Question

Choose the correct option for the total pressure (in atm.) in a mixture of 4 g O₂ and 2 g H₂ confined in a total volume of one litre at 08C is : [Given R=0.082 L atm mol⁻¹K⁻¹, T=273 K]

• A. 26.02
• B. 2.518
• C. 2.602
• D. 25.18

Answer 1

The Correct Option is D

To find the total pressure in the mixture of gases, we can use the ideal gas law. The ideal gas equation is given by:

\(PV = nRT\) 

Where:

• \(P\) = total pressure
• \(V\) = volume (in litres)
• \(n\) = total number of moles of gas
• \(R\) = universal gas constant, \(0.082 \, \text{L atm mol}^{-1}\text{K}^{-1}\)
• \(T\) = temperature (in Kelvin)

Given:

• Weight of \(\text{O}_2\) = 4 g
• Weight of \(\text{H}_2\) = 2 g
• Volume \((V)\) = 1 L
• Temperature \((T)\) = 273 K

First, we calculate the moles of each gas using their molecular weights:

• Molecular weight of \(\text{O}_2\) = 32 g/mol
• Moles of \(\text{O}_2 = \frac{4}{32} = 0.125 \, \text{mol}\)
• Molecular weight of \(\text{H}_2\) = 2 g/mol
• Moles of \(\text{H}_2 = \frac{2}{2} = 1 \, \text{mol}\)

Total number of moles, \(n\), in the mixture is the sum of the moles of \(\text{O}_2\) and \(\text{H}_2\):

\(n = 0.125 + 1 = 1.125 \, \text{mol}\)

We can now substitute the known values into the ideal gas equation to find the total pressure:

\(P \cdot 1 = 1.125 \times 0.082 \times 273\)

\(P = 1.125 \cdot 0.082 \cdot 273\)

Calculate the total pressure:

\(P = 25.17325 \, \text{atm}\)

Rounding to the significant figures based on the options provided, the total pressure is approximately \(25.18 \, \text{atm}\).

This matches with the correct answer choice: 25.18.