If $V$ is the volume of one molecule of gas under given conditions, the van der Waal?s constant $b$ is
- 4V
- $\frac{4V}{N_0}$
- $\frac{N_0}{4V}$
- $4VN_0$
The Correct Option is D
Solution and Explanation
the actual volume of $1$ mole molecules = $4 \,VN_0$
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Concepts Used:
Van Der Waals Equation
Van der Waals equation is an equation relating the relationship between the pressure, volume, temperature, and amount of real gases.
Read More: Derivation of Van Der Waals Equation
Derivation of Van der Waals equation:
For a real gas containing ‘n’ moles, the equation is written as
Where, P, V, T, n are the pressure, volume, temperature and moles of the gas. ‘a’ and ‘b’ constants specific to each gas.
Where,
Vm: molar volume of the gas
R: universal gas constant
T: temperature
P: pressure
V: volume
Thus, Van der Waals equation can be reduced to ideal gas law as PVm = RT.
The equation can further be written as;
- Cube power of volume:
- Reduced equation (Law of corresponding states) in terms of critical constants:
Units of Van der Waals equation Constants
a: atm lit² mol-²
b: litre mol-¹