A mixture of gases contains H2
and O2 gases in the ratio of 1:4 (w/w).
Let 100 g of hydrogen and 400 g of oxygen are present.
The molar masses of hydrogen and oxygen are 2 g/mol and 32 g/mol respectively.
The number of moles of hydrogen present are
2
100
​
=50 mol.
The number of moles of oxygen present are
32
400
​
=12.5 mol.
The molar ratio of the two gases in the mixture is 50:12.5 or 4:1.

Introduction:
In this question, we are given a mixture of gases containing H2 and O2 gases in a specific weight ratio, and we have to find out the molar ratio of these two gases in the mixture.

Explanation:
To find out the molar ratio of H2 and O2 in the given mixture, we must first calculate their respective mole fractions.

- Calculating mole fractions:
We know that the mole fraction of any gas in a mixture is given by the ratio of its number of moles to the total number of moles in the mixture.

Let the weight of H2 in the mixture be x and the weight of O2 be 4x.
Then, the total weight of the mixture = x + 4x = 5x.

We can calculate the number of moles of each gas using their respective molecular weights:

- Molecular weight of H2 = 2 g/mol
- Molecular weight of O2 = 32 g/mol

Number of moles of H2 = (x/2)
Number of moles of O2 = (4x/32) = (x/8)

Total number of moles in the mixture = (x/2) + (x/8) = (5x/8)

Therefore, the mole fraction of H2 in the mixture = [(x/2) / (5x/8)] = 4/5
And the mole fraction of O2 in the mixture = [(x/8) / (5x/8)] = 1/5

- Calculating molar ratio:
Now, we can use the mole fractions to find out the molar ratio of H2 and O2 in the mixture.

Molar ratio of H2 to O2 = mole fraction of H2 / mole fraction of O2
= (4/5) / (1/5) = 4

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

Conclusion:
In this way, we can find out the molar ratio of any two gases in a mixture using their respective mole fractions.