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?

Options

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

Explanation

To find the molar ratio of hydrogen (H₂) and oxygen (O₂) in a mixture given in weight/weight (w/w) ratio, we can follow these steps:

### Step 1: Understand the given ratio
The mixture contains H₂ and O₂ in the ratio of 1:4 (w/w). This means for every 1 gram of H₂, there are 4 grams of O₂.

### Step 2: Calculate the molar masses
- The molar mass of H₂ (hydrogen gas) is calculated as:
- Atomic mass of H = 1 g/mol
- Therefore, Molar mass of H₂ = 2 × 1 = 2 g/mol

- The molar mass of O₂ (oxygen gas) is calculated as:
- Atomic mass of O = 16 g/mol
- Therefore, Molar mass of O₂ = 2 × 16 = 32 g/mol

### Step 3: Convert the weight ratio to moles
Using the weight ratio, we can convert the masses into moles:
- For H₂:
- Mass of H₂ = 1 g
- Moles of H₂ = Mass / Molar mass = 1 g / 2 g/mol = 0.5 mol

- For O₂:
- Mass of O₂ = 4 g
- Moles of O₂ = Mass / Molar mass = 4 g / 32 g/mol = 0.125 mol

### Step 4: Find the molar ratio
Now we can find the molar ratio of H₂ to O₂:
- Molar ratio of H₂ to O₂ = Moles of H₂ : Moles of O₂ = 0.5 mol : 0.125 mol

To simplify this ratio, we can divide both sides by 0.125:
- Molar ratio = (0.5 / 0.125) : (0.125 / 0.125) = 4 : 1

### Conclusion
Thus, the molar ratio of H₂ to O₂ in the mixture is 4:1.