation
The physical condition or state of a gas is defined by four variables – pressure (P),temperature (T), volume (V) and the number of moles (n) of the gas present. These variableswere summarized in three Gas Laws - Boyle’s Law, Charles’s Law and Avogadro’s Law (Table 1).Each law looks at the relationship between two variables while the other two variablesare held constant. Boyle’s Law says that the pressure and volume of a gas are inversely relatedto each other if the temperature and amount of the gas (in moles) remain constant. In otherwords, as the atmospheric pressure on a gas increases, its volume decreases. Charles’ Law saysthat the temperature and volume of a gas are directly related so that as temperature increasesso does the volume of the gas if the amount of the gas and its pressure remain constant.Avogadro’s Law says that at a constant temperature and pressure, the volume of a gas isdirectly proportional to the amount of the gas in moles. Or - the more gas molecules you have,the more space (volume) they take up. Also, at a given temperature and pressure, one mole ofany gas (6.022 X 1023 gas molecules) has almost exactly the same volume. At 0oC and 1atmosphere of pressure, one mole of any gas occupies a volume of 22.41 liters. So, for gases, ifFigure 1. Used with a seatbelt, airbags in cars are estimated tohave reduced serious head injuries by up to 85% compared topassengers with no restraints. A crash sensor detects a suddendeceleration which ignites a series of 3 chemical reactions and fillsthe airbag with nitrogen gas (N2).http://3.bp.blogspot.com/_zTL2b_tTBzc/SSIDIPsEWI/AAAAAAAAAeo/g8e-v4txqD0/s400/airbag1a.gif67you know the volume of the gas, you can figure out the number of moles of the gas present.Example: If you have 5 liters of O2, N2 or Ne, how many moles of the gas do you have?5 L * (1 mol/22.41 L) = 0.22 molName of Law Two Variables of Law Relationship between the variablesBoyle’s Law Pressure and Volume Indirect P ~ 1/V - at constant n & TCharles’s Law Temperature and Volume Direct V ~T - at constant n & PAvogadro’s Law Quantity and Volume Direct V ~ n - at constant P & TTable 1. Summary of the three Gas Laws which led to the Ideal Gas Equation. The Ideal GasEquation (PV=nRT) combines all three laws into one equation and describes the effectsof pressure (P), volume (V), temperature (in Kelvin) and number of moles (n) on thephysical state of a gas. R is the gas constant.Ideal Gas Equation gives you a summary of all three gas laws (Equation 1 below). For‘ideal’ gas, we have two assumptions: 1) gas molecules don’t interact with each other (mostlytrue except at low temperatures and very high pressures); and 2) gas molecules have novolume (false but their volume is so small it usually has no significant effect on how theybehave).Keeping track of the units is very important when you're using the ideal gas law.Temperature is always reported in Kelvin for the Ideal Gas Law and Kelvin = Centigrade +273.15. There are several different units of pressure which you can use and that affects whichgas constant (R) you use. The most commonly used gas constant value or R is 0.08206 Latm/mole-Kwhich requires the pressure to be in atmospheres.EQUATION 1 PV = nRT Where: P = pressure V = volume in L n = number of moles R = 0.08206 L-atm/mole-K T = temperature in KHave you ever had an ear ache? Or wondered why yawning and swallowing can relievethe pain in your ears? Or why scuba divers get the ‘bends’ (actual bubbles of nitrogen gas) ifthey rise to the surface too quickly after a deep dive? The Gas Laws explain each of thesebarotraumas, which are physical damage to the human body due to differences in pressurebetween inner air spaces (like the middle ear or lungs) and the surrounding air or water.The Chemistry of AirbagsWhat does an airbag need to do to decrease the incidence of fatalities and head injuriesin car crashes? Airbags must: 1) detect and distinguish between serious collisions and minor 68fender-benders; 2) deploy rapidly (< 40 milliseconds); 3) begin to deflate before the passengercontacts the airbag; and 4) reduce fatalities and injuries in automobile accidents. The NationalHighway Traffic Safety Administration currently estimates that airbags reduce the risk of serioushead injury by 85 percent compared to a 