At the same temperature and pressure ,which of the following gases will have highest kinetic energy per molecule (at . Wt . Of hydrogen = 1 , nitrogen = 14 , carbon = 12, oxygen = 16)?

Options

A. Hydrogen gas
B. Nitrogen gas
C. Ethylene gas
D. All will have equal - average kinetic energy

Answer

To solve the problem of determining which gas has the highest kinetic energy per molecule at the same temperature and pressure, we can follow these steps:

### Step 1: Understand the relationship between kinetic energy and temperature
The average kinetic energy (KE) of gas molecules is given by the formula:
\[ KE = \frac{3}{2} k T \]
where \( k \) is the Boltzmann constant and \( T \) is the absolute temperature in Kelvin. This formula indicates that the average kinetic energy of gas molecules is directly proportional to the temperature.

**Hint:** Remember that kinetic energy is dependent on temperature, not the molecular weight of the gas.

### Step 2: Recognize that all gases are at the same temperature and pressure
Since the problem states that all gases are at the same temperature and pressure, we can conclude that the temperature \( T \) is constant for all gases.

**Hint:** When temperature is constant, the kinetic energy per molecule will also be constant across different gases.

### Step 3: Conclude that all gases will have the same average kinetic energy
Given that the average kinetic energy is directly proportional to temperature and that temperature is the same for all gases, we can conclude that:
\[ KE_{H_2} = KE_{N_2} = KE_{C_2H_4} = KE_{O_2} \]
This means that all gases will have the same average kinetic energy per molecule.

**Hint:** Focus on the fact that the average kinetic energy is not affected by the type of gas when temperature is constant.

### Step 4: Select the correct answer
Based on our analysis, the correct answer is that all gases will have the same average kinetic energy per molecule.

**Final Answer:** All will have the same average kinetic energy.

### Summary of Steps:
1. Understand the kinetic energy formula and its dependence on temperature.
2. Recognize that all gases are at the same temperature and pressure.
3. Conclude that all gases will have the same average kinetic energy.
4. Select the correct answer based on the conclusion.