Question

What is the pH of a 0.061 M solution of C6H5COOH

Answer 1

The pH of the solution is 1.72.

The Benzoic acid (C6H5COOH) is a weak acid, so it partially dissociates in water, and we must keep this in mind in order to solve it.

The weak acids have a very small number of Ka (acid dissociation constant). The Ka for benzoic acid is 6.3 x 10^-5.

- First, we need to write the dissociation equation of benzoic acid in water with the concentration of each specie at the beginning of the reaction, during the reaction and in the equilibrium stage:

`\begin{gathered} C_6H_5COOH+H_2O\text{ }\rightleftarrows\text{ }C_6H_5COO^-+H_3O^+ \\ \end{gathered}`

Beginning: 0.061 excess 0 0

Reaction: -x x x

Equilibrium: 0.061-x x x

In the equation H3O+ is the same as H+, so both represents the proton.

The "x" represents the amount of each compounds that it is obtained from the reaction, and it represents, at the same time, the amount of benzoic acid that is consumed in the reaction.

- Second, we write the Ka equation for this acid and replace each value:

`\begin{gathered} Ka=(\lbrack C_6H_5COO^-\rbrack.\lbrack H_3O^+\rbrack)/(\lbrack C_6H_5COOH\rbrack) \\ 6.3x10^(-5)=(x.x)/(0.061-x) \\ 6.3x10^(-5)=(x^2)/(0.061-x) \\ 6.3x10^(-5)\text{ . }(0.061-x)=x^2 \\ 3.8x10^(-6)-\text{ }6.3x10^(-5)x-x^2=0 \end{gathered}`

Here, we we need to solve by using the Bhaskara equation, then we find that the x value is 0.019.

- Finally, we replace the x value and the concentration of protons is 0.019 M.

- As the pH formula is:

`pH=\text{ -log}\lbrack H_3O^+\rbrack`

Then,

`pH=-\log \lbrack0.019\rbrack`

And the pH of the solution is 1.72.