Question

To an evacuated vessel with a movable piston under a total pressure of $1\mathrm{atm}$, $0.1\mathrm{mol}$ of He and an unknown compound (vapor pressure $0.68\mathrm{atm}$ at $0℃$) are introduced. Considering the ideal gas behavior, the total volume (in liter) of the gases at $0℃$ is close to:

Answer 1

Step 1: Given parameters

Vapor pressure is $0.68\mathrm{atm}$

The pressure of helium is

$$\begin{gathered} \mathrm{P}=1–0.68 \\ =0.32\mathrm{atm} \end{gathered}$$

The number of moles of Helium is $\mathrm{n}=0.1\mathrm{mol}$

Temperature, $T=0°C=273\mathrm{K}$

The value of the gas constant is $\mathrm{R}=0.0821\mathrm{L}·\mathrm{atm}.{\mathrm{mol}}^{-1}·{\mathrm{K}}^{-1}.$

Step 2: To find

We have to find the total volume (in liter) of the gases at $0℃$.

Step 3: Calculating Volume

By using the ideal gas equation,

$\mathrm{nRT}=\mathrm{PV}$

or,

$\mathrm{V}=\frac{\mathrm{nRT}}{\mathrm{P}}$

Where, V is the total volume, n is the number of moles, R is the standard atmospheric pressure, T is the temperature, P is the pressure.

By substituting the values,

$$\begin{gathered} =\frac{0.1\times 0.082\times 273}{0.32} \\ =7\mathrm{L} \end{gathered}$$

Therefore, the total volume of the gases at $0℃\left(273\mathrm{K}\right)$ is close to $7\mathrm{L}$.