Question

For ideal solution, activity (a) equals:

• A. Density
• B. Pressure
• C. Volume
• D. Mole fraction

Hint:

For an ideal gas, activity is represented by partial pressure ($p_i$).
For an ideal solution (liquid/solid), activity is represented by the mole fraction ($x_i$).
In both cases, the activity coefficient ($\gamma_i$ or $f_i$) is equal to $1$.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The question asks for the relationship between chemical activity ($a$) and concentration parameters for an ideal solution.
Activity is an effective concentration used in thermodynamics to account for non-ideal interactions in real systems.

Step 2: Key Formula or Approach:
The activity $a_i$ of a component $i$ in a solution is related to its mole fraction $x_i$ by:
\[ a_i = \gamma_i x_i \]
where $\gamma_i$ is the activity coefficient.

Step 3: Detailed Explanation:

• An ideal solution is defined as one where the intermolecular forces between unlike molecules are identical to those between like molecules ($\text{A-B}$ interactions are equal to $\text{A-A}$ and $\text{B-B}$ interactions).

• Because there are no energetic deviations upon mixing, the activity coefficient $\gamma_i$ becomes exactly equal to $1$ across all compositions.

• Consequently, the equation simplifies to:
\[ a_i = x_i \]

• Thus, in an ideal solution, the thermodynamic activity of any component is equal to its mole fraction.

Step 4: Final Answer:
For an ideal solution, activity equals the mole fraction.