Question

Sorbitol \(\left(\mathrm{C}_{6} \mathrm{H}_{14} \mathrm{O}_{6}\right)\), a substance used as a sweetener in foods, is prepared by the reaction of glucose with hydrogen in the presence of a catalyst: $$\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}(a q)+\mathrm{H}_{2}(g) \longrightarrow \mathrm{C}_{6} \mathrm{H}_{14} \mathrm{O}_{6}(a q)$$ Which of the following quantities are affected by the catalyst? (a) Rate of the forward reaction (b) Rate of the reverse reaction (c) Spontaneity of the reaction (d) \(\Delta H^{\circ}\) (e) \(\Delta S^{\circ}\) (f) \(\Delta G^{\circ}\) (g) The equilibrium constant (h) Time required to reach equilibrium

Short answer

(a), (b), and (h) are affected by the catalyst.

Step-by-step solution

Understand Catalyst's Effect

A catalyst increases the rate of a chemical reaction by lowering the activation energy. It does not affect the thermodynamic properties such as spontaneity (\(\Delta G^{\circ}\)), enthalpy change (\(\Delta H^{\circ}\)), entropy change (\(\Delta S^{\circ}\)), or the equilibrium constant (\(K\)).

Evaluate Impact on Reaction Rates

Both the rate of the forward reaction and the rate of the reverse reaction increase due to the catalyst's presence. This is because lowering the activation energy impacts both directions of the reaction.

Determine Influence on Equilibrium Properties

The catalyst does not change whether a reaction is spontaneous, nor does it alter the enthalpy change, entropy change, or equilibrium constant. The equilibrium position remains unchanged; thus, \(\Delta G^{\circ}\), \(\Delta H^{\circ}\), \(\Delta S^{\circ}\), and the equilibrium constant are unaffected.

Assess Time to Equilibrium

A catalyst decreases the time required to reach equilibrium because it speeds up both the forward and reverse reaction rates, allowing the system to achieve equilibrium faster.

Key concepts

Reaction Rates

In chemistry, reaction rates refer to the speed at which reactants are converted into products in a chemical reaction. The rate of a reaction can be influenced by several factors, such as concentration, temperature, surface area of reactants, and the presence of a catalyst. Catalysts play a crucial role in altering reaction rates by offering an alternative pathway with lower activation energy, thereby increasing the reaction rate.

- Catalysts are remarkable because they affect both the forward and reverse reactions equally. - By lowering the activation energy, they enable the reactants to convert into products faster. - This is significant because achieving optimal speeds can be essential in industrial processes to save time and resources.

Overall, while catalysts do not get consumed in the reaction, they are pivotal in accelerating the process without altering the final products or the amount of reactants used.

Activation Energy

Activation energy is the minimum energy that reacting molecules must have for a chemical reaction to occur. It acts as a barrier that must be overcome for reactants to transform into products.

- Think of activation energy as a hill that the reactants must climb for the reaction to take place.- Catalysts effectively "lower the hill," providing a different route that requires less energy.- This makes it easier and faster for reactants to form products, thereby increasing the reaction rate.

Importantly, while catalysts lower the activation energy, they do not alter the overall energy difference between reactants and products, signified by the enthalpy change (\(\Delta H\) of the reaction. The presence of a catalyst merely facilitates the transition state to be reached more quickly.

Chemical Equilibrium

Chemical equilibrium is the state in a reversible reaction where the rates of the forward and reverse reactions are equal, resulting in no overall change in the concentration of reactants and products. A catalyst does not affect the position of equilibrium.

- Equilibrium is characterized by a constant ratio of the concentration of products to reactants, known as the equilibrium constant (K). - The catalyst does not change this ratio but does help the system reach equilibrium faster, as it speeds up both the forward and reverse reactions equally. - This is useful in processes where reaching equilibrium quickly is desirable, but it does not influence the final equilibrium composition.

Hence, the presence of a catalyst is beneficial for increasing the efficiency of reaching equilibrium but does not disrupt the balance of equilibrium conditions.

Thermodynamic Properties

Thermodynamic properties describe the energy changes and spontaneity within a chemical reaction. Core properties include enthalpy change (\(\Delta H\)), entropy change (\(\Delta S\)), and Gibbs free energy change (\(\Delta G\)).

- Enthalpy change reflects the heat absorbed or released during a reaction under constant pressure.- Entropy change indicates the degree of disorder or randomness associated with the system.- Gibbs free energy change is the most definitive measure of spontaneity, determining whether a reaction can occur under set conditions without external energy.
A catalyst does not alter these thermodynamic properties.- It doesn't change the endothermic or exothermic nature (\(\Delta H\)) of a reaction.- It doesn't affect entropy (\(\Delta S\)) or spontaneity (\(\Delta G\)), as these are inherent characteristics.- Instead, it accelerates the path to reach what is naturally destined according to the existing thermodynamic parameters.
Therefore, while catalysts greatly impact the rate and efficiency of reactions, they leave thermodynamic fundamentals intact.