van der Waal's equation for calculating the pressure of a non ideal gas is
`(P+(an^(2))/(V^(2)))(V-nb)=nRT`
van der Waal's suggested that the pressure exerted by an ideal gas , `P_("ideal")`, is related to the experiventally measured pressure, `P_("ideal")` by the equation
`P_("ideal")=underset("observed pressure")(underset(uarr)(P_("real")))+underset("currection term")(underset(uarr)((an^(2))/(V^(2))))`
Constant 'a' is measure of intermolecular interaction between gaseous molecules that gives rise to nonideal behavior. It depends upon how frequently any two molecules approach each other closely. Another correction concerns the volume occupied by the gas molecules. In the ideal gas equation, V represents the volume of the container. However, each molecule does occupy a finite, although small, intrinsic volume, so the effective volume of the gas vecomes (V-nb), where n is the number of moles of the gas and b is a constant. The term nb represents the volume occupied by gas particles present in n moles of the gas .
Having taken into account the corrections for pressure and volume, we can rewrite the ideal gas equation as follows :
`underset("corrected pressure")((P+(an^(2))/(V^(2))))underset("corrected volume")((V-nb))=nRT`
AT relatively high pressures, the van der Waals' equation of state reduces to

Options

A. `PV=RT-a//V_(m)`
B. `PV=aRT//V_(m)^(2)`
C. `P=RT-a//V_(m)^(2)`
D. `PV_(m)=RT+Pb`

Explanation

To solve the problem using the Van der Waals equation for a non-ideal gas, we will follow these steps:

### Step-by-Step Solution:

1. **Understand the Van der Waals Equation**:
The Van der Waals equation is given by:
\[ (P + \frac{a n^2}{V^2})(V - nb) = nRT \]
where \( P \) is the pressure of the gas, \( V \) is the volume, \( n \) is the number of moles, \( R \) is the universal gas constant, \( T \) is the temperature, \( a \) is a constant that accounts for the intermolecular forces, and \( b \) is a constant that accounts for the volume occupied by the gas molecules.

2. **Consider High Pressure Conditions**:
At relatively high pressures, the interactions between gas molecules become negligible. Therefore, we can assume that the term \( a \) approaches zero. This simplifies our equation significantly.

3. **Set \( n = 1 \) for Molar Volume**:
Since we are considering the molar volume, we set \( n = 1 \). Thus, the equation simplifies to:
\[ (P + \frac{a}{V^2})(V - b) = RT \]

4. **Neglect the \( a \) Term**:
Since \( a \) is negligible at high pressures, we can ignore it:
\[ P(V - b) = RT \]

5. **Rearranging the Equation**:
Now, we can rearrange the equation to express \( P \):
\[ PV - Pb = RT \]
\[ PV = RT + Pb \]

6. **Final Form of the Equation**:
Thus, we arrive at the final form of the equation at high pressures:
\[ PV = RT + Pb \]

### Conclusion:
The Van der Waals equation reduces to:
\[ PV = RT + Pb \]
This indicates that at high pressures, the pressure of the gas is influenced by the volume occupied by the gas molecules.