Question

A mixture of hydrogen and oxygen contains 40% hydrogen by mass when the pressure is 2.2 bar. The partial pressure of hydrogen is _______ bar. (Nearest integer)

Answer 1

Correct Answer: 2

The partial pressure of a gas in a mixture can be determined using Dalton's Law of Partial Pressures, which states that the partial pressure of a component in a gas mixture is equal to the product of the total pressure of the gas mixture and the mole fraction of that component.

1. Calculate the mass of hydrogen (H) and oxygen (O) in 100 g of the mixture. Given that 40% of the mixture is hydrogen, we have:
mass of hydrogen = 0.40 × 100 g = 40 g
mass of oxygen = 0.60 × 100 g = 60 g

2. Convert these masses to moles using their molar masses (H = 2 g/mol, O = 32 g/mol):
moles of hydrogen = 40 g / 2 g/mol = 20 mol
moles of oxygen = 60 g / 32 g/mol = 1.875 mol

3. Calculate the total moles in the mixture:
total moles = 20 mol + 1.875 mol = 21.875 mol

4. Determine the mole fraction of hydrogen:
mole fraction of hydrogen = 20 mol / 21.875 mol ≈ 0.914

5. Using Dalton's Law, calculate the partial pressure of hydrogen:
partial pressure of hydrogen = mole fraction of hydrogen × total pressure
= 0.914 × 2.2 bar ≈ 2.011 bar

6. Rounding 2.011 bar to the nearest integer, we find the partial pressure of hydrogen is 2 bar.

Finally, we verify that this value is within the given range of 2,2. Thus, the partial pressure of hydrogen in the mixture is 2 bar.