Chapter 13, Problem 50A

Interpretation Introduction

Interpretation:

The Boyle’s Law, Charles’ Law, Gay-Lussac’s Law and the combined gas law needs to be stated.

Concept introduction:

The laws which are followed by gases are to be discussed which involve relationships between three variables temperature, pressure and volume of the gas.

Answer to Problem 50A

Boyle’s Law states that at constant temperature, pressure is inversely proportional to the volume for a given amount of gas.

Charles’ Law states that at constant pressure, volume is directly proportional to the temperature for a given amount of gas.

Gay-Lussac's law states that at constant volume, pressure is directly proportional to the temperature for a given amount of gas.

Combined gas law is the combined effect of temperature, pressure and volume of gas.

According to it, a gas which obeys combined gas law is ideal.

Explanation of Solution

The various relations are:

According to Boyle’s Law

$\mathrm{PV}=constant$, keeping the temperature constant

According to Charles’ Law

$\frac{V}{T}=constant$, keeping the pressure constant

According to Gay-Lussac’s Law

$\frac{\mathrm{P}}{T}=constant$, keeping the volume constant

According to Combined gas law,

$\mathrm{PV}=nRT$

Where

$\mathrm{P}$ is pressure of the gas

$\mathrm{V}$ is volume of the gas

$\mathrm{n}$ is the number of moles of the gas

$\mathrm{R}$ is the ideal gas constant

$\mathrm{T}$ is the temperature of the gas

Conclusion

Boyle’s Law relates pressure and volume at constant temperature.

Charles’ Law relates volume and temperature at constant pressure.

Gay-Lussac’s Law relates pressure and temperature at constant volume.

Combined gas law relates all the three variables simultaneously.