Solving for a gaseous reactant The airbags that protect people in car crashes ar

Question

Solving for a gaseous reactant The airbags that protect people in car crashes are inflated by the extremely rapid decomposition of sodium azide, which produces large volumes of nitrogen gas. 1. Write a balanced chemvical equation, including physical state symbols, for the decomposition of solid sodium azide (NaN) into solid sodium and gaseous dinitrogen. 242 0-1 2. Suppose 51.0 L of dinitrogen gas are produced by this reaction, at a temperature of 19.0 °C and pressure of exactly 1 atm. Calculate the mass of sodum azide that must have reacted. Be sure your answer has the correct number of significant digits

Explanation / Answer

Solution:-

A) Balanced chemical equation

2 NaN3 (s) ------> 2Na (s) + 3 N2(g). s = solid , g = gas

B) volume of dinitrogen = 51.0 L pressure = 1 atm temperature = 19 oC = 292.15 K [ 0oC = 273.15 K]

we can find the mole of dinitrogen produced by using ideal gas equation

ideal gas equation = PV = nRT --------(1)

P = pressure , V = volume, n = number of mole,T = temperature in K , R = gas constant = 0.08205 atm L mol-1 K-1

From equation 1 n = PV/RT -------(2) now put all the value in value in equation 2

n = (1atm * 51.0 L )/ ( 0.08205 atm L mol-1 K-1 * 292.15 k ) = 181,592.3 moles

now we can calculate mass of sodium azide

3 equivalent of dinitrogen is produced from 2 equivalent of sodium azide ( form chemical equation)

so 1 equivalent of dinitrogen is produced from 2/3 equivalent of sodium azide

hence 181,592.3 moles of dinitrogen is produced from = ( 181,592.3 *2)/3 = 121,061.5 moles  

molar mass of sodium azide = 65.00 g/mole 1 g = 1/1000 Kg

mass of sodium azide = mole * molar mass = 121,061.5 mole * 65 g/mole = 7,869,000 g = 7,869 Kg

So mass of azide used is 7869 Kg.

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