Chemistry

Chemistry

Problem

A 5.00 L steel cylinder at 298 K contains a mixture of four ideal gases at equilibrium. Their measured partial pressures are given below. • PH2=0.25 atmP_{\mathrm{H_2}} = 0.25\,\text{atm} • PHe=0.50 atmP_{\mathrm{He}} = 0.50\,\text{atm} • PN2=0.15 atmP_{\mathrm{N_2}} = 0.15\,\text{atm} • PO2=0.10 atmP_{\mathrm{O_2}} = 0.10\,\text{atm} (a) Calculate the mole fraction of each gas in the mixture. (b) Express the composition of the mixture as percent by volume for each gas, and comment on how your results compare to the mole fractions.
Intuitive explanation

In a mixture of ideal gases, each gas behaves independently and contributes to the total pressure in proportion to how many moles of it are present—this is Dalton's law of partial pressures. The mole fraction of each gas is simply its partial pressure divided by the total pressure, and because ideal gases occupy volume proportionally to their mole count at constant TT and PP, the percent by volume is numerically identical to the mole fraction. Start by adding up all the partial pressures to find the total, then use that to find each gas's fractional contribution.

Intuitive explanation

In a mixture of ideal gases, each gas behaves independently and contributes to the total pressure in proportion to how many moles of it are present—this is Dalton's law of partial pressures. The mole fraction of each gas is simply its partial pressure divided by the total pressure, and because ideal gases occupy volume proportionally to their mole count at constant TT and PP, the percent by volume is numerically identical to the mole fraction. Start by adding up all the partial pressures to find the total, then use that to find each gas's fractional contribution.

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