Question

A sample of air is saturated with benzene (vapour pressure $=100\mathrm{mm}\mathrm{Hg}\mathrm{at}298\mathrm{K})$$\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:

Answer 1

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,

$$\begin{gathered} {\mathrm{P}}_{\mathrm{f}}=650\times 3\mathrm{mm}\mathrm{of}\mathrm{Hg} \\ =1950\mathrm{mm}\mathrm{of}\mathrm{Hg} \end{gathered}$$

Step 3: Final pressure calculation:

• The final total pressure

$$\begin{gathered} \mathrm{PT}=(1950+100) \\ =2050\mathrm{mm}\mathrm{of}\mathrm{Hg} \\ =2050\mathrm{torr} \end{gathered}$$

• 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.