Calculate the molar volume of N2O4 gas at STP. Be sure your answer has the correct number of significant figures.

1. Break Down the Problem

To calculate the molar volume of $N_2O_4$ gas at Standard Temperature and Pressure (STP), we need to recognize that at STP (0°C or 273.15 K and 1 atm), one mole of an ideal gas occupies a volume of 22.4 L.

2. Relevant Concepts

The ideal gas law states that: $PV = nRT$ Where:

• $P$ = pressure (in atm)
• $V$ = volume (in liters)
• $n$ = number of moles (in moles)
• $R$ = universal gas constant $0.0821 \, \text{L} \cdot \text{atm} / (\text{K} \cdot \text{mol})$
• $T$ = temperature (in Kelvin)

At STP, we have 1 mole of any ideal gas occupying 22.4 liters.

3. Analysis and Detail

Given that the problem pertains to $N_2O_4$, which is a gas at STP, we directly apply the ideal gas law according to the conditions at STP without further calculation for specific pressure or temperature values, as we already know:

$\text{Volume of 1 mole of gas at STP} = 22.4 \, \text{L}$

4. Verify and Summarize

Since $N_2O_4$ behaves as an ideal gas under standard conditions, we can confirm that its molar volume at STP is the same as that of other ideal gases. The figure 22.4 L is accurate and has three significant figures, aligning with the typical precision of gas laws.

Final Answer

The molar volume of $N_2O_4$ gas at STP is $22.4 \, \text{L}$.