Statement-1: The total translational kinetic energy of fall the molecules of a given mass of an ideal gas is 1.5 times the product of its pressure and its volume because.
Statement-2: The molecules of a gas collide with each other and the velocities of the molecules change due to the collision.

Options

A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for statement-1
B. Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1
C. Statement-1 is True, Statement-2 is False
D. Statement-1 is False, Statement-2 is True.

Explanation

To analyze the given statements, we will break down the concepts involved in each statement step by step.

### Step 1: Understanding Statement 1
**Statement 1:** The total translational kinetic energy of all the molecules of a given mass of an ideal gas is 1.5 times the product of its pressure and its volume.

**Explanation:**
- According to the kinetic theory of gases, the total translational kinetic energy (KE) of an ideal gas can be expressed as:
\[ KE = \frac{3}{2} nRT \]
where:
- \( n \) = number of moles of the gas
- \( R \) = universal gas constant
- \( T \) = absolute temperature in Kelvin.

- From the ideal gas equation, we know:
\[ PV = nRT \]
where:
- \( P \) = pressure
- \( V \) = volume.

- By substituting \( nRT \) with \( PV \) in the kinetic energy equation, we get:
\[ KE = \frac{3}{2} PV \]
This can also be expressed as:
\[ KE = 1.5 PV \]
- Therefore, Statement 1 is **true**.

### Step 2: Understanding Statement 2
**Statement 2:** The molecules of a gas collide with each other and the velocities of the molecules change due to the collision.

**Explanation:**
- In a gas, molecules are in constant random motion and frequently collide with each other.
- These collisions are elastic, meaning that both momentum and kinetic energy are conserved.
- Due to these collisions, the direction of the molecules changes, which results in a change in their velocities.
- Therefore, Statement 2 is also **true**.

### Step 3: Evaluating the Relationship Between the Statements
- While both statements are true, Statement 2 does not provide a correct explanation for Statement 1.
- Statement 1 is about the relationship between kinetic energy, pressure, and volume, while Statement 2 describes the behavior of gas molecules during collisions.

### Conclusion
- **Statement 1 is true.**
- **Statement 2 is true.**
- **Statement 2 is not the correct explanation for Statement 1.**

### Final Answer
The correct answer is: Statement 1 is true, Statement 2 is true, but Statement 2 is not the correct explanation for Statement 1.

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