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Unformatted text preview: 10.37 Spring 2007 Homework 1 Due noon 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 Æ 2 Na + 3 N 2 10 Na + 2 NaNO 3 Æ N 2 + 6 Na 2 O Na 2 O + 10 SiO 2 Æ 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, ξ 1, ξ 2, and ξ 3, the extents of reactions 1,2, and 3. Note that each ξ has units of moles. Write algebraic equations for each X in terms of the ξ ‘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 r’s 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...
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