3. 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.
Well, let's do some math... that's always fun! So, we have 300 mmol of acetic acid and 150 mmol of isopentyl alcohol as starting quantities. Now, according to the equilibrium constant of 4.2, we can set up an equation as follows:
4.2 = [isopentyl acetate] / [acetic acid] * [isopentyl alcohol]
Now, since we're using moles, we can say that the moles of isopentyl acetate formed is equal to the moles of acetic acid consumed. So, let's replace [acetic acid] with 300 - [isopentyl acetate] (since it's being consumed) and [isopentyl alcohol] with 150 - [isopentyl acetate].
Putting it all together, we have:
4.2 = ([isopentyl acetate] / (300 - [isopentyl acetate])) * (150 - [isopentyl acetate])
Now, if you're still with me, let's solve this equation and find the amount of isopentyl acetate produced at equilibrium. But hey, don't feel pressured... it's not like we're in a race or anything! Take your time.
To calculate the amount of isopentyl acetate at equilibrium, we need to use the equilibrium constant (Kc) and the initial amounts of the reactants. The equilibrium constant expresses the ratio of the concentrations of the products to the concentrations of the reactants at equilibrium.
The balanced equation for the reaction is:
acetic acid + isopentyl alcohol ⇌ isopentyl acetate + water
Based on the equation, we can see that the stoichiometry is 1:1 between acetic acid and isopentyl acetate. Therefore, if x represents the moles of isopentyl acetate formed, it will also represent the moles of acetic acid consumed at equilibrium.
Using the given information:
Initial moles of acetic acid = 300 mmol
Initial moles of isopentyl alcohol = 150 mmol
Since there is a 1:1 stoichiometry between acetic acid and isopentyl acetate, the initial moles of acetic acid will also be the moles of isopentyl acetate formed.
At equilibrium, the moles of isopentyl acetate formed will be (300 - x). The moles of acetic acid consumed will also be (300 - x).
The equilibrium constant (Kc) is given as 4.2.
The equilibrium expression is:
Kc = [isopentyl acetate] / [acetic acid]
Substituting the values into the equation:
4.2 = (300 - x) / (300 - x)
Now, we can solve for x using algebra:
4.2(300 - x) = 300 - x
1260 - 4.2x = 300 - x
3.2x = 960
x = 300
Therefore, at equilibrium, the amount of isopentyl acetate present in the reaction mixture is 300 mmol.