Animated Solution for Chemistry - Solutions: If liquid $A$ and $B$ form an ideal solution, the

What is an Ideal Solution?

Imagine you are in a chemistry lab, holding two beakers. One contains pure liquid A, and the other contains pure liquid B. When you pour them together into a single flask, they mix seamlessly. If this resulting mixture perfectly obeys Raoult's Law across all possible concentrations and temperatures, we crown it with a special title: an ideal solution.

But what makes a solution truly "ideal" at the microscopic level? It all boils down to the invisible tug-of-war happening between the molecules.

To understand ideal behavior, we must zoom in and look at the intermolecular forces. In pure liquid A, the molecules are held together by $A-A$ interactions. In pure liquid B, it's the $B-B$ interactions.

When we mix them, new $A-B$ interactions are formed. For a solution to be ideal, the strength of these new attractive forces must be almost exactly the same as the original forces. Mathematically, we can express this beautiful symmetry as:

Because the molecules of A and B are perfectly comfortable with each other—just as comfortable as they are with their own kind—they mix without any resistance or extra attraction.

This perfect balance of forces has profound thermodynamic consequences. Since the $A-B$ interactions are identical in strength to the $A-A$ and $B-B$ interactions, no extra energy is required to break the old bonds, and no extra energy is released when the new bonds form.

As a result, the overall heat change of the system is zero. This means the enthalpy of mixing is exactly zero:

Similarly, because the molecules don't pull each other any closer or push each other any further apart than they did before, the total volume remains perfectly conserved. Thus, the volume of mixing is also zero ($\Delta V_{\text{mix}}=0$).

The Drivers of Spontaneity

Now, you might be wondering, "If there's no energy change, why do they mix at all?" This is where entropy steps onto the stage.

Mixing two different substances is a spontaneous process. It naturally creates more disorder, randomness, and a higher number of microstates in the system. Therefore, the entropy of mixing is always positive:

Furthermore, the Second Law of Thermodynamics dictates that for any process to happen spontaneously at a constant temperature and pressure, the change in Gibbs free energy must be negative. Hence, the free energy of mixing is always less than zero:

Let's bring it all together and evaluate our options. We know that for an ideal solution, the enthalpy of mixing ($\Delta H_{\text{mix}}$) is zero. We also know that because mixing is spontaneous, the entropy of mixing ($\Delta S_{\text{mix}}$) is positive, and the free energy of mixing ($\Delta G_{\text{mix}}$) is negative.

Therefore, the only correct statement among the choices is that the enthalpy of mixing is zero.