Using values of Δf H^∘ and S^∘, calculate the standard molar free energy of formation, Δf G^∘, f

Using values of Δf H^∘ and S^∘, calculate the standard molar...

Using values of $\Delta_{f} H^{\circ}$ and $S^{\circ},$ calculate the standard molar free energy of formation, $\Delta_{f} G^{\circ},$ for each of the following: (a) $\mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{s})$ (b) $\mathrm{Cl}(\mathrm{g})$ (c) $\mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{s})$ Compare your calculated values of $\Delta_{f} G^{\circ}$ with those listed in Appendix L. Which of these formation reactions are predicted to be product-favored at equilibrium at $25^{\circ} \mathrm{C} ?$

Using values of $\Delta_{f} H^{\circ}$ and $S^{\circ},$ calculate the standard molar free energy of formation, $\Delta_{f} G^{\circ},$ for each of the following: (a) $\mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{s})$
(b) $\mathrm{Cl}(\mathrm{g})$
(c) $\mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{s})$
Compare your calculated values of $\Delta_{f} G^{\circ}$ with those listed in Appendix L. Which of these formation reactions are predicted to be product-favored at equilibrium at $25^{\circ} \mathrm{C} ?$

Key Concepts

Gibbs Free Energy Equation

This concept is centered on the equation ?G = ?H - T?S, where ?G is the change in free energy, ?H is the change in enthalpy, T is the temperature in Kelvin, and ?S is the change in entropy. This equation links energy content with disorder, allowing one to predict whether a reaction is spontaneous under certain conditions.

Entropy

Entropy is a measure of system disorder or randomness, and its value is key in determining how energy disperses in a given process. In the context of formation reactions, the entropy of both reactants and products is used together with enthalpy to evaluate the Gibbs free energy change, impacting the spontaneity of the process.

Equilibrium and Reaction Favorability

In thermodynamics, the sign of the Gibbs free energy change (?G) is directly related to chemical equilibrium. If ?G is negative, the reaction tends to be product-favored and can proceed spontaneously under the given conditions. Conversely, a positive ?G indicates reactant-favored conditions, meaning the formation of products is not spontaneous at equilibrium.

Standard Molar Free Energy of Formation

This concept refers to the change in Gibbs free energy when one mole of a substance is formed from its elements in their standard states. It is used to determine the thermodynamic favorability of formation reactions and is calculated under standard conditions (typically 25°C and 1 atm). A negative value indicates that the formation process is spontaneous or product-favored at equilibrium.

Enthalpy of Formation

Enthalpy of formation is the energy change that occurs when one mole of a compound forms from its constituent elements in their standard states. This thermodynamic quantity is crucial because it provides part of the energetic input required to calculate the overall free energy change of a reaction, which in turn indicates the system's stability.

Transcript

00:01 So this question is really asking us to look at the appendix and the enthalpy and entropy values provided for the different substances, calculate the gibbs for energy, compare the values, and then see if they are going to be predicted to be product favored at equilibrium at 25 degrees celsius.

00:24 So the first thing we're going to talk about is why the values for delta g will be different.

00:31 They're talking about here the entropy change.

00:37 The entropy change is for that specific substance, where the enthalpy change is for the formation of that substance from the elements.

00:46 So it's not really taking into account the entropy change of the substances themselves, of the individual elements.

00:54 So you're going to have a difference in delta g values for that specific reason alone.

00:59 But other than that, we can still compare.

01:01 Pair and discuss.

01:03 So for calcium hydroxide, the very first one, it's delta g value is going to be calculated from the delta h, which is negative 9 .86 .09 kilojoules.

01:18 So it says 25 degrees celsius, which is 298k.

01:21 We have to use the value in kelvin.

01:24 And then the delta s values are presented in joules per kelvin.

01:28 So we have to convert those into kilojoules per kelvin.

01:32 So we have to convert those into so it's 83 .39, which is 0 .08339 kilojoules per kelvin.

01:43 So the delta g value for calcium hydroxide is negative 1 ,010 .94 kilojoules.

01:53 Again, this is for calcium hydroxide.

01:57 This indicates that this is product favored.

02:01 And negative delta g value says that it's going to be a favorable process it wants to create it energy will leave the system and go into the universe which is kind of the favorable process right work doesn't need to be done to that system the value for delta g in the text is negative 898 0 .43.

02:27 Now, if you look at it in this fashion, this is three different elements combining form 1, so there should be a pretty large difference in the two values...

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