The molar heat capacity of oxygen gas at `STP` is nearly `2.5 R`. As the temperature is increased, it gradually increase and approaches `3.5 R`. The most appropriate reason for this behaviour is that at high temperatures

Options

A. oxygen does not behave as an ideal gas
B. oxygen molecules dissociate into atoms
C. the molecules collide more frequenty
D. molecular vibrations gradually become effective

Answer

To solve the question regarding the behavior of the molar heat capacity of oxygen gas as temperature increases, we can follow these steps:

### Step 1: Understand Molar Heat Capacity
Molar heat capacity (C) is defined as the amount of heat required to raise the temperature of one mole of a substance by one degree Celsius. For gases, this value can depend on the temperature and the degrees of freedom of the gas molecules.

### Step 2: Identify the Values Given
- At Standard Temperature and Pressure (STP), the molar heat capacity of oxygen gas is approximately \(2.5R\).
- As the temperature increases, the molar heat capacity approaches \(3.5R\).

### Step 3: Relate Heat Capacity to Degrees of Freedom
The molar heat capacity of a gas is related to its degrees of freedom (f). For a monoatomic ideal gas, the molar heat capacity at constant volume is given by:
\[ C_v = \frac{f}{2}R \]
For diatomic gases like oxygen, at lower temperatures, the degrees of freedom are primarily translational and rotational, leading to a molar heat capacity of about \(2.5R\).

### Step 4: Analyze the Change with Temperature
As the temperature increases, the gas molecules gain energy, and additional degrees of freedom become accessible. For diatomic gases, this includes vibrational modes. At high temperatures, these vibrational modes become significant, which increases the degrees of freedom to \(f = 5\) (3 translational + 2 rotational) and approaches \(f = 6\) (adding vibrational modes), leading to:
\[ C_v \approx \frac{7}{2}R = 3.5R \]

### Step 5: Conclusion
The increase in molar heat capacity from \(2.5R\) to \(3.5R\) as temperature rises is primarily due to the activation of vibrational modes of the gas molecules. Thus, the most appropriate reason for this behavior is that at high temperatures, molecular vibrations gradually become effective.

### Final Answer
The most appropriate reason for the increase in molar heat capacity of oxygen gas at high temperatures is that molecular vibrations gradually become effective.

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