The molar heat capacity at constant volume of oxygen gas at STP is nearly `(5R)/2` and it approaches `(7R)/2` as the temperature is increased. This happens because at higher temperature

Options

A. Oxygen becomes triatomic
B. Oxygen does not behaves as an ideal gas
C. Oxygen molecules rotate more vigorously
D. Oxygen molecules start vibrating

Explanation

To solve the question regarding the change in molar heat capacity of oxygen gas at constant volume as temperature increases, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Molar Heat Capacity**:
- The molar heat capacity at constant volume (C_v) for a gas is related to its degrees of freedom (f). For a diatomic gas like oxygen, at room temperature, the degrees of freedom is typically 5, leading to:
\[ C_v = \frac{5}{2} R \]
- Here, \(R\) is the universal gas constant.

2. **Effect of Temperature on Degrees of Freedom**:
- As the temperature increases, the energy of the gas molecules increases, which allows them to access additional degrees of freedom. For diatomic gases, this typically means that they can start to vibrate in addition to rotating and translating.

3. **Transition to Higher Degrees of Freedom**:
- At higher temperatures, oxygen molecules can vibrate, which adds 2 more degrees of freedom (1 for each vibrational mode). Thus, the total degrees of freedom becomes:
\[ f = 5 + 2 = 7 \]

4. **Calculating New Molar Heat Capacity**:
- With the new degrees of freedom, the molar heat capacity at constant volume becomes:
\[ C_v = \frac{7}{2} R \]

5. **Conclusion**:
- Therefore, the molar heat capacity of oxygen gas approaches \(\frac{7R}{2}\) as the temperature increases due to the increase in degrees of freedom from vibrational motion of the molecules.

### Final Answer:
As the temperature increases, the molar heat capacity of oxygen gas approaches \(\frac{7R}{2}\) because the molecules gain vibrational degrees of freedom, increasing the total degrees of freedom from 5 to 7.

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