Given the values of ΔHrxn^∘, ΔSrxn^∘, and T, determine ΔSuniv and predict whether or not each re

Given the values of ΔHrxn^∘, ΔSrxn^∘, and T, determine...

Given the values of $\Delta H_{\mathrm{rxn}}^{\circ}, \Delta S_{\mathrm{rxn}}^{\circ}$, and $T$, determine $\Delta S_{\mathrm{univ}}$ and predict whether or not each reaction is spontaneous. a. $\Delta H_{\mathrm{rxn}}^{\circ}=+115 \mathrm{~kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=-263 \mathrm{~J} / \mathrm{K} ; T=298 \mathrm{~K}$ b. $\Delta H_{\mathrm{rxn}}^{\circ}=-115 \mathrm{~kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=+263 \mathrm{~J} / \mathrm{K} ; T=298 \mathrm{~K}$ c. $\Delta H_{\mathrm{rxn}}^{\circ}=-115 \mathrm{~kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=-263 \mathrm{~J} / \mathrm{K} ; T=298 \mathrm{~K}$ d. $\Delta H_{\mathrm{rxn}}^{\circ}=-115 \mathrm{~kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=-263 \mathrm{~J} / \mathrm{K} ; T=615 \mathrm{~K}$

Given the values of $\Delta H_{\mathrm{rxn}}^{\circ}, \Delta S_{\mathrm{rxn}}^{\circ}$, and $T$, determine $\Delta S_{\mathrm{univ}}$ and predict whether or not each reaction is spontaneous.
a. $\Delta H_{\mathrm{rxn}}^{\circ}=+115 \mathrm{~kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=-263 \mathrm{~J} / \mathrm{K} ; T=298 \mathrm{~K}$
b. $\Delta H_{\mathrm{rxn}}^{\circ}=-115 \mathrm{~kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=+263 \mathrm{~J} / \mathrm{K} ; T=298 \mathrm{~K}$
c. $\Delta H_{\mathrm{rxn}}^{\circ}=-115 \mathrm{~kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=-263 \mathrm{~J} / \mathrm{K} ; T=298 \mathrm{~K}$
d. $\Delta H_{\mathrm{rxn}}^{\circ}=-115 \mathrm{~kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=-263 \mathrm{~J} / \mathrm{K} ; T=615 \mathrm{~K}$

Key Concepts

Second Law of Thermodynamics

This law states that for any spontaneous process, the total entropy of the universe must increase. In chemical reactions and phase changes, the combined entropy change of the system and its surroundings (?S_univ) must be positive for the process to occur spontaneously, making it a fundamental criterion for assessing reaction spontaneity.

Entropy of the Universe (?S_univ)

This concept involves summing the entropy change of the system with that of the surroundings. For a reaction, ?S_univ is computed by adding the system’s entropy change to the change in the surroundings' entropy, which is typically approximated as -?H/T if the surroundings are assumed to be at constant temperature. The sign and magnitude of ?S_univ directly indicate whether a reaction is spontaneous.

Gibbs Free Energy (?G)

Gibbs free energy combines enthalpy and entropy changes into a single value (?G = ?H - T?S) that predicts spontaneity at constant temperature and pressure. A negative ?G indicates a spontaneous process, providing an alternative method to determine spontaneity that is directly related to the entropy of the universe through the relation ?S_univ = -?G/T.

Enthalpy (?H) and Entropy (?S) Balance

Enthalpy and entropy changes are key thermodynamic parameters that influence reaction spontaneity. An exothermic reaction (negative ?H) tends to favor spontaneity, while the sign and size of ?S determine the dispersal or order of energy. The balance between these quantities, modulated by temperature, ultimately decides the overall spontaneity as reflected in both ?G and ?S_univ.

Temperature Dependence of Spontaneity

Temperature plays a critical role in reaction spontaneity by scaling the entropy contribution (T?S) in the Gibbs free energy equation. At different temperatures, the same reaction may shift from non-spontaneous to spontaneous because increasing temperature can enhance the impact of entropy, especially in reactions where ?S is positive, or conversely, mitigate spontaneity when ?S is negative.

Transcript

00:01 In this question we're going to be looking into entropy and by definition entropy gives a measure of the disorderness of a system.

00:11 That is when we are looking in terms of thermodynamics, the entropy of a system is the thermal energy.

00:17 It's a measure of the thermal energy that is available to do actual and useful work.

00:23 So what we've been given here, we've been given the standard entropy change and some end -alpy changes of the reactions.

00:30 And by definition, we just have to look at the formulas that relate the entropy change of the universe.

00:40 This will know it to be the entropy change of the standard entropy change plus the entropy change of the surroundings.

00:51 This would be the standard entropy change of a system or rather a reaction.

00:57 And the entropy change of the surrounding is given by negative.

01:02 Nthalp change, the standard enthalpy change of that system divided by the temperature.

01:08 So these are the formulas that we are going to be applying in all of the cases.

01:13 So for the first one, we can calculate delta s of the surrounding.

01:19 This is equal to negative delta, the endthalp change divided by t, and this is going to be 115 times 10 to the power 3 divided by 298.

01:30 So the entropy change of the surrounding is going to be equal to negative 386 joles per kelvin.

01:40 And if we are to look at the entropy change of the universe, this is going to be the standard entropy change plus the entropy change of the surrounding.

01:51 So the entropy change of the universe, this is going to be equal to negative 263 plus negative 3...

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