For each reaction, calculate ΔHrxn^∘, ΔSrxn^∘, and ΔGrxn^∘ at 25^∘ C and state whether or not th

For each reaction, calculate ΔHrxn^∘, ΔSrxn^∘, and ΔGrxn^∘...

For each reaction, calculate $\Delta H_{\mathrm{rxn}}^{\circ}, \Delta S_{\mathrm{rxn}}^{\circ}$, and $\Delta G_{\mathrm{rxn}}^{\circ}$ at $25^{\circ} \mathrm{C}$ and state whether or not the reaction is spontaneous. If the reaction is not spontaneous, would a change in temperature make it spontaneous? If so, should the temperature be raised or lowered from $25^{\circ} \mathrm{C}$ ? a. $2 \mathrm{CH}_{4}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)+\mathrm{H}_{2}(g)$ b. $2 \mathrm{NH}_{3}(g) \longrightarrow \mathrm{N}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2}(g)$ c. $\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}(g)$ d. $2 \mathrm{KClO}_{3}(s) \longrightarrow 2 \mathrm{KCl}(s)+3 \mathrm{O}_{2}(g)$

For each reaction, calculate $\Delta H_{\mathrm{rxn}}^{\circ}, \Delta S_{\mathrm{rxn}}^{\circ}$, and $\Delta G_{\mathrm{rxn}}^{\circ}$ at $25^{\circ} \mathrm{C}$
and state whether or not the reaction is spontaneous. If the reaction is not spontaneous, would a change in temperature make it spontaneous? If so, should the temperature be raised or lowered from $25^{\circ} \mathrm{C}$ ?
a. $2 \mathrm{CH}_{4}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)+\mathrm{H}_{2}(g)$
b. $2 \mathrm{NH}_{3}(g) \longrightarrow \mathrm{N}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2}(g)$
c. $\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}(g)$
d. $2 \mathrm{KClO}_{3}(s) \longrightarrow 2 \mathrm{KCl}(s)+3 \mathrm{O}_{2}(g)$

Key Concepts

Enthalpy Change (?H)

Enthalpy change represents the heat absorbed or released during a chemical reaction. It is determined by the difference between the enthalpy of the products and that of the reactants. This parameter helps classify reactions as endothermic (absorbing heat, ?H positive) or exothermic (releasing heat, ?H negative), thus providing insight into the thermal energy transfer that occurs during the reaction.

Entropy Change (?S)

Entropy change quantifies the change in disorder or randomness in a system as a reaction proceeds. It is calculated by subtracting the total entropy of the reactants from that of the products. An increase in entropy (?S positive) indicates greater disorder which can favor spontaneity under the right conditions, while a decrease (?S negative) suggests a move towards more order.

Gibbs Free Energy Change (?G)

Gibbs free energy combines the effects of enthalpy and entropy changes through the relationship ?G = ?H - T?S, where T is the temperature in Kelvin. This parameter is crucial for predicting the spontaneity of a reaction: if ?G is negative, the reaction is spontaneous under the given conditions, and if it is positive, the reaction is non-spontaneous.

Temperature Dependence of Reaction Spontaneity

The spontaneity of a reaction can be affected by temperature because the term T?S in the Gibbs free energy equation modulates the balance between enthalpy and entropy contributions. When ?S is positive, increasing the temperature can help drive the reaction toward spontaneity even if it is endothermic. Conversely, for reactions with a negative ?S, lowering the temperature might favor spontaneity when the process is exothermic.

Transcript

00:01 In this question we've been given a set of reactions or a set of systems and we've been asked to determine the standard enthalpy change, the standard gives energy change and the standard entropy change.

00:13 So what we have to note about these parameters is that these are state parameters, that is these are state functions.

00:23 So what we can do here, for example, we can calculate, for example, the enthalpy change, the standard enthalpy change, as the sum of the standard enthalpy change of formation of the product minus the sum of the standard enthalpy change of formation of the reactants and we always have to remember to include the stoichiometric coefficients of the product and the stoichiometric coefficients of the reactors so applying this for example in the first system we're going to have the standard enthalpy change the standard enthalpy change being equal to one more of the product 8 negative 8 4 .68 plus one more of the other product which is 0 the standard end up change which is 0 because we are referencing this as the pure element under standard conditions minus the standard entropy change of formation of the reactant and in this case we have negative 2 multiplied by negative 74 .6.

01:40 So our standard endopi change of that reaction is going to be 6 .4 .5 kilobs.

01:48 We do the same for the gibbs energy.

01:53 The standard gives energy change.

01:55 This is going to be equal to negative 3, 2 plus 1 by 0 minus 2 multiplied by negative 50.

02:05 So this standard gives energy change of that reaction is going to be 6 .9 kilojolts.

02:12 So if we notice this, this value is greater than 0.

02:17 So what this tells us is this reaction is not spontaneous.

02:24 It is not spontaneous.

02:26 Now looking at the standard entropy change, this is going to be equal to 1 multiplied by 229 .2 plus 1 multiplied by 130.

02:36 0 .7 minus 2 multiplied by 1h6 .3.

02:42 So the standard entropy change of this reaction is going to be negative 1 2 .7 and this is in joules pair.

02:53 Now moving on if we look at this reaction for example the standard gives energy change.

03:04 We know this to be delta h standard minus t multiplied by delta standard so here we can tell that this is positive that is this is greater than zero and this is negative that is it is less than zero so what this implies is that negative t delta s standard is greater than zero so as we increase as we reduce the temperature to approach zero we note that the magnitude of this end of a change becomes greater than this expression.

03:46 That is, if we approach zero, if we reduce the temperature, this magnitude becomes greater than this part.

03:58 And as a result, our delta g is going to be positive.

04:03 That is, it's going to be large and greater than zero at low temperatures.

04:09 So if the reaction is non -spontaneous at low temperature, it means that as we increase the temperature now to infinity, this expression, this expression is going to be greater than this expression, because if we increase this, this is going to be large and this is going to be small.

04:36 As a result, our delta g is going to be small.

04:41 And eventually, at higher temperatures, this is going to be less than zero.

04:48 So the reaction is going to be non -spontaneous again.

04:54 So at the end of the day, we can conclude that this reaction is non -spontaneous, non -spontaneous at all temperatures.

05:06 So moving on and still applying the same principle.

05:15 Still applying the same principle for the second system, our enthalpy change, standard enthalpy change, this is going to be 95 .4 plus 0.

05:27 Minus 2 multiplied by negative 45 .9.

05:33 So our enthalpy change, the standard enthalpy change of this reaction is 187 .2 and this is in kilojoules.

05:41 The same thing applies, gives energy change.

05:44 This is going to be 159 .4, 159 .4.

06:01 And we're going to add 0 minus 2 multiplied by negative 16 .4...

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