Question

A 30.0 mL sample of hydrogen gas (H2) is collected over water at 20.00∘C and has a total pressure of 700.0 torr. The partial pressure of water vapor at 20.00∘C is 17.5 torr. Calculate the mole fraction of H2 gas in the sample.

Answer 1

Answer: The mole fraction of hydrogen gas at 20°C is 0.975  

Explanation:

We are given:

Vapor pressure of water vapor at 20°C = 17.5 torr

Total pressure at 20°C = 700.0 torr

Vapor pressure of hydrogen gas at 20°C = (700.0 - 17.5) torr = 682.5 torr

To calculate the mole fraction of hydrogen gas at 20°C, we use the equation given by Raoult's law, which is:

$p_{H_2}=p_T\times \chi_{H_2}$

where,

$p_{H_2}$ = partial pressure of hydrogen gas = 682.5 torr

$p_T$ = total pressure = 700.0 torr

$\chi_{H_2}$ = mole fraction of hydrogen gas = ?

Putting values in above equation, we get:

$682.5torr=700.0torr\times \chi_{H_2}\\\\\chi_{H_2}=\frac{682.5}{700.0}=0.975$

Hence, the mole fraction of hydrogen gas at 20°C is 0.975

Answer 2

Answer: 0.975

Explanation:

First, calculate the partial pressure of hydrogen gas. The partial pressure of hydrogen gas, PH2, is the difference between the total pressure and the partial pressure of water vapor.

PH2=700.0 torr−17.5torr=682.5torr

Now, use the following equation to calculate the mole fraction of hydrogen gas.

PH2 = XH2 × Ptotal

XH2 = PH2 / Ptotal

= 682.5 torr / 700.0 torr = 0.975