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 tend to favor the production of \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)\) since photosynthesis is an endothermic reaction, and according to Le Chatelier's principle, the reaction will shift in favor of the endothermic, forward direction when the temperature increases.

Step-by-step solution

Determine if the reaction is endothermic or exothermic

To know if the photosynthesis reaction is endothermic or exothermic, we should consider the energy involved in the reaction. In general, if a reaction absorbs energy from the surroundings (as it does in photosynthesis, where radiant energy from the sun is absorbed), it is considered endothermic. On the other hand, if a reaction releases energy to the surroundings, it is exothermic. In this case, since photosynthesis is known to absorb radiant energy from the sun, the reaction is endothermic.

Apply Le Chatelier's principle to determine how the reaction is affected by temperature changes

Le Chatelier's principle states that if a stress (change in temperature, pressure, or concentration) is applied to a system at equilibrium, the system will shift in the direction that minimizes the stress. In the case of an endothermic reaction, if we increase the temperature, the system will try to counteract this by absorbing the added heat and shifting in the direction of the endothermic reaction (the forward reaction for photosynthesis). Conversely, if we decrease the temperature, the system will try to counteract this by releasing heat, shifting the equilibrium in the direction of the exothermic reaction (the reverse reaction).

Determine if the production of \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)\) will be favored or discouraged with an increase in temperature

Since we've established that photosynthesis is an endothermic reaction and we are increasing the temperature, according to Le Chatelier's principle, the reaction will shift in favor of the endothermic, forward direction. This means it will produce more dextrose (\(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)\)) to absorb the added heat, relatively. So, an increase in temperature will tend to favor the production of \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)\).

Key concepts

Le Chatelier's Principle

Imagine a seesaw balanced perfectly with two children of equal weight. What happens if another child joins on one side? Naturally, the seesaw will tilt in that direction. The famous Le Chatelier's principle is similar to this seesaw. It's a concept in chemistry describing how a system at equilibrium reacts to disturbances or 'stresses,' like changes in temperature, pressure, or concentration of reactants and products.

Let's take a chemical reaction that's comfortably balanced — where the rate of the forward reaction equals the rate of the reverse. When a stress is applied, Le Chatelier's principle tells us the reaction will shift to oppose the change, helping the system reach a new state of balance. Think of it as the reaction's way of maintaining equilibrium.

If you warm up the system, that's like adding an extra child to the seesaw. An endothermic reaction absorbs heat, so increasing temperature makes the reaction move forward to take in that additional 'child' of heat. Likewise, if the temperature drops, the reaction favors the exothermic direction, releasing heat to 'push the child off.' The principle is indispensable for understanding how reactions adapt to changes and is key to controlling industrial chemical processes.

Endothermic Reactions

If chemistry were a blockbuster, endothermic reactions would be the heroes that keep you on the edge of your seat. These reactions are like energy enthusiasts; they absorb heat from their surroundings to push forward. It's like cooking an egg: the raw egg absorbs heat from the pan to become a delicious breakfast. In endothermic reactions, the products' total energy is higher than the reactants', because they've taken in the energy as heat.

Photosynthesis, the process that powers life on Earth, is a prime example of an endothermic reaction. Plants take in sunlight and use that energy to transform carbon dioxide and water into glucose and oxygen. It's like plants are using sunlight to bake their food – glucose, sustaining not just themselves but the entire food chain! This absorption of heat has profound implications when it comes to altering the conditions in which the reaction occurs, such as changing the temperature.

Equilibrium in Chemical Reactions

Equilibrium is the Goldilocks zone of chemical reactions, where things are 'just right.' In a state of equilibrium, the rate of the forward reaction equals the rate of the reverse reaction. As a result, the concentrations of reactants and products remain unchanged over time, even though the reactions are still happening. It's a dynamic balance – think of it as an ongoing dance where the dancers (molecules) keep swapping partners (reacting) without changing the overall makeup of the dance floor.

An equilibrium might sound static, but it's actually a state of continuous activity – a tug-of-war between the reactants and products with neither side gaining ground. When a reaction reaches this stage, we can use Le Chatelier's principle to predict the system's response to changes like temperature adjustments. For example, increasing the temperature in the photosynthesis reaction would push the equilibrium to favor the formation of glucose, the product, which is why plants thrive in sunlight.