Question

At a constant temperature, the volume of a gas was found to be $400{\mathrm{cm}}^3$ at a pressure of $760\mathrm{mm}\mathrm{of}\mathrm{Hg}$. If the pressure of the gas is increased by 25%, find the new volume.

Answer 1

The initial volume of gas$\left({\mathrm{V}}_1\right)=400{\mathrm{cm}}^3$; initial pressure of gas $\left({\mathrm{P}}_1\right)=760\mathrm{mm}\mathrm{Hg}$ at a constant temperature.

The final volume of gas$\left({\mathrm{V}}_2\right)=?$; final pressure of gas $\left({\mathrm{P}}_2\right)=760+\frac{760\times 25}{100}$ at a constant temperature.

$=760+190=950\mathrm{mm}\mathrm{Hg}$

Since the temperature is constant, According to Boyle's law,

${\mathrm{P}}_1{\mathrm{V}}_1={\mathrm{P}}_2{\mathrm{V}}_2$

Putting the values of pressure and volume

$\Rightarrow 760\mathrm{mm}\mathrm{Hg}\times 400{\mathrm{cm}}^3=950\mathrm{mm}\mathrm{Hg}\times {\mathrm{V}}_2$

$\Rightarrow \frac{760\mathrm{mm}\mathrm{Hg}\times 400{\mathrm{cm}}^3}{950\mathrm{mm}\mathrm{Hg}}={\mathrm{V}}_2$

Hence, ${\mathrm{P}}_2=320{\mathrm{cm}}^3$