Question

What does it mean if delta G naught is higher at low temperature (5 degrees celsius) and lower at high temperature( 25 degree celsius or room temp) but delta S naught is the same at both temperatures? Ksp was also lower at low temp and higher at high temp.

Details: Is this as it should be and if so please explain why. All values are positive. Delta G naught= 19.19 kJ/mol at room temp and 23.66 kJ/mol at 5 degrees. Delta S naught remained at 223.69 J/mol for both temperatures. Ksp at 5 degrees was 3.58 X 10^-5 and Ksp at room temp was 4.33 X 10^-4.

This was an experiment where i mixed borax with water and then titrated the solution with hcl. All of my data is in the details. I'm just trying to find relationships in the data to put in my discussion on my lab report. I have determined that this is an endothermic reaction and it is entropically favorable and enthapically unfavorable (if this helps).

P.S The cold solution sat out for a little bit so the real temp is probably a little higher than 5 degrees.

Answer 1

We shall employ the following set of relationships.

ΔG⁰ = ΔH⁰ – T*ΔS⁰ …..(1)

ΔG⁰ = -RTlnK_sp …..(2)

It is given that ΔG⁰ has a higher positive value at low temperature and a lower positive value at high temperature. A reaction is said to be spontaneous (i.e, proceeds from reactant side to product side easily) and hence favorable when ΔG⁰ < 0. A positive value of ΔG⁰ indicates that the reaction is unfavorable and hence doesn’t form products easily.

For the reaction studied here, the value of ΔG⁰ decreases as the temperature is raised. This means that the value of ΔG⁰ will decrease and eventually become less than zero when the temperature is very high (as per equation 1 above, T denotes the temperature). Therefore, the reaction is favored and spontaneous at very high temperatures. Since high temperatures are required (which must be supplied as heat), the reaction is endothermic. Since heat energy must be supplied from outside, enthalpy doesn’t favor the reaction.

A reaction is said to be entropically favored when the entropy of the products is higher than that of the reactants. Entropy depends on the temperature and a high positive value of entropy indicates a favorable reaction. The entropy for the said reaction increases with temperature.

From the above arguments, we can deduce that the reaction becomes favorable at high temperatures both energetically (ΔG⁰ becomes less than zero) and enthalpically (ΔS⁰ increases).