Oxygen and hydrogen in two enclosures have same mass, volume and pressure. The ratio of the temperatures of the two gases is

Options

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

Explanation

To find the ratio of the temperatures of oxygen (O₂) and hydrogen (H₂) in two enclosures where they have the same mass, volume, and pressure, we can use the ideal gas law and the relationship between temperature, pressure, volume, and the number of moles.

### Step-by-Step Solution:

1. **Understand the Ideal Gas Law**:
The ideal gas law is given by the equation:
\[ PV = nRT \]
where \( P \) is pressure, \( V \) is volume, \( n \) is the number of moles, \( R \) is the universal gas constant, and \( T \) is the temperature.

2. **Rearrange the Ideal Gas Law to Find Temperature**:
From the ideal gas law, we can express temperature \( T \) as:
\[ T = \frac{PV}{nR} \]

3. **Identify the Number of Moles**:
The number of moles \( n \) can be expressed in terms of mass \( m \) and molar mass \( M \):
\[ n = \frac{m}{M} \]
where \( m \) is the mass of the gas and \( M \) is the molar mass.

4. **Substitute for Number of Moles**:
Substituting \( n \) in the temperature equation gives:
\[ T = \frac{PV \cdot M}{mR} \]

5. **Analyze Given Conditions**:
Since the mass \( m \), volume \( V \), and pressure \( P \) are the same for both gases, we can simplify our comparison. The temperatures of the gases will be directly proportional to their molar masses:
\[ T \propto M \]

6. **Calculate Molar Masses**:
- Molar mass of oxygen (O₂) = 32 g/mol
- Molar mass of hydrogen (H₂) = 2 g/mol

7. **Set Up the Ratio of Temperatures**:
The ratio of the temperatures of oxygen to hydrogen can be expressed as:
\[ \frac{T_{O_2}}{T_{H_2}} = \frac{M_{O_2}}{M_{H_2}} = \frac{32}{2} = 16 \]

8. **Final Result**:
Thus, the ratio of the temperatures of oxygen to hydrogen is:
\[ \frac{T_{O_2}}{T_{H_2}} = 16:1 \]

### Conclusion:
The ratio of the temperatures of oxygen to hydrogen is \( 16:1 \).