Problem 102 - Chemistry

Question

Photosynthesis can be represented by $$\begin{array}{r}6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+6 \mathrm{O}_{2}(g) \\\\\Delta H^{\circ}=2801 \mathrm{~kJ} / \mathrm{mol}\end{array}$$ Explain how the equilibrium would be affected by the following changes: (a) Partial pressure of \(\mathrm{CO}_{2}\) is increased. (b) \(\mathrm{O}_{2}\) is removed from the mixture. (c) \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) (glucose) is removed from the mixture. (d) More water is added. (e) A catalyst is added. (f) Temperature is decreased.

Step-by-Step Solution

Answer

(a) The reaction shifts to the right to decrease CO2. (b) The reaction shifts to the right to produce O2. (c) The reaction shifts to the right to reproduce glucose. (d) The equilibrium shifts to the right to balance the increased water. (e) The catalyst does not alter the equilibrium position. (f) Lower temperature shifts equilibrium to the left.

Step 1: Determine impact of increased CO2

If the partial pressure of CO2 is increased, the equilibrium would shift to the right according to Le Chatelier's principle. The system stabilizes the increase in CO2 by creating more glucose and oxygen, thereby reducing the amount of excess CO2.

Step 2: Discuss removal of O2

If O2 is removed from the mixture, the equilibrium shifts to the right, again as per Le Chatelier's principle. By eliminating O2, the reaction can compensate by producing more O2 and glucose from CO2 and water.

Step 3: Explain effect of removing glucose

If glucose is removed from the system, the equilibrium would shift to the right. The reaction compensates for the absence of glucose by producing more of it from CO2 and water.

Step 4: Determine influence of adding water

Adding more water to the mixture causes the reaction to shift to the right. This is because, to balance the concentration, the reaction produces additional glucose and oxygen.

Step 5: Discuss impact of adding a catalyst

Adding a catalyst doesn't affect the position of the equilibrium. It only speeds up the rate at which the equilibrium is achieved.

Step 6: Explain effect of decreasing temperature

As photosynthesis is an endothermic reaction (absorbs heat, positive delta H), lowering the temperature would shift the equilibrium to the left, and less glucose and oxygen would be produced as the system tries to counteract the temperature drop by generating heat.

Key Concepts

Chemical Equilibrium

Chemical equilibrium refers to a state in a reversible chemical reaction where the rate of the forward reaction equals the rate of the backward reaction. At this point, the concentration of reactants and products remains constant over time. In the context of photosynthesis, represented by the equation \(6 \text{CO}_2(g) + 6 \text{H}_2\text{O}(l) \rightleftharpoons \text{C}_6\text{H}_{12}\text{O}_6(s) + 6 \text{O}_2(g)\), the equilibrium can shift depending on various changes to the system.

• If the partial pressure of \(\text{CO}_2\) increases, the equilibrium moves to produce more glucose and oxygen, thus shifting to the right.
• Removing \(\text{O}_2\) causes a similar rightward shift, as the system produces more glucose and oxygen to replenish \(\text{O}_2\).
• With the removal of glucose, more glucose and \(\text{O}_2\) will be made from \(\text{CO}_2\) and water, maintaining balance.
• Adding water also pushes the equilibrium to the right, producing more products to reestablish stability.

Understanding how equilibrium adjusts is crucial for predicting the outcomes of changes in a chemical system.

Photosynthesis

Photosynthesis is a natural process where plants, algae, and some bacteria convert light energy into chemical energy, stored in the form of glucose. The balanced chemical equation for photosynthesis is given by \(6 \text{CO}_2(g) + 6 \text{H}_2\text{O}(l) \rightleftharpoons \text{C}_6\text{H}_{12}\text{O}_6(s) + 6 \text{O}_2(g)\). This reaction is essential for life on Earth as it produces oxygen and organic compounds used for energy by various organisms.

• Photosynthesis takes place in chloroplasts, utilizing chlorophyll to capture sunlight.
• This light energy is used to convert carbon dioxide and water into glucose and oxygen.
• It is crucial for the carbon cycle, converting atmospheric \(\text{CO}_2\) into usable forms of energy.

Adjusting the conditions influencing photosynthesis, such as concentration of reactants and conditions like temperature, directly impacts the equilibrium and efficiency of the process.

Endothermic Reaction

An endothermic reaction is one that absorbs energy from its surroundings, typically in the form of heat. In photosynthesis, the reaction \(6 \text{CO}_2(g) + 6 \text{H}_2\text{O}(l) \rightleftharpoons \text{C}_6\text{H}_{12}\text{O}_6(s) + 6 \text{O}_2(g),\) with an enthalpy change \(\Delta H^{\circ} = +2801 \text{kJ/mol},\) is endothermic. This indicates that energy is absorbed to convert carbon dioxide and water into glucose and oxygen.

• In endothermic reactions, the products are generally higher in energy than the reactants. This requires an energy input, such as heat or light.
• With an increase in temperature, endothermic reactions typically shift to produce more products, as they absorb the extra energy.
• In photosynthesis, sunlight provides the necessary energy, making temperature a critical factor.
• If the temperature decreases, this reaction shifts towards reactants (shifting left) to produce heat and counter the cooling effect.

Understanding the endothermic nature of photosynthesis helps explain why certain environmental conditions favor or impede plant growth.

Reaction Kinetics

Reaction kinetics involves the study of rates at which chemical reactions occur and factors affecting these rates. In the photosynthesis process, the reaction \(6 \text{CO}_2(g) + 6 \text{H}_2\text{O}(l) \rightleftharpoons \text{C}_6\text{H}_{12}\text{O}_6(s) + 6 \text{O}_2(g)\) equates to how quickly reactants are converted to products. Kinetics can be influenced by several factors:

• Temperature: Higher temperatures increase kinetic energy, leading to more frequent and energetic molecular collisions, thus speeding up the reaction.
• Concentration: Increasing the concentration of reactants generally increases the rate of reaction, as there are more molecules available to collide and react.
• Catalyst: Introducing a catalyst does not affect the equilibrium position but speeds up the rate both forward and backward reactions equally, helping reach the equilibrium faster.

Reaction kinetics in photosynthesis affects how efficiently plants convert light energy into chemical energy, ultimately impacting their growth and productivity.