Calculate ΔG^∘ for each reaction using ΔGf^∘ values: (a) H2(g)+I2(s) ⟶2 HI(g) (b) MnO2(s)+2 CO(g

Calculate ΔG^∘ for each reaction using ΔGf^∘ values: (a)...

Calculate $\Delta G^{\circ}$ for each reaction using $\Delta G_{\mathrm{f}}^{\circ}$ values: (a) $\mathrm{H}_{2}(g)+\mathrm{I}_{2}(s) \longrightarrow 2 \mathrm{HI}(g)$ (b) $\mathrm{MnO}_{2}(s)+2 \mathrm{CO}(g) \longrightarrow \operatorname{Mn}(s)+2 \mathrm{CO}_{2}(g)$ (c) $\mathrm{NH}_{4} \mathrm{Cl}(s) \longrightarrow \mathrm{NH}_{3}(g)+\mathrm{HCl}(g)$

Calculate $\Delta G^{\circ}$ for each reaction using $\Delta G_{\mathrm{f}}^{\circ}$ values:
(a) $\mathrm{H}_{2}(g)+\mathrm{I}_{2}(s) \longrightarrow 2 \mathrm{HI}(g)$
(b) $\mathrm{MnO}_{2}(s)+2 \mathrm{CO}(g) \longrightarrow \operatorname{Mn}(s)+2 \mathrm{CO}_{2}(g)$
(c) $\mathrm{NH}_{4} \mathrm{Cl}(s) \longrightarrow \mathrm{NH}_{3}(g)+\mathrm{HCl}(g)$

Key Concepts

Gibbs Free Energy

Gibbs free energy is a thermodynamic quantity that reflects the maximum amount of reversible work obtainable from a system at constant temperature and pressure. It helps predict whether a chemical reaction will occur spontaneously. A negative change in Gibbs free energy (?G) for a reaction indicates that the process can proceed spontaneously, while a positive ?G suggests non-spontaneity under the given conditions.

Standard Gibbs Free Energy of Formation

The standard Gibbs free energy of formation (?Gf°) is defined as the change in free energy when one mole of a compound is formed from its elements in their standard states (typically 1 bar pressure and/or 298 K temperature). Using ?Gf° values provides a consistent reference point for calculating the free energy changes of reactions.

Reaction Free Energy Calculation

The overall standard Gibbs free energy change for a reaction (?G°) is calculated by taking the sum of the standard Gibbs free energies of formation of the products, each multiplied by their respective stoichiometric coefficients, and subtracting the sum of the standard Gibbs free energies of formation of the reactants similarly adjusted. This method leverages Hess's law, which states that the total free energy change is path independent.

Stoichiometry in Thermodynamic Calculations

Stoichiometry involves the quantitative relationships between reactants and products in a chemical reaction. In the context of Gibbs free energy calculations, stoichiometric coefficients are used to account for the number of moles of each substance involved, ensuring that the energy contributions of all participating species are accurately represented in the overall energy change.

Transcript

00:01 In each part of this problem, we are given a chemical reaction and we need to calculate the change in gibbs -free energy of the reaction at standard conditions.

00:11 This is the formula that we are going to apply to this problem.

00:15 We first need to find the total change and gives -free energy of the products of the reaction, then subtract the total change in gibbs -free energy of the reactants.

00:27 So starting with part a, we are given the formation reaction.

00:32 Of h2 plus i2 to form 2hi.

00:37 We can break up the terms in the formula to be the products and the reactants, b and r.

00:47 We start by looking at the product side of the given formation reaction.

00:51 We see that we have two moles of h .i.

00:54 And the moles, the stoichiometric coefficient corresponds to this n in this formula.

01:01 And so that's why we have this two here.

01:03 Then we multiply that by the change in gibbs free energy at standard conditions of formation for that compound.

01:14 And we can look that up in the appendix.

01:17 We see that comes out to this value.

01:19 And when we multiply these two together, we're left with units of kilojoules or total energy.

01:26 Since this is a formation reaction, the elements of hydrogen and iodine form h .i.

01:35 This naturally as h2 and i2.

01:38 Because of that, they do not require any energy change to form since they occur naturally.

01:45 So that means that the change in gibbs -free energy of formation at standard conditions for each one of those diatomics will be zero.

01:55 And when we add that together, we get the total gibbs -free energy change of the reactants to be zero...

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