65% reduction for seat belts alone.Airbags contain a mixture of three solids - sodium azide (NaN3), potassium nitrate(KNO3), and silicon dioxide (SiO2). When a sensor detects a sudden deceleration (an impendingcrash), an electrical circuit is switched on that ignites the sodium azide (Equation 2). Sodiumazide doesn’t react so much as explode - producing solid sodium and nitrogen gas which rapidlyfills the airbag. Look at the MSDS for sodium azide and you’ll see that it’s extremely poisonous,extremely explosive and extremely hazardous with contact. Solid sodium, a product of thesodium azide decomposition, is also very explosive and reactive. As a result, the second andthird reactions in airbags are specifically designed to convert sodium metal product into aharmless, final product – glass. The second reaction (Equation 3) also produces nitrogen gas(N2) which helps fill the airbag even more quickly. All of the sodium azide is consumed in theinitial reaction.Figure 2. This series of three chemical reactions is often used to inflate airbags with nitrogen gas. Thefinal product is a harmless but stable product – glass or silicate. The volume of nitrogen gas produceddepends on the initial number of moles of sodium azide and potassium nitrate present in the airbag.Filling an Airbag with the Gas Laws and a Balanced Chemical EquationIn order to figure out exactly how much sodium azide should be used to fill an airbag, allyou need are the ideal gas equation, a little stoichiometry and a balanced chemical equation.Let’s say that the airbag when fully inflated holds a gas volume of 10 liters. With Avogadro’sLaw and the balanced chemical equation, you can determine how many moles of sodium azideare needed to produce this much N2. The individual steps are outlined below but Equation 5 69wraps all three steps into one calculation.• STEP 1 - Convert the 10 L of N2 gas needed to fill the airbag into moles of N2 withAvogadro’s Law which says that one mole of any gas occupies 22.41liters.10 L N2 * (1 mol of N2/22.41 L) =0.44622 moles of N2 needed to fill airbag• STEP 2 – Balance the chemical equation for the reaction (Equation 2 is alreadybalanced). Then use the balanced equation to see how many moles of NaN3 are neededto produce the moles of N2 above. (0.44622 moles of N2 needed) (2 mol NaN3/3 mol of N2) = 0.29748 moles of NaN3needed• STEP 3 - Convert moles of sodium azide into grams of sodium azide.(0.29748 moles of NaN3 needed) (64.99g/mol NaN3) = 19.33 grams of NaN3needed• EQUATION 5 - Amount of sodium azide needed to fill a 10 L airbag=10L N2*(1mol of N2/22.41 L)*(2mol NaN3/3mol of N2)*(64.99g/mol NaN3)=19.33g NaN2 STEP 1 STEP 2 STEP 3[NOTE: For simplicity, we’re going to ignore the second reaction even though it also producesnitrogen gas.]PROCEDUREInstead of reactive and poisonous sodium azide, you’ll use a different reaction to fillyour airbag today (Equation 6). When acetic acid and sodium bicarbonate (baking soda) react,they produce water, sodium acetate and carbon dioxide in a neutralization reaction. Grocerystore vinegar is usually ~5% acetic acid, or every 100 mL of vinegar contains 5 mL of acetic acid.EQUATION 6: CH3COOH (l) + NaHCO3 (s) à H2O(l) + NaCH3COO(aq) + CO2(g) Acetic Sodium Water Sodium Carbon Acid bicarbonate acetate dioxidePick a ‘vehicle’ for your egg to travel and a baggie to act as the airbag. You want to makethe right amount of carbon dioxide so that the airbag inflates enough to be effective. The flowchart outlines the calculations which you’ll need to do to find those numbers. 70Flowchart of Calculations to Make the Perfect AirbagQuestion 1: What volume of gas should be in your airbag?• Airbags only work as a cushion if they inflate to just the right volume. If the reactionmakes too much gas, the airbag might explode. But if the reaction makes too little gasthere won’t be any cushion for the egg’s landing.• To determine the optimal volume of gas for the airbag is to fill it with water first. Adjustthe amount of water until you think the airbag has just about the right volume in it togive the egg a soft landing. Try to purge all the air from inside the baggy before you sealit up. Does the airbag still fit inside the vehicle you’ve chosen and still have some roomfor the egg? Is the airbag inflated enough to provide a nice cushion for the egg?