Question

a gaseous mixture contains 403.0 torr h₂(g), 331.1 torr n₂(g), and 86.1 torr ar(g). calculate the mole fraction, x, of each of these gases.
x_{h₂}=
x_{n₂}=
x_{ar}=

Explanation:

Step1: Calculate total pressure

According to Dalton's law of partial pressures, \(P_{total}=P_{H_2}+P_{N_2}+P_{Ar}\).
\(P_{total}=403.0 + 331.1+86.1=820.2\) Torr.

Step2: Calculate mole fraction of \(H_2\)

The formula for mole fraction \(x_i=\frac{P_i}{P_{total}}\).
For \(H_2\), \(x_{H_2}=\frac{403.0}{820.2}\approx0.491\).

Step3: Calculate mole fraction of \(N_2\)

For \(N_2\), \(x_{N_2}=\frac{331.1}{820.2}\approx0.404\).

Step4: Calculate mole fraction of \(Ar\)

For \(Ar\), \(x_{Ar}=\frac{86.1}{820.2}\approx0.105\).

Answer:

\(x_{H_2}=0.491\), \(x_{N_2}=0.404\), \(x_{Ar}=0.105\)