Calculate the amount of isopentyl acetate that should be present in the reaction mixture at equilibrium based on 300 mmol of acetic acid and 150 mmol of isopentyl alcohol as starting quantities. Use equilibrium constant of 4.2 for this calculation.

Question

Calculate the amount of isopentyl acetate that should be present in the reaction mixture at equilibrium based on 300 mmol of acetic acid and 150 mmol of isopentyl alcohol as starting quantities. Use equilibrium constant of 4.2 for this calculation.

Answer 1

To calculate the amount of isopentyl acetate at equilibrium, we need to use the equilibrium constant (K) and the initial amounts of the reactants.

The balanced chemical equation for the reaction is:
Acetic acid + Isopentyl alcohol ↔ Isopentyl acetate + Water

Given:
Initial moles of acetic acid (CH3COOH): 300 mmol
Initial moles of isopentyl alcohol (C5H11OH): 150 mmol
Equilibrium constant (K): 4.2

Since we know the initial quantities, we can start by determining the change in moles of each component at equilibrium.

Let's assume that at equilibrium, x moles of isopentyl acetate are formed. We can use the stoichiometry of the reaction to determine the changes in moles.

From the balanced equation, we can see that for every mole of acetic acid (CH3COOH) and isopentyl alcohol (C5H11OH) that react, one mole of isopentyl acetate (C7H14O2) is formed.

Therefore, the change in moles of isopentyl acetate is also x.

The moles of acetic acid (CH3COOH) at equilibrium will be:
300 mmol - x

The moles of isopentyl alcohol (C5H11OH) at equilibrium will be:
150 mmol - x

Now, we can calculate the equilibrium concentration of isopentyl acetate (C7H14O2) using the equation for the equilibrium constant:
K = [C7H14O2] / ([CH3COOH] * [C5H11OH])

Plugging in the values:
4.2 = x / ((300 - x) * (150 - x))

Now, we can solve this equation to find the value of x, which represents the moles of isopentyl acetate at equilibrium.

Simplifying the equation, we get:
4.2(300 - x)(150 - x) = x

Expanding and rearranging:
1260 - 630x - 210x + 105x^2 = x
105x^2 - 840x + 1260 = x
105x^2 - 841x + 1260 = 0

Now we solve this quadratic equation to find the value of x.

Using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a

In this case, a = 105, b = -841, and c = 1260.

Calculating x using the quadratic formula gives two solutions, but we discard the negative value since the quantity of a compound cannot be negative:

x ≈ 7.62

Therefore, the amount of isopentyl acetate at equilibrium would be approximately 7.62 mmol.