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. (a)`16:1`
B. (b)`2:1`
C. (c )`1:4`
D. (d)`4:1`

Explanation

To find the molar ratio of hydrogen (H₂) and oxygen (O₂) in a mixture where the weight ratio is given as 1:4, we can follow these steps:

### Step 1: Understand the weight ratio
The weight ratio of H₂ to O₂ is given as 1:4. This means that for every 1 gram of H₂, there are 4 grams of O₂.

### Step 2: Calculate the number of moles of H₂
To find the number of moles, we use the formula:
\[ \text{Number of moles} = \frac{\text{Weight}}{\text{Molar mass}} \]
The molar mass of H₂ (hydrogen) is approximately 2 g/mol (since each hydrogen atom has an atomic mass of about 1 g/mol, and there are 2 hydrogen atoms in H₂).

Using the weight of H₂:
\[ \text{Number of moles of H₂} = \frac{1 \text{ g}}{2 \text{ g/mol}} = 0.5 \text{ moles} \]

### Step 3: Calculate the number of moles of O₂
The molar mass of O₂ (oxygen) is approximately 32 g/mol (since each oxygen atom has an atomic mass of about 16 g/mol, and there are 2 oxygen atoms in O₂).

Using the weight of O₂:
\[ \text{Number of moles of O₂} = \frac{4 \text{ g}}{32 \text{ g/mol}} = 0.125 \text{ moles} \]

### Step 4: Determine the molar ratio
Now we can find the molar ratio of H₂ to O₂ by dividing the number of moles of each gas:
\[ \text{Molar ratio} = \frac{\text{Number of moles of H₂}}{\text{Number of moles of O₂}} = \frac{0.5}{0.125} \]
Calculating this gives:
\[ \text{Molar ratio} = 4 \]
Thus, the molar ratio of H₂ to O₂ is 4:1.

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

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