91Ó°ÊÓ

The reaction quotient, often denoted as \( Q \), is a critical concept in understanding chemical equilibrium. It provides a snapshot of the relative amounts of products and reactants present at any given moment during a reaction. Essentially, \( Q \) is calculated using the same method as the equilibrium constant \( K \), but for a system that is not necessarily at equilibrium.

For our problem, we calculated \( Q \) using the initial concentrations of butane and isobutane:

• \( [\text{butane}]_0 = \frac{1.75}{V} \)
• \( [\text{isobutane}]_0 = \frac{1.25}{V} \)

This leads to:
\( Q = \frac{[\text{isobutane}]_0}{[\text{butane}]_0} = \frac{1.25}{1.75} \approx 0.714 \)

Since \( Q = 0.714 \) is less than the given equilibrium constant \( K = 2.5 \), the reaction is not at equilibrium, and it will proceed in the forward direction, leading to an increase in the concentration of isobutane while decreasing the concentration of butane.

The equilibrium constant \( K \) is a crucial value that indicates the ratio of concentrations of products to reactants when a chemical reaction is at equilibrium. Specifically, it is a measure of the extent to which reactants convert to products at the condition of equilibrium.In our example, the equilibrium constant for the isomerization of butane to isobutane is \( K = 2.5 \). This numerical value implies that when the system reaches equilibrium at a given temperature, the concentration ratio of isobutane to butane will be 2.5.

To determine whether a system is at equilibrium, we compare \( Q \) with \( K \):

• If \( Q = K \), the reaction is at equilibrium.
• If \( Q < K \), it moves forward, forming more products.
• If \( Q > K \), it shifts backward, forming more reactants.

In this exercise, an initial \( Q \) of 0.714 indicated that the system was not at equilibrium. Therefore, it proceeded toward an equilibrium state by converting more butane into isobutane to reach the \( K \) value of 2.5.

The concentrations of reactants and products play a fundamental role in determining the position of chemical equilibrium. They help establish whether the reaction will proceed in the forward or backward direction.In the initial scenario, we determined the concentrations of butane and isobutane based on their moles:

• \( [\text{butane}]_0 = \frac{1.75}{V} \)
• \( [\text{isobutane}]_0 = \frac{1.25}{V} \)

Based on these, we calculated the reaction quotient \( Q \) and discovered its disparity with \( K \). This showed the system would shift to reduce \( [\text{butane}] \) and increase \( [\text{isobutane}] \) until equilibrium is reached.

Through the change \( x \), the equilibrium concentrations were found to be:

• \( [\text{butane}] = \frac{1.75 - 0.893}{V} \approx \frac{0.857}{V} \)
• \( [\text{isobutane}] = \frac{1.25 + 0.893}{V} \approx \frac{2.143}{V} \)

These concentrations align with the equilibrium constant equation \( K = \frac{[\text{isobutane}]}{[\text{butane}]} = 2.5 \), affirming the solution's correctness upon reaching equilibrium.