Question

A tank contains a mixture of $54.5g$ of oxygen gas and $68.9g$ of carbon dioxide at ${38^0}C$ . The total pressure in the tank is $10.00atm$ . How do you calculate the partial pressure (in atm) of each gas in the mixture?

Answer 1

The mass of oxygen gas and carbon dioxide were given. From the molar mass and mass of gases the number of moles can be calculated. Mole fraction can be calculated from the moles of these two gases. Substituting the mole fraction and total pressure of mixture in Dalton’s law of partial pressure the partial pressure of each gas can be obtained.
${P_i} = {\chi _i} \times {P_{total}}$
${P_i}$ is partial pressure of component $i$
${\chi _i}$ is mole fraction of component $i$
${P_{total}}$ is total pressure.

Complete answer:
The mass of oxygen gas and carbon dioxide are given. The number of moles can be calculated from the mass of these gases and molar mass. The molar mass of oxygen gas $32amu$ and molar mass of carbon dioxide gas is $44amu$
${n_{{O_2}}} = \dfrac{{54.5}}{{32}} = 1.703moles$
${n_{C{O_2}}} = \dfrac{{68.9}}{{44}} = 1.566moles$
The total number of moles of carbon dioxide and oxygen gas is ${n_{total}} = 1.703 + 1.566 = 3.269moles$
The total pressure is given as $10.00atm$
The mole fraction of each component can be written as the ratio of moles of a component to the total moles of all the components in mixture
Substitute the mole fraction and total pressure in the above formula to obtain the partial pressure of each gas in the mixture
${P_{{O_2}}} = \dfrac{{1.703}}{{3.269}} \times 10 = 5.21atm$
${P_{C{O_2}}} = \dfrac{{1.566}}{{3.269}} \times 10 = 4.79atm$
The partial pressure of oxygen gas is $5.21atm$ and the partial pressure of carbon dioxide gas is $4.79atm$ .

Note:
Given that the total pressure of the gases in the tank is $10.00atm$ . The sum of these partial pressures of gases in a tank must be equal to the total pressure. The values of partial pressures of oxygen gas and carbon dioxide obtained are equal to the total pressure given which satisfies Dalton’s law of partial pressure.