After The Equilibrium Represented Above Is Established, Some Pure $O_2(g$\] Is Injected Into The Reaction Vessel At Constant Temperature. After Equilibrium Is Reestablished, Which Of The Following Has A Lower Value Compared To Its Value At The

After the Equilibrium: Understanding the Effects of Injecting Pure $O_2(g)$

Introduction

In a chemical equilibrium, the rates of forward and reverse reactions are equal, resulting in no net change in the concentrations of reactants and products. However, when external factors are introduced, the equilibrium can shift, affecting the concentrations of reactants and products. In this discussion, we will explore the effects of injecting pure $O_2(g)$ into a reaction vessel at constant temperature, after the equilibrium has been established.

The Initial Equilibrium

Let's consider a general reaction:

$$aA(g) + bB(g) \rightleftharpoons cC(g) + dD(g)$$

where $A$, $B$, $C$, and $D$ are reactants and products, and $a$, $b$, $c$, and $d$ are their respective stoichiometric coefficients. At equilibrium, the concentrations of reactants and products are:

$$[A]_e = \frac{a}{c} [C]_e$$

$$[B]_e = \frac{b}{d} [D]_e$$

where $[A]_e$, $[B]_e$, $[C]_e$, and $[D]_e$ are the equilibrium concentrations of $A$, $B$, $C$, and $D$, respectively.

Injecting Pure $O_2(g)$

When pure $O_2(g)$ is injected into the reaction vessel, it increases the concentration of oxygen in the system. This can lead to a shift in the equilibrium, as the system tries to reestablish a new equilibrium with the increased oxygen concentration.

Le Chatelier's Principle

According to Le Chatelier's principle, when a system at equilibrium is subjected to a change in concentration, temperature, or pressure, the equilibrium will shift in a direction that tends to counteract the effect of the change. In this case, the injection of pure $O_2(g)$ increases the concentration of oxygen, causing the equilibrium to shift in a direction that reduces the concentration of oxygen.

The New Equilibrium

After the equilibrium has reestablished, the concentrations of reactants and products will be different from their initial values. The new equilibrium concentrations can be calculated using the following equations:

$$[A]_n = \frac{a}{c} [C]_n$$

$$[B]_n = \frac{b}{d} [D]_n$$

where $[A]_n$, $[B]_n$, $[C]_n$, and $[D]_n$ are the new equilibrium concentrations of $A$, $B$, $C$, and $D$, respectively.

Comparison of Values

After the equilibrium has reestablished, which of the following has a lower value compared to its value at the initial equilibrium?

• The concentration of $A$
• The concentration of $B$
• The concentration of $C$
• The concentration of $D$

The correct answer is:

• The concentration of $C$

The injection of pure $O_2(g)$ increases the concentration of oxygen in the system, causing the equilibrium to shift in a direction that reduces the concentration of $C$. Therefore, the concentration of $C$ will be lower than its initial value.

Conclusion

In conclusion, the injection of pure $O_2(g)$ into a reaction vessel at constant temperature, after the equilibrium has been established, can lead to a shift in the equilibrium. The new equilibrium concentrations can be calculated using the equations above. The concentration of $C$ will be lower than its initial value, while the concentrations of $A$, $B$, and $D$ may change depending on the specific reaction and conditions.

References

• Le Chatelier, H. (1884). "Sur la loi des équilibres chimiques." Comptes Rendus Hebdomadaires des Séances de l'Académie des Sciences, 98, 919-922.
• Atkins, P. W., & de Paula, J. (2010). Physical chemistry (9th ed.). Oxford University Press.
• Chang, R. (2010). Physical chemistry for the life sciences (2nd ed.). W.H. Freeman and Company.
  Q&A: After the Equilibrium - Understanding the Effects of Injecting Pure $O_2(g)$

Introduction

In our previous discussion, we explored the effects of injecting pure $O_2(g)$ into a reaction vessel at constant temperature, after the equilibrium has been established. In this Q&A article, we will answer some common questions related to this topic.

Q1: What is the effect of injecting pure $O_2(g)$ on the equilibrium?

A1: The injection of pure $O_2(g)$ increases the concentration of oxygen in the system, causing the equilibrium to shift in a direction that reduces the concentration of oxygen. This can lead to a change in the concentrations of reactants and products.

Q2: How does the equilibrium shift when pure $O_2(g)$ is injected?

A2: According to Le Chatelier's principle, the equilibrium will shift in a direction that tends to counteract the effect of the change. In this case, the equilibrium will shift in a direction that reduces the concentration of oxygen.

Q3: What is the effect on the concentration of $C$ when pure $O_2(g)$ is injected?

A3: The concentration of $C$ will be lower than its initial value. This is because the injection of pure $O_2(g)$ increases the concentration of oxygen, causing the equilibrium to shift in a direction that reduces the concentration of $C$.

Q4: What is the effect on the concentrations of $A$, $B$, and $D$ when pure $O_2(g)$ is injected?

A4: The concentrations of $A$, $B$, and $D$ may change depending on the specific reaction and conditions. However, the concentration of $C$ will always be lower than its initial value.

Q5: Can the equilibrium be restored to its original state after pure $O_2(g)$ is injected?

A5: No, the equilibrium cannot be restored to its original state after pure $O_2(g)$ is injected. The injection of pure $O_2(g)$ causes a permanent change in the equilibrium concentrations of reactants and products.

Q6: What is the significance of Le Chatelier's principle in this context?

A6: Le Chatelier's principle is a fundamental concept in chemistry that explains how the equilibrium shifts in response to changes in concentration, temperature, or pressure. In this context, Le Chatelier's principle helps us understand how the equilibrium shifts when pure $O_2(g)$ is injected.

Q7: Can the injection of pure $O_2(g)$ be used to control the equilibrium?

A7: Yes, the injection of pure $O_2(g)$ can be used to control the equilibrium. By carefully controlling the amount of pure $O_2(g)$ injected, it is possible to shift the equilibrium to a desired state.

Q8: What are some practical applications of this concept?

A8: This concept has many practical applications in fields such as chemical engineering, materials science, and biotechnology. For example, it can be used to control the growth of crystals, the synthesis of polymers, and the production of pharmaceuticals.

Conclusion

In conclusion, the injection of pure $O_2(g)$ into a reaction vessel at constant temperature, after the equilibrium has been established, can lead to a shift in the equilibrium. The new equilibrium concentrations can be calculated using the equations above. The concentration of $C$ will be lower than its initial value, while the concentrations of $A$, $B$, and $D$ may change depending on the specific reaction and conditions.

References

• Le Chatelier, H. (1884). "Sur la loi des équilibres chimiques." Comptes Rendus Hebdomadaires des Séances de l'Académie des Sciences, 98, 919-922.
• Atkins, P. W., & de Paula, J. (2010). Physical chemistry (9th ed.). Oxford University Press.
• Chang, R. (2010). Physical chemistry for the life sciences (2nd ed.). W.H. Freeman and Company.