Chapter 14, Problem 101A

Interpretation Introduction

Interpretation: The reason for the large departures from the ideal behavior of methane, carbon dioxide, and ammonia gas at STP needs to be determined.

Concept Introduction: The ideal gas equation and Van der Waal equations are represented as follows:

Ideal gas equation-

  $PV=nRT$

Van der Waal equation-

  $\left(P+\frac{a{n}^2}{V^2}\right)\left(V-nb\right)=nRT$

Here, P is pressure, V is volume, n is the number of moles, R is the Universal gas constant, and T is temperature. Also, the terms a and b represent attraction between gas molecules and effective volume occupied by gas molecules respectively.

Explanation of Solution

The molar volume of nitrogen and oxygen gas at STP is 22.4 L. Other gases behave non-ideal and molar volumes at STP are as follows:

Methane-22.37 L

Carbon dioxide-22.26 L

Ammonia-22.06 L

The above-given gaseous molecules have large sizes. They do not behave ideally; thus’ the real gas equation or Van der Waal equation is as follows:

  $\left(P+\frac{a{n}^2}{V^2}\right)\left(V-nb\right)=nRT$

Here, nb is subtracted from V due to the non-ideal behavior of the gases. This factor represents the volume of the container not filled by gas molecules. Due to the subtraction of this value from total V, the molar volume for such gases is always less than the molar volume for ideal gases at STP, which is 22.4 L.