Question

If pressure of CO\(_2\) (real gas) in a container is given by \( P = \frac{RT}{2v-b} - \frac{a}{4v^2} \), then mass of the gas in the container is:

• A. 11 g
• B. 22 g
• C. 33 g
• D. 44 g

Hint:

For real gases, the equation of state takes into account deviations from ideal behavior due to intermolecular forces and volume occupied by gas molecules.

Answer 1

The Correct Option is B

From the given equation, we have the general form of the equation of state for a real gas.
To find the mass of the gas, we use the ideal gas law for an approximation of molar mass.
The equation for pressure \( P \) is: \[ P = \frac{RT}{2v-b} - \frac{a}{4v^2} \] where \( R \) is the gas constant, \( T \) is temperature, \( v \) is molar volume, and \( a \) and \( b \) are constants specific to the gas. Using the ideal gas law approximation and solving for the mass, we find that the mass of the gas is \( 22 \, \text{g} \).
Thus, the correct answer is (b).