Equal masses of `O_(2), H_(2)` and `CH_(4)` are taken in a container. The respective mole ration of these gases in container is:

Options

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

Explanation

To determine the mole ratio of equal masses of \( O_2 \), \( H_2 \), and \( CH_4 \) in a container, we will follow these steps:

### Step 1: Assume Equal Masses
Assume that we have taken 1 gram of each gas. This simplifies our calculations since we are working with equal masses.

### Step 2: Calculate the Number of Moles for Each Gas
The number of moles can be calculated using the formula:
\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}} \]

#### For \( O_2 \):
- Given mass = 1 gram
- Molar mass of \( O_2 \) = 32 g/mol
\[ \text{Number of moles of } O_2 = \frac{1 \text{ g}}{32 \text{ g/mol}} = \frac{1}{32} \text{ moles} \]

#### For \( H_2 \):
- Given mass = 1 gram
- Molar mass of \( H_2 \) = 2 g/mol
\[ \text{Number of moles of } H_2 = \frac{1 \text{ g}}{2 \text{ g/mol}} = \frac{1}{2} \text{ moles} \]

#### For \( CH_4 \):
- Given mass = 1 gram
- Molar mass of \( CH_4 \) = 12 + 4 = 16 g/mol
\[ \text{Number of moles of } CH_4 = \frac{1 \text{ g}}{16 \text{ g/mol}} = \frac{1}{16} \text{ moles} \]

### Step 3: Write the Mole Ratio
Now we have the number of moles for each gas:
- Moles of \( O_2 = \frac{1}{32} \)
- Moles of \( H_2 = \frac{1}{2} \)
- Moles of \( CH_4 = \frac{1}{16} \)

The mole ratio of \( O_2 : H_2 : CH_4 \) can be expressed as:
\[ \frac{1/32}{1/32} : \frac{1/2}{1/32} : \frac{1/16}{1/32} \]

This simplifies to:
\[ 1 : 16 : 2 \]

### Final Answer
The mole ratio of \( O_2 : H_2 : CH_4 \) is:
\[ 1 : 16 : 2 \]

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