Equilibrium (Le Chatelier’s Principle)

Introduction:

In chemistry, equilibrium refers to the state in which both the reactants and products are present in concentrations that have no further tendency to change with time. This dynamic condition occurs when the rates of the forward and reverse reactions are equal.

Le Chatelier’s Principle states that if a system at equilibrium is subjected to a disturbance (such as a change in concentration, temperature, or pressure), the system will adjust itself to counteract the disturbance and restore a new equilibrium.

Equilibrium Constant ($K_c$):

The equilibrium constant ($K_c$) is a number that expresses the relationship between the amounts of products and reactants present at equilibrium in a reversible chemical reaction at a given temperature.

Equation for the Equilibrium Constant:

$K_c=\frac{[\text{Products}]}{[\text{Reactants}]}$

Where:

• $[\text{Products}]$ = the concentration of the products at equilibrium
• $[\text{Reactants}]$ = the concentration of the reactants at equilibrium

Example 1: Calculating the Equilibrium Constant

Question: Given the reaction $A+B\rightleftharpoons C+D$, the equilibrium concentrations of the substances are:

• $[A]=2,M$
• $[B]=1,M$
• $[C]=3,M$
• $[D]=4,M$

Calculate the equilibrium constant, $K_c$.

Answer:

Step 1: Given Data:

• $[A]=2,M$
• $[B]=1,M$
• $[C]=3,M$
• $[D]=4,M$

Step 2: Solution:

The equilibrium constant, $K_c$, is given by:

$K_c=\frac{[C][D]}{[A][B]}$

Substitute the values into the equation:

$K_c=\frac{(3)(4)}{(2)(1)}$

Step 3: Final Answer:

$K_c=\frac{12}{2}=6$

Thus, the equilibrium constant is $K_c=6$.

Example 2: Effect of Temperature on Equilibrium

Question: Consider the exothermic reaction $A+B\rightleftharpoons C+D$. What will happen to the equilibrium position if the temperature is increased?

Answer:

Step 1: Given Data:

• The reaction is exothermic, meaning it releases heat.
• Increasing temperature will add heat to the system.

Step 2: Solution:

According to Le Chatelier’s Principle:

• Since heat is a product in this exothermic reaction, increasing the temperature will shift the equilibrium position to the left (towards the reactants) to absorb the added heat.

Step 3: Final Answer:

When the temperature is increased, the equilibrium will shift to favor the formation of reactants, reducing the amount of products formed.

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Example 3: Effect of Pressure on Equilibrium

Question: For the reaction $2A(g)+B(g)\rightleftharpoons 2C(g)$, predict the effect of increasing pressure on the equilibrium position.

Answer:

Step 1: Given Data:

• The number of moles of gas on the reactant side: $2A+1B=3,\text{moles}$
• The number of moles of gas on the product side: $2C=2,\text{moles}$

Step 2: Solution:

According to Le Chatelier’s Principle:

• An increase in pressure will shift the equilibrium towards the side with fewer moles of gas to reduce the pressure.
• Since there are fewer moles of gas on the product side (2 moles) than on the reactant side (3 moles), the equilibrium will shift to the right, favoring the formation of products.

Step 3: Final Answer:

Increasing the pressure will shift the equilibrium towards the products, increasing the formation of $C$.

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Example 4: Calculating $K_c$ from Concentrations

Question: For the reaction $P+Q\rightleftharpoons R+S$, the equilibrium concentrations are:

• $[P]=0.5,M$
• $[Q]=0.5,M$
• $[R]=2,M$
• $[S]=1,M$

Calculate the equilibrium constant, $K_c$.

Answer:

Step 1: Given Data:

• $[P]=0.5,M$
• $[Q]=0.5,M$
• $[R]=2,M$
• $[S]=1,M$

Step 2: Solution:

The equilibrium constant is given by:

$K_c=\frac{[R][S]}{[P][Q]}$

Substitute the values into the equation:

$K_c=\frac{(2)(1)}{(0.5)(0.5)}$

Step 3: Final Answer:

$K_c=\frac{2}{0.25}=8$

Thus, the equilibrium constant is $K_c=8$.

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Example 5: Effect of Adding a Reactant

Question: In the reaction $A+B\rightleftharpoons C+D$, what happens to the equilibrium if more of reactant $A$ is added?

Answer:

Step 1: Given Data:

• Reactant $A$ is increased.

Step 2: Solution:

According to Le Chatelier’s Principle:

• Adding more $A$ will cause the system to shift towards the right (towards the products) to counteract the increase in $A$ concentration.

Step 3: Final Answer:

The equilibrium will shift to the right, increasing the formation of $C$ and $D$.

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Example 6: Using $K_c$ to Predict the Direction of Reaction

Question: Given $K_c=10$ for the reaction $A+B\rightleftharpoons C+D$. If the initial concentrations are:

• $[A]=0.1,M$
• $[B]=0.1,M$
• $[C]=1,M$
• $[D]=1,M$

Predict the direction in which the reaction will proceed to reach equilibrium.

Answer:

Step 1: Given Data:

• $K_c=10$
• $[A]=0.1,M$
• $[B]=0.1,M$
• $[C]=1,M$
• $[D]=1,M$

Step 2: Solution:

First, calculate the reaction quotient ($Q_c$):

$Q_c=\frac{[C][D]}{[A][B]}$

Substitute the initial concentrations:

$Q_c=\frac{(1)(1)}{(0.1)(0.1)}$

$Q_c=\frac{1}{0.01}=100$

Since $Q_c>K_c$, the reaction will proceed to the left (towards the reactants) to reach equilibrium.

Step 3: Final Answer:

The reaction will shift towards the reactants to reach equilibrium.

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Conclusion:

Le Chatelier’s Principle is a powerful tool in predicting the behavior of chemical systems at equilibrium. It can be used to predict the effects of changes in concentration, temperature, and pressure on a system. The equilibrium constant ($K_c$) helps quantify the relative amounts of products and reactants at equilibrium, allowing chemists to understand and control reactions more effectively.