Question

For an ideal gas mixture, the fugacity of a component is equal to

• A. Vapour pressure of that component
• B. Partial pressure of the component
• C. The total pressure of the mixture
• D. The vapour pressure of the component at STP

Hint:

In an ideal gas mixture, the fugacity of a component equals its partial pressure (\( f_i = P_i \)), simplifying calculations since there are no non-ideal interactions.

Answer 1

The Correct Option is B

Step 1: Understand the concept of fugacity. 
Fugacity is a measure of the effective pressure of a gas, adjusted for non-ideal behavior. It represents the tendency of a component to escape or expand from its current phase. For an ideal gas, fugacity simplifies because ideal gases follow the ideal gas law (\( PV = nRT \)) and do not exhibit intermolecular interactions that cause deviations from ideality. 
Step 2: Analyze fugacity in an ideal gas mixture. 
In an ideal gas mixture, each component behaves as if it occupies the entire volume independently (Dalton’s Law of Partial Pressures). The partial pressure of a component \( i \) in the mixture is: \[ P_i = x_i P, \] where \( x_i \) is the mole fraction of component \( i \), and \( P \) is the total pressure of the mixture. For an ideal gas, the fugacity \( f_i \) of a component \( i \) is equal to its partial pressure \( P_i \). This is because:
Fugacity is defined such that for an ideal gas, the chemical potential \( \mu_i \) can be expressed as: \[ \mu_i = \mu_i^0 + RT \ln \left( \frac{f_i}{P^0} \right), \] where \( \mu_i^0 \) is the standard chemical potential at pressure \( P^0 \). For an ideal gas, \( f_i = P_i \), because there are no non-ideal interactions to correct for. Thus, in an ideal gas mixture, the fugacity of a component is simply its partial pressure. 
Step 3: Evaluate the options. 
(1) Vapour pressure of that component: Incorrect, as vapour pressure is relevant for a pure component in equilibrium with its liquid phase, not for a component in an ideal gas mixture. Incorrect.
(2) Partial pressure of the component: Correct, as the fugacity of a component in an ideal gas mixture equals its partial pressure. Correct.
(3) The total pressure of the mixture: Incorrect, as fugacity is specific to each component and equals the partial pressure, not the total pressure. Incorrect.
(4) The vapour pressure of the component at STP: Incorrect, as vapour pressure at STP is not relevant to the fugacity of a component in an ideal gas mixture. Incorrect.

Step 4: Select the correct answer. 
For an ideal gas mixture, the fugacity of a component is equal to its partial pressure, matching option (2).