Problem 152 - A Complete Resource Book in Chemistry for JEE Main

Question

If liquids A and B form an ideal solution, the [2003] (a) enthalpy of mixing is zero(b) entropy of mixing is zero (c) free energy of mixing is zero (d) free energy as well as the entropy of mixing are each zero

Step-by-Step Solution

Answer

Only the enthalpy of mixing is zero in an ideal solution.

Step 1: Understanding Ideal Solutions

In an ideal solution, interactions between the molecules of the different components are equal to the interactions between the molecules of each pure component. This implies that the physical forces do not change upon mixing.

Step 2: Enthalpy of Mixing

For an ideal solution, there is no heat absorbed or evolved when the components are mixed. Therefore, the enthalpy change associated with the mixing process, or the enthalpy of mixing, is zero.

Step 3: Entropy of Mixing

Entropy measures the degree of disorder or randomness. When two different substances are mixed, the disorder increases, leading to a positive change in entropy. Therefore, the entropy of mixing is never zero.

Step 4: Free Energy of Mixing

The free energy change, or Gibbs free energy of mixing, is determined by both enthalpy and entropy changes. For an ideal solution, while the enthalpy change is zero, the positive entropy change ensures that the Gibbs free energy change is negative, indicating that the mixing process is spontaneous.

Step 5: Conclusion

Only the enthalpy of mixing is zero in an ideal solution. Entropy of mixing is positive, leading to a decrease in Gibbs free energy. Therefore, the correct answer is (a) enthalpy of mixing is zero.

Key Concepts

Enthalpy of Mixing in Ideal Solutions

The term 'enthalpy of mixing' refers to the heat absorbed or released when substances are mixed together. In the context of an ideal solution, this concept takes on a unique characteristic. In an ideal solution, the interactions between molecules of different components are exactly the same as the interactions between molecules of the same type. This means that when you mix two substances, there is no net change in the intermolecular forces.
As a result, no heat is absorbed or released, making the enthalpy of mixing equal to zero. This is a fundamental property of ideal solutions and holds true for any pair of substances that mix ideally. The lack of heat exchange indicates that the mixing process occurs without any energy input or output in the form of heat.

Entropy of Mixing in Ideal Solutions

Entropy can be thought of as a measure of randomness or disorder. When two different substances are mixed, the resulting solution is more random than the separate pure substances. This increase in randomness is what we refer to as an increase in entropy. For ideal solutions, the entropy of mixing is always positive. This positive change occurs because the molecules of the different components are evenly distributed throughout the mixture. This increased molecular distribution leads to a more disordered system, increasing the total entropy. This happens because there's a larger number of possible ways to arrange the molecules within the solution, thus increasing its randomness.

Gibbs Free Energy of Mixing in Ideal Solutions

Gibbs free energy (\( G \)) is a valuable concept when discussing the spontaneity of processes. In an ideal solution, the Gibbs free energy of mixing depends on both the enthalpy and the entropy changes during mixing.Despite the enthalpy of mixing being zero in ideal solutions, spontaneous mixing does still occur due to the positive entropy change. This positive entropy effectively reduces the Gibbs free energy of the system. The formula for the change in Gibbs free energy (\( \Delta G \)) during mixing is given by:\[\Delta G = \Delta H - T\Delta S\]Here, \( \Delta H \) is the change in enthalpy, \( T \) is the temperature, and \( \Delta S \) is the change in entropy.
Since \( \Delta H = 0 \), the change in Gibbs free energy primarily depends on the entropy term, making \( \Delta G \) negative. A negative Gibbs free energy indicates a spontaneous mixing process, demonstrating that the mixing of substances in ideal solutions is a naturally favorable process.