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

Answer

To solve the problem, we need to determine the molar ratio of hydrogen gas (H₂) and oxygen gas (O₂) in a mixture where they are present in a weight ratio of 1:4.

### Step 1: Define the weights of the gases
Given the weight ratio of H₂ to O₂ is 1:4, we can assume:
- Weight of H₂ = 1 part = 100 grams
- Weight of O₂ = 4 parts = 400 grams

### Step 2: Calculate the molar mass of each gas
- Molar mass of H₂ = 2 g/mol
- Molar mass of O₂ = 32 g/mol

### Step 3: Calculate the number of moles of each gas
To find the number of moles, we use the formula:
\[ \text{Number of moles} = \frac{\text{Weight}}{\text{Molar mass}} \]

**For H₂:**
\[ \text{Number of moles of H₂} = \frac{100 \text{ g}}{2 \text{ g/mol}} = 50 \text{ moles} \]

**For O₂:**
\[ \text{Number of moles of O₂} = \frac{400 \text{ g}}{32 \text{ g/mol}} = 12.5 \text{ moles} \]

### Step 4: Determine the molar ratio
Now, we can find the molar ratio of H₂ to O₂:
\[ \text{Molar ratio} = \frac{\text{Number of moles of H₂}}{\text{Number of moles of O₂}} = \frac{50}{12.5} = 4 \]

Thus, the molar ratio of H₂ to O₂ is:
\[ \text{Molar ratio} = 4:1 \]

### Final Answer
The molar ratio of H₂ to O₂ in the mixture is **4:1**.

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