Question

There are 100g of CH4 and 100g of Cl2 gas in a 5 L flask at 35C. Calculate the partial pressure of each gas and the total pressure

Answer 1

Assuming the ideal gas behavior of CH₄ and Cl₂, the partial pressure $p$ can be calculated using the ideal gas law:

$p=\frac{nRT}{V}$ ,

where $n$ is the number of the moles of a gas, $R$ is the ideal gas constant, 8.314 m³·Pa/(mol·K) , $T$ is the temperature in kelvin, 35+273.15 = 308.15 K and $V$ is the volume of the system, 5 L or 5·10^-3 m³.

The number of the moles of a gas $n$ is:

$n = \frac{m}{M}$,

where $m$ is the mass and $M$ is the molar mass of a gas. The molar masses of CH₄ and Cl₂ are 16.04 g/mol and 70.91 g/mol, respectively. Therefore:

$n(CH_4) = \frac{100 \text{ g}}{16.04 \text{ g/mol}} = 6.23$ mol,

$n(Cl_2) = \frac{100\text{ g}}{70.91\text{ g/mol}} = 1.41$ mol.

The partial pressures of CH₄ and Cl₂ are:

$p_{CH_4} = \frac{6.23·8.314·308.15}{5·10^{-3}} = 3.19·10^6$ Pa

$p_{Cl_2} = \frac{1.41·8.314·308.15}{5·10^{-3}} = 7.22·10^5$ Pa.

According to the Dalton's law of partial pressures, the total pressure is the sum of the partial pressures:

$p_{tot} = p_{CH_4} + p_{Cl_2} = (3.19 + 0.722)·10^6 = 3.91·10^6$ Pa.

Answer: the partial pressures of CH₄ and Cl₂ are 3.19·10⁶ Pa and 7.22·10⁵ Pa, respectively. The total pressure of the system is 3.91·10⁶ Pa.