Problem 76 - Chemistry: The Central Science in SI Units, Global Edition

Question

Indicate whether \(\Delta G\) increases, decreases, or does not change when the partial pressure of \(\mathrm{H}_{2}\) is increased in each of the following reactions: (a) \(\mathrm{H}_{2}(g)+\mathrm{NiO}(s) \longrightarrow \mathrm{Ni}(s)+\mathrm{H}_{2} \mathrm{O}(g)\) (b) \(\mathrm{H}_{2}(g)+\mathrm{S}(s) \longrightarrow \mathrm{H}_{2} \mathrm{~S}(g)\) (c) \(\mathrm{C}(s)+\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{CO}(g)+\mathrm{H}_{2}(g)\)

Step-by-Step Solution

Answer

For all three reactions (a) H2(g) + NiO(s) -> Ni(s) + H2O(g), (b) H2(g) + S(s) -> H2S(g), and (c) C(s) + H2O(g) -> CO(g) + H2(g), increasing the partial pressure of H2 leads to an increase in the Gibbs free energy (∆G).

Step 1: (a) Examine the reaction: H2(g) + NiO(s) -> Ni(s) + H2O(g)

In this reaction, the reaction quotient (Q) depends on the partial pressures of H2 and H2O since only those substances are in gaseous form. The relationship between Q and ∆G is given by the equation: \[ ∆G = ∆G^0 + RT\ln{Q}\] where ∆G is the Gibbs free energy, ∆G^0 is the standard Gibbs free energy, R is the gas constant, T is the temperature, and Q is the reaction quotient. Now, when the partial pressure of H2 increases, the reaction quotient (Q) also increases. According to the equation above, this means that ∆G will increase.

Step 2: (b) Examine the reaction: H2(g) + S(s) -> H2S(g)

In this reaction, the reaction quotient (Q) depends on the partial pressures of H2 and H2S, since both substances are in gaseous form. The relationship between Q and ∆G remains the same as in the previous example. When the partial pressure of H2 increases, the reaction quotient (Q) also increases. Therefore, ∆G will increase for this reaction as well.

Step 3: (c) Examine the reaction: C(s) + H2O(g) -> CO(g) + H2(g)

In this reaction, the reaction quotient (Q) depends on the partial pressures of H2O, CO, and H2; only C(s) in solid state doesn't affect Q. The relationship between Q and ∆G remains the same. When the partial pressure of H2 increases, the reaction quotient (Q) also increases. Thus, ∆G will also increase for this reaction. So, in summary, for all three reactions (a), (b), and (c), the Gibbs free energy (∆G) increases when the partial pressure of H2 is increased.

Key Concepts

Gibbs Free Energy

The concept of Gibbs Free Energy (∆G) is essential in understanding chemical reactions and their spontaneity. Gibbs free energy measures the maximum reversible work that may be performed by a thermodynamic system at a constant temperature and pressure. It is a thermodynamic potential helpful in predicting the direction of chemical processes. Simply put, if the value of ∆G is negative, the reaction is spontaneous, meaning it can proceed without external input. Conversely, if ∆G is positive, the reaction is non-spontaneous.
When analyzing a reaction, we need to account for the reaction's change in Gibbs free energy using the equation: \[ ∆G = ∆G^0 + RT\ln{Q}\] where ∆G is Gibbs free energy, ∆G^0 is the standard Gibbs free energy, R is the gas constant, T is the temperature, and Q is the reaction quotient. This equation is essential in determining how the free energy changes as the reaction proceeds.

Reaction Quotient

The Reaction Quotient (Q) is a crucial parameter in thermodynamics and tells us about the direction in which a reaction is proceeding at a given moment. It is defined in the same way as the equilibrium constant (K), but it applies to any point in the reaction, not just at equilibrium.
For a general reaction:

• \( aA + bB \rightleftharpoons cC + dD \)

The reaction quotient is given by:\[ Q = \frac{{[C]^c[D]^d}}{{[A]^a[B]^b}} \] where [C], [D], [A], and [B] are the activities (or concentrations for an ideal solution) of the species at that time.
In gaseous reactions, like those in the original exercise, Q can be expressed in terms of partial pressures. An increase in the partial pressure of a reactant, as is the case with H\(_2\), will directly affect Q. According to the equation ∆G = ∆G^0 + RT\ln{Q}, changes in Q will influence ∆G, thereby affecting the spontaneous nature and feasibility of the reaction.

Partial Pressure

Partial pressure is a vital concept in gas-phase reactions. It refers to the pressure that a single gas component in a mixture would exert if it occupied the entire volume on its own at the same temperature. When dealing with reactions involving gases, like those noted in the exercise, understanding partial pressure helps predict how changes will affect the overall reaction.

• The total pressure of a gas mixture is the sum of the partial pressures of all its components.
• Partial pressure is a way to account for the individual contribution of each gaseous substance to a system's overall pressure.

In the exercise provided, the increase in the partial pressure of hydrogen (H\(_2\)) affects the reaction quotient (Q), thereby influencing the Gibbs free energy (∆G).
When the partial pressure of H\(_2\) is increased, it causes Q to rise, resulting in an increase in ∆G based on the equation \( ∆G = ∆G^0 + RT\ln{Q} \). This shows a direct relationship between partial pressure and the thermodynamic favorability of a reaction.