At extremely low pressure the Van der Waals equation of one mole may be written as :

Options

A. `pV=RT+pb`
B. `(p+a)(V-b)=RT`
C. `pV=RT-(a)/(V)`
D. `pV=RT`

Explanation

To solve the question regarding the Van der Waals equation at extremely low pressure for one mole of gas, we can follow these steps:

### Step-by-Step Solution:

1. **Write the Van der Waals Equation**:
The Van der Waals equation for n moles of a gas is given by:
\[ P + \frac{a n^2}{V^2} \left( V - nb \right) = nRT \]
For one mole (n = 1), this simplifies to:
\[ P + \frac{a}{V^2} \left( V - b \right) = RT \]

2. **Substitute n = 1**:
Since we are dealing with one mole, we can substitute n = 1 into the equation:
\[ P + \frac{a}{V^2} \left( V - b \right) = RT \]
This simplifies to:
\[ P + \frac{a}{V^2} (V - b) = RT \]

3. **Consider Extremely Low Pressure**:
At extremely low pressure, the volume (V) of the gas will be very high. This means that the term \( b \) (which accounts for the volume occupied by the gas particles) becomes negligible compared to V. Therefore, we can ignore \( b \):
\[ P + \frac{a}{V^2} V = RT \]

4. **Simplify the Equation**:
The equation now simplifies to:
\[ P + \frac{a}{V} = RT \]
Rearranging gives us:
\[ P = RT - \frac{a}{V} \]

5. **Final Form**:
Thus, at extremely low pressure, the Van der Waals equation for one mole can be expressed as:
\[ PV = RT - a \]

### Conclusion:
The final expression for the Van der Waals equation at extremely low pressure for one mole of gas is:
\[ PV = RT - a \]