Question

112 cm³ of nitrogen is collected at a pressure of 720 mm of mercury. If the temperature remains constant, find its volume when the pressure is:

760 mm of mercury.

Answer 1

Step-1: Understand the given conditions

• Temperature is constant.
• Volume of Nitrogen = $112{\mathrm{cm}}^3$
• Pressure of Nitrogen= $720\mathrm{mm}\mathrm{of}\mathrm{mercury}$
• Volume to be calculated at $760\mathrm{mm}\mathrm{of}\mathrm{mercury}$

Step-2: Apply Boyle's law equation to find out the volume at the given pressure of $760\mathrm{mm}\mathrm{of}\mathrm{mercury}$

Boyle's' law: According to Boyle's law, at 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 Nitrogen at pressure 720 mm of mercury= ${\mathrm{V}}_1$i.e.; $112{\mathrm{cm}}^3$
• Let pressure of Nitrogen at volume ${\mathrm{V}}_1$= ${\mathrm{P}}_1$i.e.; $720\mathrm{mm}\mathrm{of}\mathrm{mercury}$
• Let pressure of Nitrogen at volume ${\mathrm{V}}_2$= ${\mathrm{P}}_2$i.e.; $760\mathrm{mm}\mathrm{of}\mathrm{mercury}$
• Let volume of Nitrogen at pressure $760\mathrm{mm}\mathrm{of}\mathrm{mercury}$= ${\mathrm{V}}_2$ (to be calculated)

Substituting the values in the above equation

$$\begin{gathered} 720\times 112=760\times {\mathrm{V}}_2 \\ {\mathrm{V}}_2=\frac{720\times 112}{760} \\ {\mathrm{V}}_2=\frac{80640}{760}=106.105{\mathrm{cm}}^3 \end{gathered}$$

${\mathrm{V}}_2=106.105{\mathrm{cm}}^3$