during the preparation of synthetic banana oil lab. 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. Moles can be used in place of concentration as volumes cancel out.
To calculate the amount of isopentyl acetate at equilibrium, we need to use the given equilibrium constant and the initial amounts of acetic acid and isopentyl alcohol.
The balanced chemical equation for the formation of isopentyl acetate (also known as banana oil) is:
acetic acid + isopentyl alcohol -> isopentyl acetate + water
According to the equation, the mole ratio between acetic acid, isopentyl alcohol, isopentyl acetate, and water is 1:1:1:1.
Given:
Initial amount of acetic acid = 300 mmol
Initial amount of isopentyl alcohol = 150 mmol
Equilibrium constant (Kc) = 4.2
At equilibrium, let's assume the amount of isopentyl acetate formed is x.
Using the mole ratio, the change in the amount of acetic acid, isopentyl alcohol, and water will also be x.
Therefore, the equilibrium amount of acetic acid and isopentyl alcohol will be:
Acetic acid = Initial amount - Change
= 300 mmol - x
Isopentyl alcohol = Initial amount - Change
= 150 mmol - x
And the equilibrium amount of isopentyl acetate and water will be:
Isopentyl acetate = Change = x
Water = Change = x
Since the equilibrium constant expression is given by:
Kc = [Isopentyl acetate] / ([Acetic acid] * [Isopentyl alcohol])
Plugging in the values, we get:
4.2 = x / ([300 - x] * [150 - x])
Now we can solve this equation to find the value of x, which represents the amount of isopentyl acetate at equilibrium.