Chapter 14, Problem 1E

Interpretation Introduction

Interpretation:

The comparison in the volumes of $1\times {10}^{23}$ hydrogen molecules, $1\times {10}^{23}$ oxygen molecules, and $2\times {10}^{23}$ nitrogen molecules is to be stated.

Concept Introduction:

The ideal gas law is the compilation of Charles’s Law $\left(\text{V}\propto \text{T}\right)$, Boyle’s Law $\left(\text{V}\propto \frac{\text{1}}{\text{P}}\right)$ and Avogadro’s Law $\left(\text{V}\propto \text{n}\right)$. The ideal gas equation is shown below.

$\text{PV}=\text{nRT}$

Where,

• $\text{P}$ is the pressure.

• $\text{V}$ is the volume.

• $\text{n}$ is the number of moles.

• $\text{R}$ is gas constant.

• $\text{T}$ is temperature.

Answer to Problem 1E

The volume of $1\times {10}^{23}$ hydrogen molecules and $1\times {10}^{23}$ oxygen molecules is same at the same temperature and pressure. The volume of $2\times {10}^{23}$ nitrogen molecules is double the volume of $1\times {10}^{23}$ hydrogen molecules and $1\times {10}^{23}$ oxygen molecules at the same temperature and pressure.

Explanation of Solution

According to Avogadro’s Law, “volume of a gas is directly proportional to number of molecules at constant temperature and pressure.”

The number of molecules of hydrogen molecules and oxygen molecules is same. Therefore, the volume of $1\times {10}^{23}$ hydrogen molecules and $1\times {10}^{23}$ oxygen molecules is same at the same temperature and pressure.

The number of molecules of nitrogen molecules is double the number of mole of hydrogen molecules and oxygen molecules. Therefore, the volume of $2\times {10}^{23}$ nitrogen molecules is double the volume of $1\times {10}^{23}$ hydrogen molecules and $1\times {10}^{23}$ oxygen molecules at the same temperature and pressure.

Conclusion

The volume of $1\times {10}^{23}$ hydrogen molecules and $1\times {10}^{23}$ oxygen molecules is same at the same temperature and pressure. The volume of $2\times {10}^{23}$ nitrogen molecules is double the volume of $1\times {10}^{23}$ hydrogen molecules and $1\times {10}^{23}$ oxygen molecules at the same temperature and pressure.