Question

Automobile air bags inflate during a crash or sudden stop by the rapid generation of nitrogen gas from sodium azide. 2NaN3(s) -->2Na(s) + 3N2 (g)How many moles of sodium azide are needed to produce sufficient nitrogen to fill a 50.0 L air bag to a pressure of 1.25 atm at 25C?

Answer 1

Answer:

1.71 moles of sodium azide are needed to produce sufficient nitrogen to fill a 50.0 L air bag to a pressure of 1.25 atm at 25 C.

Explanation:

An ideal gas is characterized by three state variables: absolute pressure (P), volume (V), and absolute temperature (T). The relationship between them constitutes the ideal gas law, an equation that relates the three variables if the amount of substance, number of moles n, remains constant and where R is the molar constant of the gases:

P * V = n * R * T

In this case, you know:

• P= 1.25 atm
• V= 50 L
• n= ?
• R= 0.082 $\frac{atm*L}{mol*K}$
• T= 25 C= 298 K

Replacing:

1.25 atm* 50 L= n* 0.082 $\frac{atm*L}{mol*K}$ *298 K

Solving:

$n=\frac{1.25 atm* 50 L}{0.082\frac{atm*L}{mol*K}*298 K}$

n= 2.56 moles

By reaction stoichiometry (that is, the relationship between the amount of reagents and products in a chemical reaction), the following amounts of each compound participate in the reaction:

• NaN₃: 2 moles
• Na: 2 moles
• N₂: 3 moles

Then you can apply the following rule of three: if by reaction stoichiometry 3 moles of N₂ are produced from 2 moles of NaN₃, 2.56 moles of N₂ are produced from how many moles of NaN₃?

$moles of NaN_{3} =\frac{2.56 moles of N_{2}* 2 moles of NaN_{3} }{3 moles of N_{2}}$

moles of NaN₃= 1.71

1.71 moles of sodium azide are needed to produce sufficient nitrogen to fill a 50.0 L air bag to a pressure of 1.25 atm at 25 C.