Air bags are activated when a severe impact causes a steel ball to compress a spring and electrically ignite a detonator cap. This causes sodium azide (NaN3) to decompose explosively according to the following reaction.

2 NaN3(s)--> 2 Na(s) + 3 N2(g)
What mass of NaN3(s) must be reacted in order to inflate an air bag to 67.5 L at STP?

never mind, I figured it out.

To calculate the mass of NaN3 required to inflate an airbag, we need to use the ideal gas law and stoichiometry of the reaction.

First, let's find the number of moles of N2 gas required to fill the airbag at STP (Standard Temperature and Pressure).

Given:
Volume (V) = 67.5 L
Temperature (T) = 273 K (STP)
Pressure (P) = 1 atm (STP)

From the ideal gas law (PV = nRT), we can rearrange the equation to solve for the number of moles (n):
n = PV / RT

Substituting the values:
n = (1 atm * 67.5 L) / (0.0821 * 273 K)

Simplifying:
n = 2.74 moles of N2

From the balanced chemical equation, we know that 2 moles of NaN3 decompose to produce 3 moles of N2.

Now, we can use stoichiometry to find the number of moles of NaN3 required:
2 moles of NaN3 --> 3 moles of N2

So, if 2 moles of NaN3 produce 3 moles of N2, then:
2 moles of NaN3 --> 3 moles of N2
x moles of NaN3 --> 2.74 moles of N2

x = (2.74 moles of NaN3 * 2 moles of NaN3) / 3 moles of N2

Simplifying:
x = 1.83 moles of NaN3

Finally, we can calculate the mass of NaN3 using its molar mass.

The molar mass of NaN3 is:
Na = 22.99 g/mol
N = 14.01 g/mol

Molar mass of NaN3 = 22.99 g/mol + 3 * 14.01 g/mol = 65.02 g/mol

Now, we can calculate the mass of NaN3 required:
Mass = 1.83 moles of NaN3 * 65.02 g/mol

Mass ≈ 119.10 g

Therefore, approximately 119.10 grams of NaN3 must be reacted in order to inflate an airbag to 67.5 L at STP.