Question

a sample of natural gas contains 8.24 moles of methane, 0.421 moles of ethane, and 0.116 moles of propane. if the total pressure of the gas is 1.37 atm, what are the partial pressures of the gases?

Answer 1

The partial pressure (Px) of a gas in a gas mixture is equal to its mole fraction (Xi) multiplied by the total pressure (P) of the gas mixture. That means that we have to calculate the mole fraction of each gas, then calculate its partial pressure. The mole fraction of a gas is its number of moles (n) divided by the total number of moles.

$Mole fraction of methane: \\ \chi_{\text {methane }}=\frac{\mathrm{n}_{\text {methane }}}{\mathrm{n}_{\text {total }}} \chi_{\text {methane }}=\frac{8.24 \mathrm{~mol}}{8.24 \mathrm{~mol}+0.421 \mathrm{~mol}+0.116 \mathrm{~mol}} \chi_{\text {methane }}=\frac{8.24 \mathrm{~mol}}{8.78 \mathrm{~mol}} \chi_{\text {methane }}=0.938$

$Partial Pressure of methane:\\ \mathrm{P}_{\text {methane }}=\chi_{\text {methane }} \times \mathrm{PP}_{\text {methane }}=0.938 \times 1.37 \mathrm{~atm} \mathbf{P}_{\text {methane }}=\mathbf{1 . 2 8} \mathbf{~ a t m}$

$Mole fraction of ethane: \\ \chi_{\text {ethane }}=\frac{\mathrm{n}_{\text {ethane }}}{\mathrm{n}_{\text {total }}} \chi_{\text {ethane }}=\frac{0.421 \mathrm{~mol}}{8.78 \mathrm{~mol}} \chi_{\text {ethane }}=0.0479$

$Partial pressure of ethane:\\ \mathrm{P}_{\text {ethane }}=\chi_{\text {ethane }} \times \mathrm{PP}_{\text {ethane }}=0.0479 \times 1.37 \mathrm{~atm} \mathrm{P}_{\text {ethane }}=\mathbf{0 . 0 6 5 6} \mathbf{~ a t m}$

$Mole fraction of propane:\\ \chi_{\text {propane }}=\frac{\mathrm{n}_{\text {propane }}}{\mathrm{n}_{\text {total }}} \chi_{\text {propane }}=\frac{0.116 \mathrm{~mol}}{8.78 \mathrm{~mol}} \chi_{\text {propane }}=0.0132$

What is Dalton’s Law?

Dalton's law of partial pressures is a gas law that states that the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures exerted by each individual gas in the mixture. The mole fraction of a given gas in a gas mixture is equal to the ratio of the partial pressure of that gas to the total pressure exerted by the gas mixture. This mole fraction can also be used to calculate the total number of moles of constituent gas if the total number of moles of the mixture is known. In addition, the mole fraction can also be used to calculate the volume of a certain gas in a mixtur.

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