Question

Plants synthesize the sugar dextrose according to the following reaction by absorbing radiant energy from the sun (photosynthesis). $$ 6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+6 \mathrm{O}_{2}(g) $$ Will an increase in temperature tend to favor or discourage the production of $$ \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s) ? $$

Short answer

An increase in temperature will favor the production of dextrose (\(C_{6}H_{12}O_{6}\)) in the photosynthesis reaction, as it is an endothermic process. According to Le Chatelier's principle, the system will shift to the right to absorb the increased heat and maintain equilibrium.

Step-by-step solution

Understand the balanced equation

Given the balanced chemical equation for photosynthesis: \( 6CO_{2}(g)+6H_{2}O(g) \rightleftharpoons C_{6}H_{12}O_{6}(s)+6O_{2}(g) \)

Determine the effect of temperature on the reaction

Since plants absorb radiant energy from the sun during photosynthesis, the reaction is endothermic. We can represent the energy absorption with the addition of heat (as a reactant) to our equation: \( 6CO_{2}(g)+6H_{2}O(g) + \text{Heat} \rightleftharpoons C_{6}H_{12}O_{6}(s)+6O_{2}(g) \)

Apply Le Chatelier's Principle

According to Le Chatelier's principle, when a change in temperature, pressure, or concentration is applied to a system in equilibrium, the system will shift to counteract the change and restore equilibrium. Since the reaction is endothermic, an increase in temperature will cause the system to shift to the right (favoring the production of products) in order to absorb the additional heat and restore equilibrium: \( 6CO_{2}(g)+6H_{2}O(g) + \text{Increased Heat} \rightarrow C_{6}H_{12}O_{6}(s)+6O_{2}(g) \)

Conclusion

Based on Le Chatelier's principle, an increase in temperature will favor the production of dextrose (C_{6}H_{12}O_{6}) in the photosynthesis reaction since it is an endothermic process. The system will shift to the right to absorb the increased heat and maintain equilibrium.

Key concepts

Chemical Equilibrium

Chemical equilibrium occurs when a chemical reaction proceeds at the same rate in both the forward and reverse directions, resulting in no net change in the concentration of reactants and products. It is a dynamic state because the reactions continue to occur, but the overall concentrations stay consistent.

For example, in the photosynthesis reaction, when the rate at which carbon dioxide and water react to form glucose and oxygen equals the rate at which glucose and oxygen break down into carbon dioxide and water, the reaction has reached chemical equilibrium. Any changes in the conditions of a system at equilibrium, like temperature or concentration, can shift the balance, affecting the yield of products or reactants.

Le Chatelier's Principle

Le Chatelier's principle provides insight into how a reaction at equilibrium responds to external changes. This principle states that if a system at equilibrium experiences a change, such as variations in temperature, pressure, or concentration of components, the equilibrium will shift to counteract that change.

Applying this to photosynthesis, if the temperature increases, according to Le Chatelier's principle, the equilibrium will shift to utilize this additional heat energy. Because the reaction is endothermic (absorbs heat), the reaction shifts to produce more glucose and oxygen, effectively reducing the added heat and restoring a new equilibrium state.

Endothermic Reactions

Endothermic reactions are chemical processes that absorb energy from their surroundings, typically in the form of heat. This is in contrast to exothermic reactions, which release energy.

In photosynthesis, plants take in sunlight as a source of energy, which is used to convert carbon dioxide and water into glucose and oxygen. The inclusion of heat as a reactant in the balanced equation indicates that the process is endothermic. Therefore, when the temperature rises, photosynthesis speeds up as it absorbs more heat energy, which is consistent with the nature of endothermic reactions.

Balanced Chemical Equations

Balanced chemical equations provide a representation of a chemical reaction where the number of atoms for each element in the reactants equals the number of atoms in the products. It reflects the conservation of mass and allows us to predict the amounts of substances produced or used in a given reaction.

The photosynthesis equation is balanced, meaning it correctly shows that six molecules of carbon dioxide and six molecules of water react to form one molecule of glucose and six molecules of oxygen, adhering to the law of conservation of mass. This balance is essential for understanding the stoichiometry of the reaction – the quantitative relationship between reactants and products in a chemical reaction.