Question

# A sample of air is saturated with benzene (vapour pressure $=100\mathrm{mm}\mathrm{Hg}\mathrm{at}298\mathrm{K}\right)$$\mathrm{at}298\mathrm{K},750\mathrm{mm}\mathrm{Hg}\mathrm{pressure}$. If it is isothermally compressed to one-third of its initial volume, the final pressure of the system is:

Open in App
Solution

## Step 1: Formula for total pressure:The total pressure = vapor pressure of benzene + pressure of air. The pressure of air $=750-100=650\mathrm{mm}\mathrm{of}\mathrm{Hg}.$Step 2: Pressure after compression:The mixture is compressed to one-third of its volume. Now, Since, $\mathrm{P}\propto {\mathrm{V}}_{1}$.So, the pressure of the air after compression, ${\mathrm{P}}_{\mathrm{f}}=650×3\mathrm{mm}\mathrm{of}\mathrm{Hg}\phantom{\rule{0ex}{0ex}}=1950\mathrm{mm}\mathrm{of}\mathrm{Hg}$Step 3: Final pressure calculation:The final total pressure $\mathrm{PT}=\left(1950+100\right)\phantom{\rule{0ex}{0ex}}=2050\mathrm{mm}\mathrm{of}\mathrm{Hg}\phantom{\rule{0ex}{0ex}}=2050\mathrm{torr}$Therefore, $1\mathrm{mm}\mathrm{of}\mathrm{Hg}\approx 1\mathrm{torr}$The total pressure is equal to the vapor pressure of benzene and the pressure of air.

Suggest Corrections
1
Explore more