Here’s another example calculation question involving these quantities

[H3O+], [OH–], pH, and pOH CalculationsExample 2

Remember, the square can be used as a guide to help you come up with a plan to solve problems involving these quantities

[H3O+

][OH–

]

pH pOH

pH =–log[H3O+]

[OH–] =10–pOH

pOH =–

log[OH–][H3O+]

=10–pH

[H3O+][OH–] = 1.00 × 10–14

pH + pOH = 14.00

The Squareat 25°C

Here’s a simpler version we can use.

[H3O+

][OH–

]

pH pOH

We’re given that the pOH of a solution of HCl is 11.819 and we’re asked to find the concentration of HCl.

[H3O+

][OH–]

pH pOH

The pOH of a solution of HCl is 11.819.Find the [HCl].

We can identify HCl as a strong acid, so the concentration of HCl is the same as the concentration of hydronium

[H3O+

][OH–]

pH pOH

The pOH of a solution of HCl is 11.819.Find the [HCl].

Strong Acid[HCl] = [H3O+]

Which we’ll make a note of here.

[H3O+

][OH–]

pH pOH

The pOH of a solution of HCl is 11.819.Find the [HCl]. ([HCl] = [H3O+])

So in this problem, we’re given the pOH and we need to find the hydronium concentration.

[H3O+

][OH–

]

pH pOH

The pOH of a solution of HCl is 11.819.Find the [HCl]. ([HCl] = [H3O+])

Given

?

The easiest plan here is to start by (click) converting pOH to pH.

[H3O+

][OH–

]

pH pOH

The pOH of a solution of HCl is 11.819.Find the [HCl]. ([HCl] = [H3O+])

Given

?

And then (click) converting pH to hydronium concentration.

[H3O+

][OH–

]

pH pOH

The pOH of a solution of HCl is 11.819.Find the [HCl]. ([HCl] = [H3O+])

Given

?

So the plan we can use is pOH to pH to hydronium concentration

[H3O+

][OH–

]

pH pOH

The pOH of a solution of HCl is 11.819.Find the [HCl]. ([HCl] = [H3O+])

Given

?

pOH pH [H3O+]

Plan

Here’s the problem again, along with the plan we came up with

[H3O+

][OH–]

pH pOH

The pOH of a solution of HCl is 11.819.Find the [HCl]. ([HCl] = [H3O+])

pOH pH [H3O+]

PlanPro

blem

We’re given the pOH, so the first step (click) is to convert pOH to pH

[H3O+

][OH–]

pH pOH

The pOH of a solution of HCl is 11.819.Find the [HCl]. ([HCl] = [H3O+])

pOH pH [H3O+]

14.000 pOH 14.000 11.819p 2 1H .18 pH 2.181

3[H [H O ] 10 10 0.00659MCl]

We use the formula pH is equal to 14 minus the pOH

[H3O+

][OH–]

pH pOH

The pOH of a solution of HCl is 11.819.Find the [HCl]. ([HCl] = [H3O+])

pOH pH [H3O+]

14.000pH 14. 11.000 pOH 819 2.181 pH 2.181

3[H [H O ] 10 10 0.00659MCl]

Which is 14 minus 11.819

[H3O+

][OH–]

pH pOH

The pOH of a solution of HCl is 11.819.Find the [HCl]. ([HCl] = [H3O+])

pOH pH [H3O+]

14.000pH 14. 11.000 pO 81H 2.1819 pH 2.181

3[H [H O ] 10 10 0.00659MCl]

Which comes out to a pH of 2.181

[H3O+

][OH–]

pH pOH

The pOH of a solution of HCl is 11.819.Find the [HCl]. ([HCl] = [H3O+])

pOH pH [H3O+]

14.000 pOH 14.000 11.819pH 2.181 pH 2.181

3[H [H O ] 10 10 0.00659MCl] pH

The second step is to convert (click) pH to hydrochloric acid or hydronium concentration

[H3O+

][OH–]

pH pOH

The pOH of a solution of HCl is 11.819.Find the [HCl]. ([HCl] = [H3O+])

pOH pH [H3O+]

pH 14.000 pOH 14.000 11.819 2.181 pH 2.181

3[H [H O ] 10 10 0.00659MCl]

Because HCl is a strong acid, the concentration of HCl is the same as the hydronium concentration.

[H3O+

][OH–]

pH pOH

The pOH of a solution of HCl is 11.819.Find the [HCl]. ([HCl] = [H3O+])

pOH pH [H3O+]

pH 14.000 pOH 14.000 11.819 2.181 pH

32.181[H 10 10Cl] [H 0.00659MO ]

We know the pH, so the formula we use to find hydronium concentration is the concentration of H3O+ is 10 to the negative pH.

[H3O+

][OH–]

pH pOH

The pOH of a solution of HCl is 11.819.Find the [HCl]. ([HCl] = [H3O+])

pOH pH [H3O+]

14.000 pOH 14.000 11.819pH 2.181 pH

32.181[HCl] 10 0.0065[H O 0 M] 91

Which is 10 to the negative2.181.

[H3O+

][OH–]

pH pOH

The pOH of a solution of HCl is 11.819.Find the [HCl]. ([HCl] = [H3O+])

pOH pH [H3O+]

14.000 pOH 14.000 11.819pH 2.181 pH

32.181[ 1HCl] [H O ] 10 0.0 00659M

Which comes out to 0.00659 M. This has 3 significant figures because the given pOH was expressed to three decimal places.

[H3O+

][OH–]

pH pOH

The pOH of a solution of HCl is 11.819.Find the [HCl]. ([HCl] = [H3O+])

pOH pH [H3O+]

pH 14.000 pOH 14.000 11.819 2.181 pH 2.181

3[ [H O ] 10 10HCl] 0.00659M

So the final answer is the concentration of HCl is equal to 0.00659 M

[H3O+

][OH–]

pH pOH

The pOH of a solution of HCl is 11.819.Find the [HCl]. ([HCl] = [H3O+])

pOH pH [H3O+]

3[HCl] 0.00659M 6.59 10 M

Or, in Scientific notation, 6.59 × 10–3 M

[H3O+

][OH–]

pH pOH

The pOH of a solution of HCl is 11.819.Find the [HCl]. ([HCl] = [H3O+])

pOH pH [H3O+]

30.00659[HCl] 6.59 10 MM