At the same temperature and pressure, which of the following will have highest `KE` per mole

Options

A. `H_(2)`
B. `O_(2)`
C. `CH_(4)`
D. equal

Explanation

To determine which substance has the highest kinetic energy (KE) per mole at the same temperature and pressure, we can follow these steps:

### Step 1: Understand the formula for kinetic energy per mole
The kinetic energy per mole of an ideal gas is given by the equation:
\[ KE = \frac{3}{2} RT \]
where:
- \( KE \) is the kinetic energy per mole,
- \( R \) is the gas constant (8.314 J/(mol·K)),
- \( T \) is the absolute temperature in Kelvin.

### Step 2: Analyze the parameters
In this case, the question specifies that the temperature (T) and pressure are the same for all substances being considered (hydrogen, oxygen, and methane).

### Step 3: Determine the dependency of kinetic energy on temperature
Since the formula for kinetic energy per mole shows that it is directly proportional to the temperature (T), if the temperature is constant, the kinetic energy per mole will also be constant for all gases.

### Step 4: Conclude the results
Given that the kinetic energy per mole is independent of the type of gas and solely dependent on the temperature, we can conclude that:
- The kinetic energy per mole for hydrogen, oxygen, and methane will be the same at the same temperature and pressure.

### Final Answer
At the same temperature and pressure, hydrogen, oxygen, and methane will all have the same kinetic energy per mole.

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