At constant volume, for a fixed number of moles of a gas, the pressure of the gas increases with the rise in temperature due to

Options

A. increase in the average molecular speed
B. decrease in rate of collision amongst molecules
C. increase in molecular attraction
D. decrease in mean free path

Answer

To solve the question, we need to understand the relationship between pressure, volume, temperature, and the behavior of gas molecules. Here’s a step-by-step breakdown of the reasoning:

### Step 1: Understand the Conditions
We are given that the volume of the gas is constant and the number of moles is fixed. This means we are dealing with a closed system where the only variable changing is the temperature.

**Hint:** Remember that when volume and the number of moles are constant, the ideal gas law simplifies our analysis.

### Step 2: Recall the Ideal Gas Law
The ideal gas law is expressed as:
\[ PV = nRT \]
Where:
- \( P \) = pressure
- \( V \) = volume
- \( n \) = number of moles
- \( R \) = ideal gas constant
- \( T \) = temperature in Kelvin

Since \( V \) and \( n \) are constant, any change in temperature \( T \) will directly affect the pressure \( P \).

**Hint:** Think about how the equation relates pressure and temperature when volume is constant.

### Step 3: Analyze the Effect of Temperature on Pressure
As the temperature \( T \) increases, the equation indicates that pressure \( P \) must also increase to maintain the equality. This is because \( R \) is a constant and \( n \) is fixed.

**Hint:** Consider what happens to the kinetic energy of gas molecules as temperature increases.

### Step 4: Understand Molecular Motion
The pressure of a gas is caused by the collisions of gas molecules with the walls of the container. When the temperature increases, the average kinetic energy of the gas molecules also increases. This results in an increase in the average speed of the molecules.

**Hint:** Relate the increase in temperature to the kinetic theory of gases.

### Step 5: Conclude the Reason for Increased Pressure
With the increase in the average speed of the gas molecules, they collide with the walls of the container more forcefully and more frequently. This increase in the frequency and intensity of collisions leads to an increase in pressure.

**Hint:** Think about how the speed of molecules affects their collisions with the container walls.

### Final Answer
At constant volume, for a fixed number of moles of a gas, the pressure of the gas increases with the rise in temperature due to the increase in the average molecular speed of the gas molecules, leading to more frequent and forceful collisions with the walls of the container.

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