Question

A mixture of gases contains H2andO2 gases in the ratio of 1 : 4 (w/w). What is the molar ratio of the two gases in the mixture?

Answer 1

The molar ratio of H2 to O2 in a mixture with a given weight ratio of 1:4 is obtained by converting grams to moles using their respective molar masses. Upon calculation, the molar ratio of H2 to O2 is 4:1.

Step-by-step explanation:

To find the molar ratio of H2 and O2 in a mixture given a weight ratio (w/w) of 1:4, we need the molar masses of each gas. Hydrogen gas (H2) has a molar mass of approximately 2 g/mol, and oxygen gas (O2) has a molar mass of approximately 32 g/mol. Using the weight ratio, if you have 1 gram of H2, you have 4 grams of O2.

Here's how you convert the weight ratio to the molar ratio:

1. Determine the moles of H2 for the given weight:
   1 gram H2 ÷ 2 g/mol = 0.5 mol H2
2. Determine the moles of O2 for the given weight:
   4 grams O2 ÷ 32 g/mol = 0.125 mol O2
3. Divide the moles of each gas to find the molar ratio:
   0.5 mol H2 / 0.125 mol O2 = 4:1

Therefore, the molar ratio of H2 to O2 in the mixture is 4:1.