Explain qualitatively how ΔG changes for each of the following reactions as the partial pressure

Explain qualitatively how ΔG changes for each of the...

Explain qualitatively how $\Delta G$ changes for each of the following reactions as the partial pressure of $\mathrm{O}_{2}$ is increased: (a) $2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)$ (b) $2 \mathrm{H}_{2} \mathrm{O}_{2}(l) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{O}_{2}(g)$ (c) $2 \mathrm{KClO}_{3}(s) \longrightarrow 2 \mathrm{KCl}(s)+3 \mathrm{O}_{2}(g)$

Explain qualitatively how $\Delta G$ changes for each of the following reactions as the partial pressure of $\mathrm{O}_{2}$ is increased:
(a) $2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)$
(b) $2 \mathrm{H}_{2} \mathrm{O}_{2}(l) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{O}_{2}(g)$
(c) $2 \mathrm{KClO}_{3}(s) \longrightarrow 2 \mathrm{KCl}(s)+3 \mathrm{O}_{2}(g)$

Key Concepts

Stoichiometry and Its Impact on the Free Energy Change

The stoichiometric coefficients in a balanced chemical equation determine the exponents in the reaction quotient expression. As a result, the extent to which changes in partial pressures affect Q—and thus ?G—depends on the number of moles of the gaseous species involved. Reactions that involve more moles of a particular gas will exhibit a more pronounced shift in the free energy change when the partial pressure of that gas is altered.

Gibbs Free Energy and Its Dependence on Reaction Conditions

Gibbs free energy (?G) is a thermodynamic quantity that indicates the spontaneity of a reaction. Under non?standard conditions, ?G is related to its standard state value (?G°) by the equation ?G = ?G° + RT ln Q, where R is the gas constant, T the temperature, and Q the reaction quotient. This equation shows that changes in the concentrations or partial pressures of reactants and products will affect the overall free energy change of the reaction.

Reaction Quotient (Q)

The reaction quotient, Q, is a dimensionless number calculated by inserting the current activities, concentrations, or partial pressures of the reactants and products into the expression derived from the balanced chemical equation. It provides a snapshot of the reaction conditions at any moment and plays a critical role in determining how far a system is from equilibrium, thereby influencing ?G through the logarithmic term in the free energy equation.

Effect of Partial Pressure of a Gas on Q

For reactions involving gases, the partial pressures directly enter the expression for Q. Changing the partial pressure of a gaseous component alters the value of Q. For example, if a reaction consumes oxygen, an increased partial pressure of O2 will decrease Q, making ln Q more negative and thereby driving ?G towards more negative values (more spontaneous). Conversely, for reactions that produce oxygen, raising the O2 partial pressure increases Q, making ln Q more positive and ?G less favorable.

Transcript

00:01 Let's take a look at the effect of the delta g of a system if we increase the partial pressure of oxygen in several cases.

00:10 Recall that to figure out the gibbs free energy, we have an equation delta g is equal to delta g0 plus rt natural log of q, where q is the reaction quotient.

00:22 So we have to go back to our understanding of equilibrium to be able to write a law of mass action expression for each reaction.

00:30 Individually in order to figure out what's going on.

00:34 So the first reaction we have has all gases in it.

00:37 They're all going to participate in writing the reaction quotient then.

00:43 We have carbon monoxide and oxygen becoming carbon dioxide.

00:47 And what we have to do then is figure out what the effective q is going to be when we increase the o2 and see how that value of q affects delta g.

00:59 So let's first figure out what the reaction.

01:01 Action quotient is in this case.

01:03 Remember, we take any aqueous or gaseous product and we raise it to the power of the coefficient.

01:10 So we have carbon dioxide, which is going to be squared because the coefficient is two.

01:16 And then we have our carbon monoxide, which is going to be squared, and our oxygen, which isn't because its coefficient is only one.

01:25 And so if we increase the pressure of the system, what we're really doing, is we're increasing the amount of o2.

01:34 If we increase the amount of o2, what that does to q is decrease q.

01:41 So we're gonna have a lower value of q than we originally did.

01:46 And if we have a lower value of q, then that means that delta g is going to wind up getting smaller over, or i should say over adding the o2.

02:07 Now for, let's take a look at another one...

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