Question

nan₃(s) → na(s) + n₂(g)
when the air bag inflates, the nitrogen gas is at a pressure of 1.30 atmospheres, a temperature of 301 k, and has a volume of 40.0 liters. calculate the volume of the nitrogen gas at stp. your response must include both a correct numerical setup and the calculated volume.

Explanation:

Step1: Write the combined gas law

The combined gas law is $\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}$.

Step2: Identify the values

Given $P_1 = 1.30\ atm$, $V_1=40.0\ L$, $T_1 = 301\ K$, $P_2 = 1\ atm$ (standard pressure at STP), $T_2=273\ K$.

Step3: Rearrange the formula for $V_2$

$V_2=\frac{P_1V_1T_2}{P_2T_1}$.

Step4: Substitute the values

$V_2=\frac{1.30\ atm\times40.0\ L\times273\ K}{1\ atm\times301\ K}$.

Step5: Calculate the value

$V_2=\frac{1.30\times40.0\times273}{301}\ L=\frac{14196}{301}\ L\approx47.2\ L$.

Answer:

The volume of nitrogen gas at STP is approximately $47.2\ L$.