Question

Consider the reaction \(\mathrm{A}(g)+\mathrm{B}(g) \rightleftharpoons \mathrm{C}(g)+\mathrm{D}(g) . \mathrm{A}\) friend asks the following: “I know we have been told that if a mixture of A, B, C, and D is at equilibrium and more of A is added, more C and D will form. But how can more C and D form if we do not add more B?” What do you tell your friend?

Short answer

When more A is added to the system at equilibrium, the concentration of A increases. According to Le Chatelier's Principle, the system will shift towards the right to form more C and D, counteracting the change. The reaction can proceed without adding more B because the initial B concentration was high enough to react with the added A. As the reaction proceeds, the concentrations of A and B decrease, while more C and D are formed, until a new equilibrium is established. This new equilibrium will have a higher concentration of C and D and lower concentrations of A and B compared to the original equilibrium.

Step-by-step solution

State the problem and Le Chatelier's principle

Your friend has a valid question about the reaction at equilibrium. To understand how the reaction responds when more A is added, it is crucial to recall Le Chatelier's Principle. Le Chatelier's Principle states that if a chemical system at equilibrium is perturbed, the system will adjust to minimize the effect of the change.

Describe the initial equilibrium state

Initially, the system is at equilibrium, which means that the forward and reverse reaction rates are equal. As a result, the concentrations of A, B, C, and D remain constant over time.

Describe the effect of adding more A

When more A is added to the system, the concentration of A increases. According to Le Chatelier's Principle, the system will respond by shifting in the direction that minimizes the effect of this change. In this case, the system will shift towards the right to form more C and D to decrease the concentration of A.

Explain how the reaction proceeds without adding more B

The reaction can proceed without adding more B because the overall reaction is still at equilibrium, and the initial B concentration was high enough to react with the added A. As the reaction proceeds, more C and D are formed, while the concentrations of A and B decrease. This change in concentrations continues until a new equilibrium is established.

Describe the new equilibrium state

After the reaction has proceeded, a new equilibrium state is reached where the forward and reverse reaction rates are again equal, and the concentrations of A, B, C, and D are constant. This new equilibrium will have a higher concentration of C and D than the original equilibrium because A was added. The concentrations of A and B will end up lower as some of their moles have been converted to form C and D. In conclusion, by applying Le Chatelier's Principle, we can understand that the system can still shift toward forming more products (C and D) when more reactant A is added, even without adding more of reactant B, because the reaction will proceed in a way that counteracts the disturbance in the equilibrium and establish a new equilibrium state.

Key concepts

Chemical Equilibrium

In the wonderful world of chemistry, reactions can reach a state where they appear to be at rest. This is known as chemical equilibrium. At this point, the rate at which reactants convert to products is exactly balanced by the rate at which products revert back to reactants. Imagine a busy street with cars moving smoothly in both directions—that's equilibrium!

Even though the concentrations of reactants and products remain unchanged over time, reactions continue to occur on a microscopic level. Equilibrium doesn't mean that the reactants and products stop converting; it just means they occur at the same rates.

Reactions can reach equilibrium in closed systems where the conditions are constant. For dynamic systems, any change in conditions will tinker with this balance. When these changes happen, our faithful friend Le Chatelier comes into play, guiding us on how the equilibrium will 'shift' to accommodate the change.

Reaction Rates

Reaction rates refer to how fast or slow a reaction proceeds. In equilibrium, the forward and reverse reaction rates are identical—imagine two teams perfectly balanced on a seesaw.

Several factors can influence these rates, including temperature, pressure, and concentration. However, during equilibrium, changes in these factors have to be smoothened out by adjusting the rates to keep the system balanced.

This understanding is critical, as it tells us why disturbances in equilibrium don't disrupt the entire system. If more A is added as mentioned in the problem, the reaction rate towards the products will increase temporarily, until a new equilibrium is found. It ensures that the system remains stable even when conditions change.

Equilibrium Shift

Le Chatelier's Principle explains how an equilibrium shifts when a system is disturbed. An equilibrium shift is the reaction's response to counteract a change.

When the concentration of a reactant, such as A, is increased, the system reacts by making more products (C and D in this case). This shift to the right decreases the concentration of A, restoring equilibrium. It's like sitting on a seesaw: when one end gets heavier, the seesaw must adjust to return to balance.

Balance is always key in equilibrium shifts. What you add or change, the system will try to remove or neutralize. The system will continue this balancing act until a stable state is achieved.

Concentration Changes

Concentration changes play a pivotal role in altering the equilibrium state of a chemical reaction. When you tweak the amount of a reactant or product, the equilibrium will adjust accordingly.

In the reaction \(\mathrm{A}(g)+\mathrm{B}(g) \rightleftharpoons\mathrm{C}(g)+\mathrm{D}(g)\), adding more \(\mathrm{A}\) means there are now more reactant molecules ready to transform into products. The reaction shifts to form more \(\mathrm{C}\) and \(\mathrm{D}\) until a new balance is reached.

The system adapts by reducing the concentration of \(\mathrm{A}\) and relies on the presence of \(\mathrm{B}\) to facilitate the balance. Integration of concentration changes is a natural adjustment to maintain order in the chemical realm.