Urea spontaneous dissolves in water (to a high concentration). When urea dissolves in water, the solution cools before reaching thermal equilibrium with its surroundings. What can you say about the direction of change in the solution's entropy

If the amount of heat released by the solution, when it cools, is greater than the decrease in the free energy, the entropy will decrease, and if the amount of heat released by the solution is less than the decrease in the free energy, the entropy decreases.

Explanation:

In an spontaneus reaction the free energy decreases: ΔG < 0.

Since, the solution cools its enthalpy decreases: ΔH < 0.

By definition ΔG = ΔH - TΔS

Then, you can solve for TΔS:

TΔS = ΔH - ΔG

Since ΔG is negative, - ΔG is positive.

Then, TΔS will be a negative value (ΔH) plus a positive value (-ΔG).

If the magnitue of the negative value is greater than the positive value, TΔS will be negative, and the entropy decreases.

If, on the other hand, the magnitude of the negative value is less than the positive value, TΔS will be positive, and the entropy increases.

That means, that if the amount of heat released by the solution, when it cools, is greater than the decrease in the free energy, the entropy will decrease, and if the amount of heat released by the solution is less than the decrease in the free energy, the entropy decreases.