A bag contains `0.32 g` of oxygen. The same valume of an unknown gas `A` under similar conditions of temperature and pressure weigh `0.26 g`. The gas `A` is known to contain only `C` and `H` in 1:1 ratio. The molecular formula of the compound is

Options

A. `C_(2)H_(2)`
B. `C_(4)H_(4)`
C. `C_(3)H_(4)`
D. `CH`

Explanation

To find the molecular formula of gas A, we will follow these steps:

### Step 1: Calculate the moles of oxygen (O₂)
Given:
- Mass of O₂ = 0.32 g
- Molar mass of O₂ = 32 g/mol

Using the formula for moles:
\[ \text{Moles of O₂} = \frac{\text{Given mass}}{\text{Molar mass}} = \frac{0.32 \, \text{g}}{32 \, \text{g/mol}} = 0.01 \, \text{moles} \]

### Step 2: Determine the moles of gas A
Since gas A occupies the same volume as O₂ under similar conditions of temperature and pressure, it will also have the same number of moles:
\[ \text{Moles of gas A} = 0.01 \, \text{moles} \]

### Step 3: Calculate the molar mass of gas A
Given:
- Mass of gas A = 0.26 g

Using the formula for molar mass:
\[ \text{Molar mass of gas A} = \frac{\text{Mass}}{\text{Moles}} = \frac{0.26 \, \text{g}}{0.01 \, \text{moles}} = 26 \, \text{g/mol} \]

### Step 4: Determine the empirical formula of gas A
It is given that gas A contains carbon (C) and hydrogen (H) in a 1:1 ratio. Therefore, the empirical formula is:
\[ \text{Empirical formula} = \text{CH} \]

### Step 5: Calculate the empirical formula weight
To find the empirical formula weight:
- Atomic mass of C = 12 g/mol
- Atomic mass of H = 1 g/mol

\[ \text{Empirical formula weight} = 12 + 1 = 13 \, \text{g/mol} \]

### Step 6: Calculate the value of n
Using the formula:
\[ n = \frac{\text{Molecular weight}}{\text{Empirical formula weight}} = \frac{26 \, \text{g/mol}}{13 \, \text{g/mol}} = 2 \]

### Step 7: Determine the molecular formula
The molecular formula can be found using:
\[ \text{Molecular formula} = n \times \text{Empirical formula} = 2 \times \text{CH} = \text{C}_2\text{H}_2 \]

### Final Answer
The molecular formula of gas A is:
\[ \text{C}_2\text{H}_2 \]

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