Problem 64 - Chemistry An Atoms First Approach

Question

Predict the shift in the equilibrium position that will occur for each of the following reactions when the volume of the reaction container is increased. a. \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)\) b. \(\mathrm{PCl}_{5}(g) \rightleftharpoons \mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g)\) c. \(\mathrm{H}_{2}(g)+\mathrm{F}_{2}(g) \rightleftharpoons 2 \mathrm{HF}(g)\) d. \(\operatorname{COCl}_{2}(g) \rightleftharpoons \operatorname{CO}(g)+\mathrm{Cl}_{2}(g)\) e. \(\mathrm{CaCO}_{3}(s) \rightleftharpoons \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)\)

Step-by-Step Solution

Answer

For the given reactions, the shift in equilibrium position when the volume of the reaction container is increased is as follows: a. The equilibrium will shift to the left (towards reactants). b. The equilibrium will shift to the right (towards products). c. There will be no effect on the equilibrium position. d. The equilibrium will shift to the right (towards products). e. The equilibrium will shift to the right (towards products).

Step 1: Observe the stoichiometry of the reaction

In this reaction, 1 mole of nitrogen and 3 moles of hydrogen produce 2 moles of ammonia. The total moles of gas on the left side are 4, and on the right side, there are 2.

Step 2: Apply Le Chatelier's principle

According to Le Chatelier's principle, increasing the volume will cause the equilibrium to shift to the side with more moles of gas. In this case, the equilibrium will shift to the left. #b - Phosphorus Pentachloride reaction#

Step 3: Observe the stoichiometry of the reaction

In this reaction, 1 mole of phosphorus pentachloride produces 1 mole of phosphorus trichloride and 1 mole of chlorine. The total moles of gas on both sides of the reaction are equal: 1 on the left and 2 on the right.

Step 4: Apply Le Chatelier's principle

The principle states that the equilibrium will shift to the side with more moles of gas when the volume is increased. In this case, the equilibrium will shift to the right. #c - Hydrogen and Fluorine reaction#

Step 5: Observe the stoichiometry of the reaction

In this reaction, 1 mole of hydrogen and 1 mole of fluorine produce 2 moles of hydrogen fluoride. The total moles of gas on both sides of the reaction are equal: 2 on the left and 2 on the right.

Step 6: Apply Le Chatelier's principle

Since the total moles of gas on both sides of the reaction are equal, increasing the volume will have no effect on the equilibrium position. #d - Carbonyl Chloride reaction#

Step 7: Observe the stoichiometry of the reaction

In this reaction, 1 mole of carbonyl chloride produces 1 mole of carbon monoxide and 1 mole of chlorine. The total moles of gas on both sides of the reaction are equal: 1 on the left and 2 on the right.

Step 8: Apply Le Chatelier's principle

According to Le Chatelier's principle, increasing the volume will cause the equilibrium to shift to the side with more moles of gas. In this case, the equilibrium will shift to the right. #e - Calcium Carbonate reaction#

Step 9: Observe the stoichiometry of the reaction

In this reaction, 1 mole of calcium carbonate produces 1 mole of calcium oxide and 1 mole of carbon dioxide. The left side has no moles of gas (only solid), and the right side has 1 mole of gas (CO2).

Step 10: Apply Le Chatelier's principle

According to the principle, increasing the volume will cause the equilibrium to shift to the side with more moles of gas. In this case, the equilibrium will shift to the right.

Key Concepts

Chemical Equilibrium

Chemical equilibrium is the state in a chemical reaction where the rate of the forward reaction equals the rate of the backward reaction. This results in the concentrations of reactants and products remaining constant over time. However, it is important to note that this does not mean the concentrations are equal. At equilibrium, a dynamic balance is achieved where the reactions continue to occur, but there is no net change in the amounts of substances present. This balance can be disturbed by changes in conditions, such as pressure, temperature, or concentration. By understanding chemical equilibrium, we can predict how a reaction will respond to such changes, aiding in control and optimization processes in both research and industry. Le Chatelier's Principle is particularly useful in predicting these responses.

Reaction Stoichiometry

Reaction stoichiometry refers to the quantitative relationships between reactants and products in a chemical reaction. It is derived from the balanced chemical equation, where coefficients indicate the proportion of moles of each substance involved. Understanding stoichiometry is crucial in predicting how changes in concentration or pressure can affect chemical equilibrium. For example, if we increase the volume of a container, stoichiometry helps us calculate the change in the concentration of each component. Through stoichiometry, we can decide whether the system will shift its equilibrium position to the left, favoring reactants, or to the right, favoring products. Each mole's participation is vital to determining how the reaction will respond to changes based on Le Chatelier's Principle. This mathematical relationship is fundamental in experimental chemistry and industrial applications, where precise measurements and ratios are essential.

Gas Laws

Gas laws describe how gases behave under different conditions of pressure, volume, and temperature. These laws are vital in understanding shifts in equilibrium in chemical reactions involving gases. For instance, Boyle's Law states that at constant temperature, the pressure of a gas is inversely proportional to its volume. Thus, increasing the volume of a reaction container decreases the pressure, leading to a shift in equilibrium according to Le Chatelier's Principle. The reaction will shift towards the side with more moles of gas to oppose the decrease in pressure. Gas laws also include Charles's Law and Avogadro's Law, which together provide a comprehensive understanding of how gases react to different conditions. These laws are essential tools on our path to mastering reactions and equilibrium.

Shifts in Equilibrium

Shifts in equilibrium refer to the change in the position of equilibrium in response to outside disturbances. When we change the conditions of a chemical reaction, such as pressure by altering the volume, the system will adjust to counteract the change and re-establish equilibrium. According to Le Chatelier's Principle, if we increase the volume, the equilibrium will shift toward the side with more moles of gas. This response aims to increase the pressure, restoring balance in the reaction. Conversely, decreasing the volume shifts the equilibrium to the side with fewer gas moles. The concept of shifts in equilibrium is foundational in predicting and manipulating reactions in chemical processing, ensuring maximum yield and efficiency. This principle empowers chemists and engineers to optimize reactions for various industrial applications.