Question

A gas occupies 400 cm³ at normal pressure. Find the volume occupied by the gas at a pressure of 60 cm of mercury, temperature remaining constant.

Answer 1

Step-1: Understand the given conditions

• Temperature is constant.
• Volume of gas = $400{\mathrm{cm}}^3$
• Pressure of gas = normal pressure
• Value of normal pressure= $76\mathrm{cm}\mathrm{of}\mathrm{mercury}\mathrm{or}760\mathrm{mm}\mathrm{of}\mathrm{mercury}$
• Volume to be calculated at $60\mathrm{cm}\mathrm{of}\mathrm{mercury}$

Note that here $76\mathrm{cm}\mathrm{of}\mathrm{mercury}$ will be used as the normal pressure value as another value of pressure given i.e.; 60 is also in cm of mercury.

Step-2: Apply Boyle's law equation to find out the volume at the given pressure of $60\mathrm{cm}\mathrm{of}\mathrm{mercury}$

Boyle's' law: According to Boyle's law, at a constant temperature, pressure is inversely proportional to volume for a given mass of the gas.
or PV= constant

Therefore, for two different conditions i.e. 1 and 2, Boyle's law can be written as:
${\mathrm{P}}_1{\mathrm{V}}_1={\mathrm{P}}_2{\mathrm{V}}_2$

• Let volume of gas at pressure 720 mm of mercury= ${\mathrm{V}}_1$i.e.; $400{\mathrm{cm}}^3$
• Let pressure of gas at volume ${\mathrm{V}}_1$= ${\mathrm{P}}_1$i.e.; $76\mathrm{cm}\mathrm{of}\mathrm{mercury}$
• Let pressure of gas at volume ${\mathrm{V}}_2$= ${\mathrm{P}}_2$i.e.; $60\mathrm{cm}\mathrm{of}\mathrm{mercury}$
• Let volume of gas at pressure $60\mathrm{cm}\mathrm{of}\mathrm{mercury}$= ${\mathrm{V}}_2$ (to be calculated)

Substituting the values in the above equation

$$\begin{gathered} 76\times 400=60\times {\mathrm{V}}_2 \\ {\mathrm{V}}_2=\frac{76\times 400}{60} \\ {\mathrm{V}}_2=\frac{30400}{60}=506.67{\mathrm{cm}}^3 \end{gathered}$$

${\mathrm{V}}_2=506.67{\mathrm{cm}}^3$