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General Chemistry Principles, Patterns, and Applications, 2011

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Sodium azide (NaN 3) decomposes to form sodium metal <strong>and</strong> nitrogen gas according to the following<br />

balanced chemical equation:<br />

2NaN3(s) ® D2Na(s)+ 3N2(g)<br />

This reaction is used to inflate the air bags that cushion passengers during automobile collisions. The<br />

reaction is initiated in air bags by an electrical impulse <strong>and</strong> results in the rapid evolution of gas. If the<br />

N 2 gas that results from the decomposition of a 5.00 g sample of NaN 3 could be collected by displacing<br />

water from an inverted flask, as inFigure 10.12 "An Apparatus for Collecting Gases by the Displacement of<br />

Water", what volume of gas would be produced at 22°C <strong>and</strong> 762 mmHg?<br />

Given: reaction, mass of compound, temperature, <strong>and</strong> pressure<br />

Asked for: volume of nitrogen gas produced<br />

Strategy:<br />

A Calculate the number of moles of N 2 gas produced. From the data in Table 10.4 "Vapor Pressure of<br />

Water at Various Temperatures", determine the partial pressure of N 2 gas in the flask.<br />

B Use the ideal gas law to find the volume of N 2 gas produced.<br />

Solution:<br />

A Because we know the mass of the reactant <strong>and</strong> the stoichiometry of the reaction, our first step is to<br />

calculate the number of moles of N 2 gas produced:<br />

moles N2 = (5.00 g NaN 3)((1 mol NaN 365.01 g NaN 3))<br />

/((3 mol N22 mol NaN 3) = 0.115 mol N2<br />

The pressure given (762 mmHg) is the total pressure in the flask, which is the sum of the pressures due to<br />

the N 2 gas <strong>and</strong> the water vapor present. Table 10.4 "Vapor Pressure of Water at Various<br />

Temperatures" tells us that the vapor pressure of water is 19.84 mmHg at 22°C (295 K), so the partial<br />

pressure of the N 2 gas in the flask is only 762 − 19.84 = 742 mmHg = 0.976 atm.<br />

B Solving the ideal gas law for V <strong>and</strong> substituting the other quantities (in the appropriate units), we get<br />

V = nRTP = (0.115 mol N2)<br />

[0.08206 (L ×atm) / (K ×mol)](295 K)0.976 atm = 2.85 L<br />

Exercise<br />

Saylor URL: http://www.saylor.org/books<br />

Saylor.org<br />

935

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