Problem 77 - Chemistry The Molecular Science

Question

Predict whether the equilibrium for the photosynthesis reaction described by the equation $$ \begin{array}{r} 6 \mathrm{CO}_{2}(\mathrm{~g})+6 \mathrm{H}_{2} \mathrm{O}(\ell) \rightleftharpoons \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(\mathrm{~s})+6 \mathrm{O}_{2}(\mathrm{~g}) \\ \Delta_{1} H^{\circ}=2801.69 \mathrm{~kJ} / \mathrm{mol} \end{array} $$ would (i) shift to the right, (ii) shift to the left, or (iii) remain unchanged for each of these changes: (a) decrease the concentration of \(\mathrm{CO}_{2}\) at constant volume. (b) increase the partial pressure of \(\mathrm{O}_{2}\) at constant volume. (c) remove one half of the \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) (d) decrease the total pressure by increasing the volume. (e) increase the temperature. (f) introduce a catalyst into a constant-volume system.

Step-by-Step Solution

Answer

(a) left, (b) left, (c) right, (d) unchanged, (e) right, (f) unchanged.

Step 1: Understanding the Reaction

The reaction given is the photosynthesis process:\[ 6 \mathrm{CO}_{2}(\mathrm{~g})+6 \mathrm{H}_{2} \mathrm{O}(\ell) \rightleftharpoons \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(\mathrm{~s})+6 \mathrm{O}_{2}(\mathrm{~g}) \] This is an equilibrium reaction involving gases and a solid. We will use Le Chatelier's Principle to predict the shift of equilibrium. Additionally, the reaction is endothermic, so heat acts as a reactant as indicated by the positive \(\Delta H = 2801.69 \text{ kJ/mol} \).

Step 1: Decrease CO2 concentration

If we decrease the concentration of \(\mathrm{CO}_{2}\), according to Le Chatelier's Principle, the system will try to oppose this change by producing more \(\mathrm{CO}_{2}\). Therefore, the equilibrium will shift to the left, favoring the reactants side.

Step 2: Increase O2 partial pressure

Increasing the partial pressure of \(\mathrm{O}_{2}\) in the system will cause the equilibrium to shift in the direction that will use up the excess \(\mathrm{O}_{2}\). Therefore, the equilibrium will shift to the left, towards the reactants.

Step 3: Remove C6H12O6

Removing \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) will cause the equilibrium to shift in the direction to produce more \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\). Thus, the equilibrium shifts to the right, favoring the product side.

Step 4: Decrease Total Pressure

Decreasing the total pressure by increasing the volume affects the side of the reaction with more moles of gas. Initially, there are 6 moles of gas on both sides (ignoring the solid, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\)), so there is no net change in moles of gas. The equilibrium remains unchanged.

Step 5: Increase Temperature

Since the reaction is endothermic (absorbs heat), increasing the temperature adds more heat, shifting the equilibrium to the right to consume the excess heat.

Step 6: Introduce a Catalyst

A catalyst speeds up the rate of the reaction but does not affect the position of the equilibrium. Thus, introducing a catalyst leaves the equilibrium unchanged.

Key Concepts

Chemical Equilibrium

In chemical systems, equilibrium is where reactants and products are formed at the same rate, leading to no net change in their concentrations over time. This state is dynamic, meaning reactions continue to occur, but they balance each other out. In the context of the photosynthesis reaction, equilibrium is reached when the rate of carbon dioxide and water turning into glucose and oxygen is equal to the rate of glucose and oxygen reverting to carbon dioxide and water.

Le Chatelier's Principle is crucial here. It predicts how a system at equilibrium responds to various changes such as concentration, temperature, and pressure. If an external change is applied, the system adjusts to minimize that disturbance and restore equilibrium. For instance, altering the concentration of CO₂ or O₂ affects the direction of the equilibrium shift, which is predictable using this principle.

Photosynthesis Reaction

The photosynthesis reaction is the chemical process plants use to convert carbon dioxide and water into glucose and oxygen, with the help of sunlight. This equation can be expressed as: \[6 \mathrm{CO}_{2}(\mathrm{~g})+6 \mathrm{H}_{2} \mathrm{O}(\ell) \rightleftharpoons \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(\mathrm{~s})+6 \mathrm{O}_{2}(\mathrm{~g}) \] Photosynthesis is a key process impacting not only plant life but also the entire ecosystem, as it represents a major source of oxygen and organic materials. This reaction reaches equilibrium only under controlled laboratory conditions, as photosynthesis in nature continuously draws on external sources of energy and materials. Understanding the equilibrium in this reaction helps us see how changes in environmental conditions might affect the rate and balance of these essential processes.

Endothermic Reaction

An endothermic reaction is one that absorbs energy, usually in the form of heat. The photosynthesis reaction is endothermic, requiring an input of energy to proceed. This is evident from its enthalpy change, \(\Delta H = 2801.69 \text{ kJ/mol} \), which is positive, thus indicating that heat acts as a reactant in the process.In the case of the photosynthesis equation, when temperature increases, it effectively adds more 'reactant' to the system in terms of heat, thereby shifting the equilibrium to the right, to favor the formation of glucose and oxygen. This feature of endothermic reactions is pivotal in applications like understanding plant responses to climate changes.

Catalysis in Equilibrium

Catalysts play a vital role in both speeding up reactions and reaching equilibrium faster, without altering the position of the equilibrium itself. Introducing a catalyst to the photosynthesis reaction, or any equilibrium system, increases the rate at which equilibrium is achieved. However, it does not change the concentrations of reactants and products at equilibrium. A catalyst provides alternative pathways with lower activation energy, allowing both forward and backward reactions to proceed more quickly. This can be crucial in industrial and biochemical processes where time efficiency is critical but without altering the desired balance of chemical products.