Question

A gaseous mixture contains 430.0 Torr H2(g), 383.5 Torr N2(g), and 93.5 torr Ar(g). Calculate the mole fraction, X, of each of these gases

Answer 1

Please see below for the steps.

To begin, convert the pressures of each gas to moles using the Ideal Gas Law which is illustrated by the formula PV = nRT.

For H2

⇒ 430 Torr * (0.0821 L · atm / mol · K) / 760 Torr / atm * 273 K = 0.125 moles H2

For N2

⇒ 383.5 Torr * (0.0821 L∙atm/mol∙K) / 760 Torr/atm * 273 K = 0.11 moles N2

For Ar

93.5 Torr * (0.0821 L∙atm/mol∙K) / 760 Torr/atm * 273 K = 0.025 moles Ar

Secondly, we would calculate the total moles of gas in the mixture.

• Total moles = Moles H2 + Moles N2 + Moles Ar
• = 0.125 + 0.11 + 0.025
• = 0.26 moles

Thirdly and finally, we would calculate the mole fraction of each gas:

• X(H2) = Moles H2 / Total moles = 0.125 / 0.26 = 0.48
• X(N2) = Moles N2 / Total moles = 0.11 / 0.26 = 0.42
• X(Ar) = Moles Ar / Total moles = 0.025 / 0.26 = 0.10

So the mole fractions are:

• X(H2) = 0.48
• X(N2) = 0.42
• X(Ar) = 0.10