Percentage Composition by Volume of CH4 Gas

To find the percentage composition by volume of CH4 gas in the gaseous mixture of HCl and CH4, we need to consider the mole fraction of CH4 and the ideal gas law.

Step 1: Calculate the mole fraction of CH4
Given that the mole fraction of He is 0.4, we can calculate the mole fraction of CH4 using the equation:

Mole fraction of CH4 = 1 - Mole fraction of He

Mole fraction of CH4 = 1 - 0.4
Mole fraction of CH4 = 0.6

Step 2: Apply the ideal gas law
The ideal gas law states that the volume of a gas is directly proportional to the number of moles of the gas, given constant temperature and pressure.

Since the volume of the container is constant, the initial volume of CH4 gas can be considered proportional to the initial number of moles of CH4.

Step 3: Calculate the percentage composition by volume of CH4 gas
To find the percentage composition by volume of CH4 gas, we need to calculate the ratio of the volume of CH4 to the total volume of the gaseous mixture.

Percentage composition by volume of CH4 gas = (Volume of CH4 / Total volume of the gaseous mixture) * 100

Since the volume of the container is constant, the ratio of the volume of CH4 to the total volume of the gaseous mixture is equal to the ratio of the number of moles of CH4 to the total number of moles of the gaseous mixture.

Percentage composition by volume of CH4 gas = (Mole fraction of CH4 / Sum of mole fractions of all gases) * 100

Percentage composition by volume of CH4 gas = (0.6 / (0.6 + 0.4)) * 100
Percentage composition by volume of CH4 gas = (0.6 / 1) * 100
Percentage composition by volume of CH4 gas = 60%

Summary:
The percentage composition by volume of CH4 gas in the gaseous mixture of HCl and CH4 is 60%. This is calculated by considering the mole fraction of CH4 and applying the ideal gas law to find the ratio of the volume of CH4 to the total volume of the gaseous mixture.

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