Question

For each of the questions, four choices have been provided. Select the correct alternative. According to Le Chatelier's principle, (a) an increase in pressure always causes a change in position of equilibrium for any reaction (b) the yield of \(\mathrm{NH}_{3}\) decreases from its constituents at lower temperature (c) an increase in temperature causes a decrease in the value of \(\mathrm{K}_{\mathrm{c}}\) for an exothermic reaction (d) the \(\mathrm{K}_{\mathrm{c}}\) is decreased for the reaction \(\mathrm{A}_{(\mathrm{s})}+\mathrm{B}_{(\mathrm{g})}\) \(\rightarrow \mathrm{C}_{(\mathrm{g})}\), if the concentration of \(\mathrm{A}\) is increased

Short answer

Based on Le Chatelier's principle and the analysis of all options, the correct statement regarding the principle is option (b): "The yield of NH3 from nitrogen and hydrogen decreases at a low temperature." This is because, in exothermic reactions like the formation of NH3, a decrease in temperature causes the system to compensate by favoring the forward direction, leading to a decrease in yield.

Step-by-step solution

Understanding Le Chatelier's Principle

Le Chatelier's principle states that if a change (e.g., increase or decrease in concentration, pressure, or temperature) is made to a system at equilibrium, the system will adjust itself to partially counteract the applied change, in order to regain a new equilibrium. We will now analyze each option to find the correct alternative.

Analyzing option (a)

In option (a), the statement is not always true. An increase in pressure will cause a change in the position of equilibrium in a reaction involving gaseous reactants and/or products, but only if the reaction has different numbers of moles of gas molecules on the reacting and product side.

Analyzing option (b)

Option (b) mentions the yield of \(\mathrm{NH}_{3}\) from its constituents, i.e., the reaction \(\mathrm{N}_{2(g)} + 3\mathrm{H}_{2(g)} \rightleftharpoons 2\mathrm{NH}_{3(g)}\). This reaction is exothermic. According to Le Chatelier's principle, the yield of NH\(_{3}\) will indeed decrease at a lower temperature since the system will try to counteract the decrease in temperature by favoring the exothermic direction (i.e., the forward direction). Thus, option (b) is correct.

Analyzing option (c)

In option (c), an increase in temperature causes a decrease in the value of \(\mathrm{K}_{\mathrm{c}}\) for an exothermic reaction. This statement is also true. For an exothermic reaction, increasing the temperature will shift the equilibrium towards the reactant side, which leads to a decrease in the value of \(\mathrm{K}_{\mathrm{c}}\).

Analyzing option (d)

In option (d), the statement claims that the \(\mathrm{K}_{\mathrm{c}}\) is decreased for the reaction \(\mathrm{A}_{(\mathrm{s})}+\mathrm{B}_{(\mathrm{g})} \to \mathrm{C}_{(\mathrm{g})}\), if the concentration of \(\mathrm{A}\) is increased. This statement is false, as the \(\mathrm{K}_{\mathrm{c}}\) remains constant for a reaction regardless of the concentration of the reactants and products. Le Chatelier's principle only predicts the shift in position of the equilibrium, not the change in the equilibrium constant. In conclusion, the correct alternative is (b).

Key concepts

Chemical Equilibrium

Chemical equilibrium is a state in a chemical reaction where the rates of the forward and reverse reactions are equal, resulting in no net change in the amounts of reactants and products over time. It's a dynamic balance, meaning that the reactions continue to occur, but because they happen at the same rate, the composition of the reaction mixture remains constant.
Understanding chemical equilibrium is crucial because it determines how much product can be produced in a reaction and helps in the formulation of strategies to increase the yield of desired products. For instance, consider the synthesis of ammonia (hlatex{NH_3}) from nitrogen (hlatex{N_2}) and hydrogen (hlatex{H_2}) gases. This reaction reaches chemical equilibrium, with a specific ratio of reactants to products depending on various conditions such as temperature and pressure.
In the context of Le Chatelier's principle, if any of the conditions at the equilibrium state are altered, the system responds to counteract the disturbance and a new equilibrium is established. For instance, if additional nitrogen is introduced into the system, the equilibrium will shift towards producing more ammonia to reduce the effect of this change.

Reaction Yield

The reaction yield refers to the amount of product formed in a chemical reaction. It is often expressed as a percentage of the maximum possible amount, based on the stoichiometry of the balanced equation. Factors such as temperature, pressure, concentration of reactants, presence of catalysts, and the equilibrium position influence the reaction yield.
Using Le Chatelier's principle, we can predict how changes to the system conditions will affect the yield. For example, in the production of ammonia mentioned above, a lower temperature would decrease the yield of ammonia based on the principle. However, in industrial processes, other considerations like reaction rate might favor higher temperatures despite a lower equilibrium yield. Therefore, achieving optimal yield requires a balance of kinetics (reaction rate) and thermodynamics (equilibrium position).

Improving Reaction Yield

To increase the reaction yield, one could change the reaction conditions to favor product formation by, for example, removing the product from the reaction mixture, altering pressures or temperatures, or adding catalysts. These methods shift the equilibrium position toward the products, enhancing the yield.

Equilibrium Constant Kc

The equilibrium constant, denoted as hlatex{K_c}, is a numerical value that provides a measure of the extent of a chemical reaction at equilibrium at a given temperature. It is calculated using the concentrations of the products raised to the power of their coefficients divided by the concentrations of the reactants raised to the power of their coefficients, according to the balanced chemical equation. This value is constant for a particular reaction at a specific temperature and does not vary with changes in concentrations, pressures, or the presence of catalysts.
When the reaction quotient (hlatex{Q})—which is calculated in the same way as hlatex{K_c} but at any point in time, not just at equilibrium—equals the equilibrium constant, the system is at equilibrium. If hlatex{Q} is different from hlatex{K_c}, the system is not at equilibrium and will shift to establish a new equilibrium state. Adjustments to the reaction conditions, as per Le Chatelier's principle, do not alter the value of hlatex{K_c} but will shift the ratio of reactants to products until the reaction quotient equals the equilibrium constant once again.
For an exothermic reaction, an increase in temperature will cause a shift in equilibrium that favors reactants, leading to a decrease in the value of hlatex{K_c}. Conversely, for an endothermic reaction, an increase in temperature will lead to an increase in the value of hlatex{K_c} as the system responds by creating more products.