Problem 12 - Chemistry The Central Science

Question

The following graph represents the yield of the compound \(\mathrm{AB}\) at equilibrium in the reaction \(\mathrm{A}(g)+\mathrm{B}(g) \longrightarrow \mathrm{AB}(g)\) at two different pressures, \(x\) and \(y\), as a function of temperature. (a) Is this reaction exothermic or endothermic? (b) Is \(P=x\) greater or smaller than $P=y ?

Step-by-Step Solution

Answer

(a) The reaction is exothermic. (b) P=x is greater than P=y.

Step 1: Identify Le Chatelier's Principle

Le Chatelier's principle states that if a change is made to a system in equilibrium, the system will adjust to counteract that change and reestablish equilibrium. In this exercise, we need to understand how changes in pressure and temperature affect the position of equilibrium and the reaction yield.

Step 2: Analyze the effect of temperature on the reaction

According to the graph, as the temperature increases, the equilibrium yield of compound AB decreases. This behavior suggests that the forward reaction (A + B -> AB) releases heat energy while the reverse reaction (AB -> A + B) absorbs heat energy. In other words, raising the temperature of this reaction promotes the endothermic reverse reaction, meaning the forward reaction is exothermic. Thus, with the information from the graph: (a) The reaction is exothermic.

Step 3: Analyze pressure changes by Le Chatelier's Principle

According to Le Chatelier's principle, increasing pressure for a reaction in a closed system will shift the equilibrium toward the side of the reaction with fewer moles of gas. In this case, the forward reaction (A + B -> AB) reduces the total mole count of gas species, implying that an increase in pressure leads to an increase in the yield of compound AB. Considering any of the pressures P=x or P=y shown in the graph, and noting that temperatures are fixed: (b) P=x must be greater than P=y because the yield of compound AB is higher at the same temperature, which indicates the equilibrium has shifted more in favor of the forward reaction, in response to the increased pressure.

Key Concepts

Le Chatelier's Principle

Le Chatelier's principle is a fascinating concept in chemistry that helps predict how a reaction will respond to changes in its environment. When a system at equilibrium is disturbed, it adjusts to diminish the change and restore balance. This principle applies to various changes, including concentration, pressure, and temperature.

Consider a seesaw balanced perfectly on a fulcrum—an equilibrium of sorts. If a weight is added to one side, the seesaw will tip in that direction. Similarly, in a chemical reaction, if the concentration of a reactant is increased, the system will 'tip' to produce more product to counteract the change. If pressure or volume is altered in a reaction involving gases, the reaction will shift towards the side that helps reduce the pressure change, according to the number of gas molecules involved. Le Chatelier's principle is not only a guiding theory but also an essential tool for chemists to optimize the conditions for chemical reactions to get the desired yield.

Exothermic Reactions

To get a grasp on exothermic reactions, imagine warming your hands by a campfire. The fire releases heat to the surroundings; similarly, in an exothermic reaction, energy is released in the form of heat. These reactions can occur everywhere, from the combustion in car engines to the cellular respiration in our bodies.

Chemically, exothermic reactions are characterized by the release of heat as the bonds in the products are stronger—hence more stable—than the bonds in the reactants. The excess energy is let out into the environment. This is significant because the temperature of the system increases unless the heat is removed. An everyday example is burning natural gas (methane) on your stove to cook food. The methane reacts with oxygen to produce carbon dioxide, water, and heat—quite essential for preparing that delicious meal.

Reaction Yield and Temperature

Let's dive into the relationship between reaction yield and temperature. This connection is pivotal in chemistry, especially in the industrial synthesis of compounds. By manipulating temperature, chemists can nudge a reaction to produce more of a desired product.

The yield of a chemical reaction refers to the amount of product formed under certain conditions. Temperature, being a measure of thermal energy, greatly influences the speed and extent of reactions. For exothermic reactions, an increase in temperature can shift the equilibrium towards the reactants due to Le Chatelier's principle, resulting in a lower yield of the product. The opposite holds true for endothermic reactions; higher temperatures can raise the yield. The trick lies in finding the optimal temperature to maximize the reaction yield while maintaining efficiency and cost-effectiveness. This is crucial in industries where the scale of production can mean the difference between profit and loss.