Chemical Equilibrium - SS3 Chemistry Past Questions and Answers - page 2

The equilibrium constant (Kc) for the reaction is given by the following expression:

Kc = ([C]eq)⁴ / ([A]eq)² X ([B]eq)³

Given [A]eq = 0.25 M, [B]eq = 0.10 M, and [C]eq = 0.30 M, we can substitute these values into the equation to calculate Kc:

Kc = (0.30)⁴ / (0.25)² X (0.10)³

Kc = 0.0081 / 0.00625 X 0.001

Kc = 0.0081 / 0.00000625

Kc ≈ 1296

Therefore, the equilibrium constant (Kc) for the reaction at this temperature is approximately 1296.

Let's denote the initial concentrations of N2 and H2 as [N2]0 and [H2]0, respectively, and the change in concentration of NH3 as x (since 2 moles of NH3 are formed for every mole of N2 reacted).

Initial concentrations:

[N2]0 = 0.20 moles / 2.0 litres = 0.10 M

[H2]0 = 0.40 moles / 2.0 litres = 0.20 M

[NH3]0 = 0 M (since no NH3 is present initially)

At equilibrium, the concentrations will be:

[N2]eq = [N2]0 - x

[H2]eq = [H2]0 - 3x

[NH3]eq = [NH3]0 + 2x

The equilibrium constant expression for the reaction is:

Kc = [NH3]eq² / ([N2]eq X [H2]eq³)

Substitute the given values into the equilibrium constant expression:

0.050 = (0 + 2x)² / ((0.10 - x) X (0.20 - 3x)³)

Expand and rearrange the equation to solve for x:

0.050 = (4x²) / ((0.10 - x) X (0.20 - 3x)³)

Now, solve for x:

0.050 = 4x² / (0.10 - x) X (0.008 - 0.144x + 0.648x²)

Multiply both sides by (0.10 - x) X (0.008 - 0.144x + 0.648x²):

0.050 X (0.10 - x) X (0.008 - 0.144x + 0.648x²) = 4x²

Distribute and rearrange:

0.0048 - 0.072x + 0.324x² = 4x²

Bring all terms to one side and simplify:

0.324x² - 4x² + 0.072x - 0.0048 = 0

Combine like terms:

3.676x² + 0.072x - 0.0048 = 0

Use the quadratic formula to find the values of x:

x = [-0.072 ± √(0.072² - 4 X 3.676 X (-0.0048))] / 2 X 3.676

x ≈ [-0.072 ± √(0.005184 + 0.070656)] / 7.352

x ≈ [-0.072 ± √0.07584] / 7.352

x ≈ [-0.072 ± 0.2754] / 7.352

x ≈ 0.203 or x ≈ -0.032

Since concentrations cannot be negative, we discard the negative value for x.

Now, calculate the equilibrium concentrations:

[N2]eq = [N2]0 - x ≈ 0.10 - 0.203 ≈ -0.103 M (discard negative value)

[H2]eq = [H2]0 - 3x ≈ 0.20 - 3 X 0.203 ≈ -0.009 M (discard negative value)

[NH3]eq = [NH3]0 + 2x ≈ 0 + 2 X 0.203 ≈ 0.406 M

Since concentrations cannot be negative, we consider the equilibrium concentration of N2 to be 0 M, the equilibrium concentration of H2 to be 0 M, and the equilibrium concentration of NH3 to be 0.406 M.

Therefore, at equilibrium, [N2]eq ≈ 0 M, [H2]eq ≈ 0 M, and [NH3]eq ≈ 0.406 M.

According to Le Chatelier's Principle, if the concentration of reactants in a chemical equilibrium is increased, the system will shift in the direction that reduces the concentration of reactants. This means the reaction will shift toward the reactants to consume the additional reactants and establish a new equilibrium position.

An endothermic reaction absorbs heat from the surroundings. According to Le Chatelier's Principle, if the temperature of the system is increased, the system will shift in the direction that absorbs heat to counteract the temperature increase. Therefore, the reaction will shift to favour the endothermic direction, which absorbs more heat to restore equilibrium.

When the pressure of a system at equilibrium is increased by decreasing the volume, Le Chatelier's Principle predicts that the system will shift in the direction that reduces the pressure. This means the reaction will shift to the side with fewer moles of gas since it occupies less volume, thereby reducing the pressure and restoring equilibrium.

A catalyst is a substance that increases the rate of both the forward and reverse reactions in a chemical equilibrium. However, it does not affect the position of the equilibrium. The catalyst provides an alternative reaction pathway with lower activation energy, allowing the reaction to reach equilibrium faster, but the equilibrium concentrations of reactants and products remain unchanged.

Le Chatelier's Principle states that when a system at equilibrium is subjected to a change in conditions, it will respond in a way that counteracts the change and re-establishes a new equilibrium. This principle applies to chemical equilibrium, where reversible reactions reach a point where the rates of the forward and reverse reactions are equal, and the concentrations of reactants and products remain constant over time.

1.    Effect of Changes in Concentration:

●     If the concentration of a reactant is increased, the system will shift to consume some of the additional reactants by favouring the forward reaction until a new equilibrium is reached. This shift increases the concentration of products.

●     If the concentration of a product is increased, the system will shift to consume some of the additional product by favouring the reverse reaction until a new equilibrium is established. This shift increases the concentration of reactants.

Example: Consider the reaction N2(g) + 3H2(g) ⇌ 2NH3(g). If more N2 is added, the system will shift to the right to produce more NH3 and consume the extra N2.

2.    Effect of Changes in Pressure (for Gaseous Reactions):

●     An increase in pressure will shift the equilibrium position towards the side with fewer moles of gas to reduce the pressure.

●     A decrease in pressure will shift the equilibrium towards the side with more moles of gas to increase the pressure.

Example: For the reaction N2(g) + 3H2(g) ⇌ 2NH3(g), increasing the pressure will shift the equilibrium to the right (towards NH3) since there are fewer moles of gas on the product side.

3.    Effect of Changes in Temperature:

●     If a reaction is exothermic (releases heat), an increase in temperature will shift the equilibrium position to the left, favouring the endothermic direction to absorb the extra heat.

●     If a reaction is endothermic (absorbs heat), an increase in temperature will shift the equilibrium to the right, favouring the exothermic direction to produce more heat.

Example: For the reaction N2(g) + O2(g) ⇌ 2NO(g) + heat, increasing the temperature will shift the equilibrium to the right, favouring the endothermic direction to absorb the additional heat.

Le Chatelier's Principle is a fundamental concept in understanding the behaviour of chemical equilibria and provides insights into how systems respond to external changes. It has practical applications in industries where reversible reactions are essential, such as the Haber-Bosch process for ammonia production, where optimising reaction conditions based on Le Chatelier's Principle increases efficiency and yield.