• The volume of water in the airbag equals the volume of gas you want your reaction tomake. Add the water from your airbag into one of the large graduated cylinders andread the volume. Now you know what volume of gas you want your reaction to make.Record this on your Data Sheet.• Thoroughly dry your airbag inside and out.Question 2: How many moles of CO2 gas are required to fill the volume of gas in Question 1?• First, convert the volume calculated in question 1 from mL to L. Now convert liters ofgas into moles. Show your calculations on the Data Sheet. Look at STEP 1 if you need ahint on the calculations.Question 3: Is the chemical equation for the reaction balanced?• On the Data Sheet, balance the equation for the sodium bicarbonate and acetic acidreaction. 71Question 4: How many grams of sodium bicarbonate are needed to produce the needednumber of moles of CO2?• Use the balanced chemical equation to determine how many grams of sodiumbicarbonate are needed to make the # moles of CO2 to fill the airbag. No sodiumbicarbonate should remain when the reaction is complete.• Show your calculations and record your answer on the Data Sheet. Check out STEPS 2and 3 for help.Question 5: How many moles of acetic acid are needed to make the required number ofmoles of CO2?• Use the balanced chemical equation to determine how many moles of acetic acid areneeded to make the desired amount of CO2. No reactant should remain at the end ofthe reaction.Question 6: How much vinegar contains the required number of moles of acetic acid needed?• Since vinegar is 5% acetic acid and pure acetic acid is 14.7 moles/L, it takes 1360.54 mLof vinegar to equal one mole of acetic acid (Equation 7).• Determine the volume of vinegar (in mL) which contains the number of moles of aceticacid your reaction needs. Since the molarity of acetic acid is 14.7 M, it takes 1360.54 mLof vinegar to equal one mole of acetic acid.EQUATION 7(100 mL vinegar/5 mL acetic acid) * (1000 mL acetic acid/14.7 mol acetic acid)= 1360.54 mL vinegar/mole of acetic acidQuestion 7: What’s the Pressure Inside the Air Bag?• Assuming that your reaction produces CO2 with 100% yield, use the ideal gas equationto calculate the pressure in atmospheres inside your air bag when it’s inflated.• In order to use the ideal gas equation, you’ll need to know the ambient temperature.Check the thermometer on the front bench for the current temperature.• Show your calculations used to determine the airbag’s pressure on the Data Sheet.Testing your Calculations with the Airbag:• Mass the calculated number of grams of baking soda (Question 4) and wrap it in a smallpiece of paper towel. Place the paper towel containing the baking soda inside your dryairbag; keeping the baking soda inside its paper towel envelope.• Measure out the volume of vinegar which you calculated in Question 6. As the papertowel absorbs the acetic acid, the reaction should begin to make CO2 gas and inflate thebag inflate. Pour the vinegar into the baggie and quickly remove as much air as possible 72and seal it. Any air trapped in the baggie could add enough extra volume to make itexplode.• If your calculations are correct, essentially no acetic acid and sodium bicarbonate shouldremain at the end of the reaction. Swish the ingredients in the bag around to check thatthe reaction is really complete. Did the air bag fill to about the volume you wanted itto?The egg takes a two-meter ride with your airbag: Does it survive?• Retrieve an egg and pack it with the airbag into their vehicle.• Go to the drop station where your TA should be. Hold your vehicle + egg + airbag at thetwo-meter mark over the cardboard box on the tarp and let go.• Record the outcome for your egg on your Data Sheet and have your TA initial it.§ If the egg survived, congratulations! Write a mark on the egg to indicate that your egghas survived a fall and return the egg to where you got it.§ If it didn't, consider what might be the problem and try one more time.• Cleaning Up:o Put broken or cracked eggs, along with any contaminated airbags into the largecontainer under the fume hood. Clean out your vehicle as thoroughly aspossible with soap and hot water.o Clean and return everything to its original location and be sure to wash yourhands well before you leave lab.