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Unformatted text preview: 10.37 Spring 2007 Homework 1 Due Wednesday, Feb. 14. Problem 1. Airbags contain a mixture of NaN 3 , NaNO 3 , and SiO 2 . When the vehicle is in a crash, the following reactions are initiated: 2 NaN 3 2 Na + 3 N 2 10 Na + 2 NaNO 3 N 2 + 6 Na 2 O Na 2 O + 10 SiO 2 glass a) If 150 g of NaN 3 are used in an airbag, how many grams of NaNO 3 and SiO 2 must be included so that all of the sodium in the system can be safely sequestered as glass? Note the sodium-containing compounds NaN 3 , Na, and Na 2 O are all dangerous and toxic. b) The most important species for airbag performance in a crash are NaN 3 and N 2 , so there are two obvious definitions of conversion: X NaN3 = (moles NaN 3 reacted)/(initial moles NaN 3 ) and X N2 = (moles of N 2 )/(total moles of N 2 when all reactions are completed). What units do X NaN3 and X N2 have? Does X NaN3 equal X N2 ? If not, how different could they be? There are three other related quantities, 1, 2, and 3, the extents of reactions 1,2, and 3. Note that each has units of moles. Write algebraic equations for each X in terms of the s. c) Suppose that reaction 1 has a rate expression r 1 =k 1 /V (this reaction proceeds at a steady rate as a reaction front moves through the solid NaN 3 ), reaction 2 has a rate expression r 2 =k 2 [Na][NaNO 3 ], and reaction 3 has a rate expression r 3 =k 3 [Na 2 O]/V. By the convention used in this course, all the rs have units of moles/second/liter. Write r N2 , the rate of production of N 2 per unit volume, in terms of r 1 , r 2 , and r 3 . Write the equations for rate of change of the number of moles, dn i /dt, for all the chemical species (i=N 2 , NaN 3 , Na, NaNO 3 , Na 2 O, SiO 2 , glass). d) Of course the volume of the airbag, V, is dramatically changing during the course of the reaction due to the creation of a gas, N 2 , inside the bag. If the bag can expand fast enough to so that the pressure inside the bag is similar to the pressure outside the bag, by the ideal gas law one would expect: V = Vo + V N * n N2 and under this condition the bag would expand depending on the rate at which gas is created: dV/dt = V N * dn N2 /dt where V N is the molar volume of a gas at atmospheric pressure (~22 liter/mole) and n N2 is the number of moles of N 2 in the airbag. The initial volume of the airbag Vo ~70 cm 3 . However there is a physical limit on how fast the airbag can expand. When an airbag is expanded by gas pressure, the radius of the bag cannot grow faster than the speed of pressure fronts in the gas, approximately the speed of sound: dR/dt < c sound c sound ~ 300 m/s in air....
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This note was uploaded on 11/27/2011 for the course CHEMICAL E 10.302 taught by Professor Clarkcolton during the Fall '04 term at MIT.
- Fall '04