Problem 151 - A Complete Resource Book in Chemistry for JEE Main

Question

If liquids A and B form an ideal solution, the (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

(a) Enthalpy of mixing is zero.

Step 1: Understanding Ideal Solutions

First, let's define what an ideal solution is. In an ideal solution, the components mix perfectly, meaning that the intermolecular forces between the different molecules are similar to those in the pure components. This leads to specific thermodynamic properties, especially during the mixing process.

Step 2: Checking Enthalpy of Mixing

For ideal solutions, the enthalpy of mixing, denoted as \(



\Delta H_{mix}



\), is zero. This means that no heat is either absorbed or released when the components mix, as the interactions between unlike molecules are similar to those between like molecules.

Step 3: Determining Entropy of Mixing

The entropy of mixing, \(
\Delta S_{mix}

\), is never zero for ideal solutions. As the components mix, randomness and disorder in the system increase, leading to a positive entropy change. Therefore, \(
\Delta S_{mix} > 0

\) in ideal solutions.

Step 4: Evaluating Free Energy of Mixing

The free energy of mixing \(
\Delta G_{mix}

\), for an ideal solution is generally negative, indicating that mixing is a spontaneous process. Therefore, \(
\Delta G_{mix}

\) is not zero but rather less than zero due to the increase in entropy.

Step 5: Conclusion

Given these properties, only option (a) is true; the enthalpy of mixing being zero is characteristic of an ideal solution.

Key Concepts

Enthalpy of Mixing

In an ideal solution, when two liquids mix, the enthalpy of mixing is zero. This is because the forces between unlike molecules are similar to those between like molecules. As a result, no heat energy is either absorbed or evolved throughout the mixing process. This characteristic is represented by the equation \( \Delta H_{mix} = 0 \).

• In an ideal solution, the components mix without any enthalpic change.
• The absence of heat exchange implies that the energetic landscape remains unchanged during mixing.

The concept of zero enthalpy is crucial as it reinforces the idea that ideal solutions behave predictably without energetic disturbances, maintaining the same energy level as in their pure states.

Entropy of Mixing

Entropy is a measure of disorder or randomness in a system. For ideal solutions, the entropy of mixing, denoted as \( \Delta S_{mix} \), is never zero. This is because, upon mixing, the system becomes more disordered.

In an ideal solution, the components distribute uniformly, leading to an increase in randomness. This can be described mathematically, but the key takeaway is that \( \Delta S_{mix} > 0 \).

• An increase in entropy implies a higher degree of disorder.
• Mixing leads to a more dispersed and randomized distribution of molecules.
• This increase in disorder is a natural tendency in most systems.

Thus, when two liquids form an ideal solution, entropy facilitates the mixing by encouraging the system's evolution towards maximum disorder.

Free Energy of Mixing

The free energy of a system combines enthalpy and entropy to predict the spontaneity of processes. For an ideal solution, the free energy of mixing, \( \Delta G_{mix} \), is negative. This indicates that the mixing process occurs spontaneously.

The relationship \( \Delta G_{mix} = \Delta H_{mix} - T \Delta S_{mix} \) helps explain this, where \( \Delta H_{mix} = 0 \) for ideal solutions and \( \Delta S_{mix} > 0 \) as discussed. Therefore, the equation simplifies to \( \Delta G_{mix} < 0 \).

• A negative free energy change suggests that mixing lowers the system's free energy.
• This tendency for a decrease in free energy drives the process spontaneously.

Overall, the free energy of mixing demonstrates the natural progression towards equilibrium when forming an ideal solution, making the process favorable without any external intervention.