Consider the reaction: 2 NO(g)+O2(g) ⟶2 NO2(g) Estimate ΔG^∘ for this reaction at each temperatu

Consider the reaction: 2 NO(g)+O2(g) ⟶2 NO2(g) Estimate ΔG^∘...

Consider the reaction: $$2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)$$ Estimate $\Delta G^{\circ}$ for this reaction at each temperature and predict whether or not the reaction is spontaneous. (Assume that $\Delta H^{\circ}$ and $\Delta S^{\circ}$ do not change too much within the given temperature range.) a. $298 \mathrm{~K}$ b. $715 \mathrm{~K}$ c. $855 \mathrm{~K}$

Consider the reaction: $$2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)$$
Estimate $\Delta G^{\circ}$ for this reaction at each temperature and predict whether or not the reaction is spontaneous. (Assume that $\Delta H^{\circ}$ and $\Delta S^{\circ}$ do not change too much within the given temperature range.)
a. $298 \mathrm{~K}$
b. $715 \mathrm{~K}$
c. $855 \mathrm{~K}$

Key Concepts

Temperature Dependence

Temperature plays a crucial role in determining the spontaneity of a reaction through its effect on the T?S term in the Gibbs free energy equation. Changes in temperature can shift the balance between the contributions of enthalpy and entropy, thereby making a reaction spontaneous at one temperature and non-spontaneous at another.

Entropy

Entropy (?S) is a measure of the randomness or disorder within a system. An increase in entropy (positive ?S) generally favors the spontaneous progress of a reaction, especially at higher temperatures, where the T?S term in the Gibbs free energy equation becomes more significant.

Enthalpy

Enthalpy (?H) represents the total heat content of a system and is a measure of the energy absorbed or released during a chemical reaction. In many reactions, a negative ?H (exothermic reaction) contributes favorably to the spontaneity of the reaction by releasing heat.

Gibbs Free Energy

Gibbs free energy (?G) is a thermodynamic potential that indicates the maximum reversible work a system can perform at constant temperature and pressure. It is calculated using the equation ?G = ?H - T?S, where ?H is the change in enthalpy and ?S is the change in entropy. A negative value of ?G means the reaction is spontaneous, while a positive value indicates non-spontaneity.

Transcript

00:02 Here we're going to calculate the delta g value of the reaction 2n0 plus 0 gives 2 in 0.

00:18 First we have to find out the delta h and the delta s value of this reaction.

00:27 So let's get our delta h and delta s values for each of these elements.

00:35 From the appendix in the textbook, the delta h of the...

00:44 N0 is 91 .3, delta h of 02 is 0, and delta h of n02 is 33 .2.

00:58 And delta s of no is 210 .8, o2 is 205 .2, and n02 is 2040 .1.

01:18 So, using these individual values, we're going to calculate delta h for the entire reaction.

01:28 And for that, we're going to use the equation.

01:35 Delta h is equal to summation n delta h of the products minus summation in delta h of the reactants.

01:45 At this point, it's just as simple as putting in these numbers here.

01:52 So for the products, we have no2, but we have two moles of n02.

01:57 So i'll be moles, 2 moles into delta age of no2 is 33 .2 kilojoules per mole.

02:10 And for our reactants, we have two reactors.

02:16 First is enno, which is 2 moles.

02:18 At the age of no is 91 .3 kilojoules per mole, plus o2 is 0 .2 is 0.

02:34 So, mole and more gets cancelled, mole and more gets cancelled.

02:51 So the final answer here is minus 116 .2 kilojoules.

03:00 Similarly, we're going to calculate delta s for the equation.

03:09 Using the formula, delta s is equal to summation of n, delta s of the products, minus summation n delta s of the reactants.

03:22 So once again, just putting in the numbers, we have two moles.

03:28 N02 is 240 .1 jules per kelvin mole, minus two moles of n2 is 20010 .10 .8 jules per kelvin mole, plus, please disregard these lines, plus o2 is one mole of 205...

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