Question

A student prepares a aqueous solution of acetic acid . Calculate the fraction of acetic acid that is in the dissociated form in his solution. Express your answer as a percentage. You will probably find some useful data in the ALEKS Data resource.

Answer 1

10.71%

Step-by-step explanation:

The dissociation of acetic acid can be well expressed as follow:

CH₃COOH ⇄ CH₃COO⁻ + H⁺

Let assume that the prepared amount of the aqueous solution is 14mM since it is not given:

Then:

The I.C.E Table is expressed as follows:

CH₃COOH ⇄ CH₃COO⁻ + H⁺

Initial 0.0014 0 0

Change - x +x +x

Equilibrium (0.0014 - x) x x

Recall that:

Ka for acetic acid CH₃COOH = 1.8×10⁻⁵

∴

`K_a = ([x][x]])/([0.0014-x])`

`1.8*10^(-5) = ([x][x]])/([0.0014-x])`

`1.8*10^(-5) = ([x]^2)/([0.0014-x])`

`1.8*10^(-5)(0.0014-x) = x^2`

`2.52*10^(-8) -1.8*10^(-5)x = x^2`

`2.52*10^(-8) -1.8*10^(-5)x - x^2 =0`

By rearrangement:

`- x^2 -1.8*10^(-5)x +2.52*10^(-8)= 0`

Multiplying through by (-) and solving the quadratic equation:

`x^2 +1.8*10^(-5)x-2.52*10^(-8)= 0`

`(-0.00015 + x) (0.000168 + x) =0`

x = 0.00015 or x = -0.000168

We will only consider the positive value;

so x=[CH₃COO⁻] = [H⁺] = 0.00015

CH₃COOH = (0.0014 - 0.00015) = 0.00125

However, the percentage fraction of the dissociated acetic acid is:

`= ( 0.00015)/(0.0014)* 100`

= 10.71%