Question

A mixture of gases contains $H_2$ and $O_2$ gases in the ratio of 1 : 4 (w/w). What is the molar ratio of the two gases in the mixture?

• A. 16 : 1
• B. 2 : 1
• C. 1 : 4
• D. 4 : 1

Answer 1

The Correct Option is D

To determine the molar ratio of the gases H_2 and O_2 in the mixture, we start by understanding the weight ratio given in the problem. The mixture has H_2 and O_2 gases in a ratio of 1:4 by weight.

First, let's calculate the molar masses of the gases:

• Molar mass of H_2 = 2 g/mol
• Molar mass of O_2 = 32 g/mol

Next, using the weight ratio, assume we have 1 g of H_2 and 4 g of O_2.

Now, calculate the number of moles of each gas:

• Moles of H_2 = \frac{1 \text{ g}}{2 \text{ g/mol}} = 0.5 \text{ mol}
• Moles of O_2 = \frac{4 \text{ g}}{32 \text{ g/mol}} = 0.125 \text{ mol}

Finally, calculate the molar ratio:

• Molar ratio of H_2:O_2 = \frac{0.5}{0.125} = 4:1

The correct molar ratio of the gases H_2 and O_2 in the mixture is 4:1, which matches the given answer option. Therefore, the correct answer is:

4 : 1