(i) Explain why the freshman criterion for sponteneity: G=H-TS < 0 is just a statement of the second law of thermodynamics (that the entropy of the universe always increases).


Now apply this concept to some ice cubes sitting in a mojito, where the chemical process of interest is: H2O(s)  H2O (l)

ii) Are S and H for the system positive or negative? Explain why
iii) Explain what the relative magnitude of H/T to S is (i.e. are the terms larger, smaller or equal?) at 260K and 340K.
iv) 10g of ethanol at 290K are mixed with 10g of ethanol at 310K in an insulated beaker. Show that heat transfer from the warmer ethanol is a spontaneous process

Look up the second law of thermodynamics, memorize it, and apply it to (i).

(ii) What does the delta G tall you?
(iii) Use delta G = delta H - Tdelta S

(i) The freshman criterion for spontaneity, ΔG = ΔH - TΔS < 0, can be explained as a statement of the second law of thermodynamics, which states that the entropy (disorder) of the universe always increases. ΔG represents the change in Gibbs free energy of a system, where Gibbs free energy is a thermodynamic potential that determines the spontaneity of a process. When ΔG is negative, it indicates that the process is spontaneous.

Now let's apply this concept to the chemical process of ice cubes melting in a mojito, where the equation is H2O(s) ⇌ H2O(l).

(ii) In this case, ΔS and ΔH refer to the change in entropy and enthalpy of the system, respectively. Entropy represents the degree of disorder in a system, and enthalpy is a measure of the heat absorbed or released during a chemical reaction.

For the process of ice cubes melting, the solid H2O(s) turns into liquid H2O(l). This transition leads to an increase in entropy as the molecules in the liquid phase have more freedom of movement compared to the crystal lattice structure of the solid phase. Hence, ΔS is positive.

Enthalpy, on the other hand, is the amount of heat absorbed or released during a reaction. In the case of ice cubes melting, heat is absorbed from the surroundings to break the hydrogen bonds and convert the solid into a liquid. This process requires an input of energy, so ΔH is positive.

(iii) The relative magnitude of ΔH/T to ΔS can provide insights into the spontaneity of a reaction at different temperatures. When comparing these two terms, we can consider the following scenarios:

a) If ΔH/T is much larger than ΔS, the system tends to be non-spontaneous. This is because the positive ΔH dominates the equation, causing a positive ΔG.

b) If ΔH/T is much smaller than ΔS, the system tends to be spontaneous. In this case, the positive entropy change dominates the equation and results in a negative ΔG.

c) If ΔH/T is roughly equal to ΔS, the system can be either spontaneous or non-spontaneous, depending on the temperature.

(iv) To show that heat transfer from the warmer ethanol is a spontaneous process, we need to analyze the change in Gibbs free energy (ΔG) for the system. Since the beaker is insulated, there is no heat exchange with the surroundings (q = 0), and the only transfer of energy is between the two ethanol samples.

When the warmer ethanol at 310K mixes with the cooler ethanol at 290K, the heat transfers from the warmer to the cooler sample. This transfer of heat is spontaneous because it occurs naturally without the need for an external input.

A spontaneous process results in a negative ΔG. In this case, as heat transfers from the warmer to the cooler ethanol, the entropy of the system increases since the molecules become more distributed and disordered. Thus, ΔS is positive. As for ΔH, it remains constant since there is no change in the chemical identity of ethanol.

With a positive ΔS and a constant ΔH, the only factor left to consider is the temperature. Given that the warmer ethanol at 310K is transferring heat to the cooler ethanol at 290K, T will be larger than 0K, resulting in a negative ΔG. Therefore, the heat transfer from the warmer ethanol is a spontaneous process.