Equal masses of oxygen, hydrogen and methane are taken in a container in identical conditions. Find the ratio of their moles.

Options

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

Explanation

To find the ratio of moles of equal masses of oxygen, hydrogen, and methane, we can follow these steps:

### Step 1: Assume Equal Masses
Let’s assume that we have equal masses of each gas. For simplicity, let’s take the mass of each gas to be \( X \) grams.

### Step 2: Calculate Moles of Each Gas
Using the formula for moles, which is given by:

\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]

we can calculate the number of moles for each gas.

#### Moles of Oxygen (O₂)
- Molar mass of oxygen (O₂) = 32 g/mol
- Moles of oxygen = \( \frac{X}{32} \)

#### Moles of Hydrogen (H₂)
- Molar mass of hydrogen (H₂) = 2 g/mol
- Moles of hydrogen = \( \frac{X}{2} \)

#### Moles of Methane (CH₄)
- Molar mass of methane (CH₄) = 16 g/mol
- Moles of methane = \( \frac{X}{16} \)

### Step 3: Write the Ratio of Moles
Now we can write the ratio of the moles of oxygen, hydrogen, and methane:

\[ \text{Ratio} = \left( \frac{X}{32} : \frac{X}{2} : \frac{X}{16} \right) \]

### Step 4: Simplify the Ratio
To simplify the ratio, we can divide each term by the smallest term, which is \( \frac{X}{32} \):

\[ \text{Ratio} = \left( \frac{X/32}{X/32} : \frac{X/2}{X/32} : \frac{X/16}{X/32} \right) \]

This simplifies to:

\[ \text{Ratio} = (1 : \frac{X/2 \cdot 32}{X} : \frac{X/16 \cdot 32}{X}) = (1 : 16 : 2) \]

### Final Result
Thus, the ratio of the moles of oxygen, hydrogen, and methane is:

\[ \text{Ratio} = 1 : 16 : 2 \]