Equal masses of oxygen, hydrogen and methane kept under identical conditions. The ratio of the volumes of gases will be

Options

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

Explanation

To solve the problem of finding the ratio of the volumes of equal masses of oxygen, hydrogen, and methane kept under identical conditions, we can follow these steps:

### Step 1: Determine the Molar Masses
- **Oxygen (O2)**: The molar mass of oxygen is calculated as follows:
\[ \text{Molar mass of } O_2 = 16 \, \text{g/mol} \times 2 = 32 \, \text{g/mol} \]

- **Hydrogen (H2)**: The molar mass of hydrogen is:
\[ \text{Molar mass of } H_2 = 1 \, \text{g/mol} \times 2 = 2 \, \text{g/mol} \]

- **Methane (CH4)**: The molar mass of methane is:
\[ \text{Molar mass of } CH_4 = 12 \, \text{g/mol} + (1 \, \text{g/mol} \times 4) = 12 + 4 = 16 \, \text{g/mol} \]

### Step 2: Use the Ideal Gas Law
According to the ideal gas law, under identical conditions of temperature and pressure, the volume of a gas is directly proportional to the number of moles of the gas.

### Step 3: Calculate the Moles of Each Gas
Given that we have equal masses of each gas, we can express the number of moles (n) for each gas using the formula:
\[ n = \frac{\text{mass}}{\text{molar mass}} \]

Let’s assume we have a mass \( m \) for each gas:
- For Oxygen:
\[ n_{O_2} = \frac{m}{32} \]

- For Hydrogen:
\[ n_{H_2} = \frac{m}{2} \]

- For Methane:
\[ n_{CH_4} = \frac{m}{16} \]

### Step 4: Calculate the Volume Ratio
Since the volume of a gas is proportional to the number of moles, we can write the volume ratio as:
\[ \text{Volume ratio} = \frac{V_{H_2}}{V_{O_2}} : \frac{V_{CH_4}}{V_{O_2}} : \frac{V_{O_2}}{V_{O_2}} = n_{H_2} : n_{CH_4} : n_{O_2} \]

Substituting the values we calculated:
\[ \text{Volume ratio} = \frac{m/2}{m/32} : \frac{m/16}{m/32} : \frac{m/32}{m/32} \]

This simplifies to:
\[ = \frac{32}{2} : \frac{32}{16} : 1 = 16 : 2 : 1 \]

### Step 5: Final Ratio
Thus, the final ratio of the volumes of hydrogen, methane, and oxygen is:
\[ \text{Volume ratio} = 16 : 2 : 1 \]

### Conclusion
The ratio of the volumes of hydrogen, methane, and oxygen is **16 : 2 : 1**.

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