Van Der Waal's equation reduces itself to the ideal gas equation at

Options

A. High pressure and low temperature
B. Low pressure and low temperature
C. Low pressure and high temperature
D. High pressure and high temperature

Explanation

To determine the conditions under which Van der Waals equation reduces to the ideal gas equation, we can follow these steps:

### Step 1: Understand the Van der Waals Equation
The Van der Waals equation is given by:
\[ P + \frac{n^2A}{V^2}(V - nB) = nRT \]
Where:
- \( P \) = pressure of the gas
- \( V \) = volume of the gas
- \( n \) = number of moles of the gas
- \( R \) = universal gas constant
- \( T \) = absolute temperature
- \( A \) and \( B \) = Van der Waals constants

### Step 2: Simplify for One Mole of Gas
For one mole of gas (\( n = 1 \)), the equation simplifies to:
\[ P + \frac{A}{V^2}(V - B) = RT \]

### Step 3: Analyze Conditions for Ideal Gas Behavior
The ideal gas law is given by:
\[ PV = nRT \]
For one mole, it becomes:
\[ PV = RT \]

To find when the Van der Waals equation approaches the ideal gas equation, we need to consider the effects of pressure and temperature on the gas behavior.

### Step 4: Consider Low Pressure
At low pressure, the volume of the gas increases, and the distance between gas molecules increases. This means that the intermolecular forces become negligible, allowing the gas to behave more ideally.

### Step 5: Consider High Temperature
At high temperatures, the kinetic energy of the gas molecules increases, and they move faster. This also reduces the effect of intermolecular attractions, making the gas behave more like an ideal gas.

### Step 6: Conclusion
Thus, under conditions of low pressure and high temperature, the intermolecular forces become negligible, and the Van der Waals equation reduces to the ideal gas equation.

### Final Answer
The Van der Waals equation reduces itself to the ideal gas equation at **low pressure and high temperature**.

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