Here’s another example calculation question involving these quantities [H 3 O + ], [OH – ], pH, and pOH Calculations Example 2

Remember, the square can be used as a guide to help you come up with a plan to solve problems involving these quantities [H 3 O + ] [OH – ] pH pOH pH = –log[H 3 O + ] [OH – ] = 10 –pOH pOH = –log[OH – ] [H 3 O + ] = 10 –pH [H 3 O + ][OH–] = 1.00 × 10 –14 pH + pOH = 14.00

Here’s a simpler version we can use. [H 3 O + ] [OH – ] pH pOH

We’re given that the pOH of a solution of HCl is and we’re asked to find the concentration of HCl. [H 3 O + ] [OH – ] pH pOH The pOH of a solution of HCl is Find the [HCl].

We can identify HCl as a strong acid, so the concentration of HCl is the same as the concentration of hydronium [H 3 O + ] [OH – ] pH pOH The pOH of a solution of HCl is Find the [HCl]. Strong Acid [HCl] = [H 3 O + ]

Which we’ll make a note of here. [H 3 O + ] [OH – ] pH pOH The pOH of a solution of HCl is Find the [HCl]. ( [HCl] = [H 3 O + ] )

So in this problem, we’re given the pOH and we need to find the hydronium concentration. [H 3 O + ] [OH – ] pH pOH The pOH of a solution of HCl is Find the [HCl]. ([HCl] = [H 3 O + ]) Given ?

The easiest plan here is to start by (click) converting pOH to pH. [H 3 O + ] [OH – ] pH pOH The pOH of a solution of HCl is Find the [HCl]. ([HCl] = [H 3 O + ]) Given ?

And then (click) converting pH to hydronium concentration. [H 3 O + ] [OH – ] pH pOH The pOH of a solution of HCl is Find the [HCl]. ([HCl] = [H 3 O + ]) Given ?

So the plan we can use is pOH to pH to hydronium concentration [H 3 O + ] [OH – ] pH pOH The pOH of a solution of HCl is Find the [HCl]. ([HCl] = [H 3 O + ]) Given ? pOH  pH  [H 3 O + ] Plan

Here’s the problem again, along with the plan we came up with [H 3 O + ] [OH – ] pH pOH The pOH of a solution of HCl is Find the [HCl]. ([HCl] = [H 3 O + ]) pOH  pH  [H 3 O + ] Plan Problem

We’re given the pOH, so the first step (click) is to convert pOH to pH [H 3 O + ] [OH – ] pH pOH The pOH of a solution of HCl is Find the [HCl]. ([HCl] = [H 3 O + ]) pOH  pH  [H 3 O + ]

We use the formula pH is equal to 14 minus the pOH [H 3 O + ] [OH – ] pH pOH The pOH of a solution of HCl is Find the [HCl]. ([HCl] = [H 3 O + ]) pOH  pH  [H 3 O + ]

Which is 14 minus [H 3 O + ] [OH – ] pH pOH The pOH of a solution of HCl is Find the [HCl]. ([HCl] = [H 3 O + ]) pOH  pH  [H 3 O + ]

Which comes out to a pH of [H 3 O + ] [OH – ] pH pOH The pOH of a solution of HCl is Find the [HCl]. ([HCl] = [H 3 O + ]) pOH  pH  [H 3 O + ] pH

The second step is to convert (click) pH to hydrochloric acid or hydronium concentration [H 3 O + ] [OH – ] pH pOH The pOH of a solution of HCl is Find the [HCl]. ([HCl] = [H 3 O + ]) pOH  pH  [H 3 O + ]

Because HCl is a strong acid, the concentration of HCl is the same as the hydronium concentration. [H 3 O + ] [OH – ] pH pOH The pOH of a solution of HCl is Find the [HCl]. ([HCl] = [H 3 O + ]) pOH  pH  [H 3 O + ]

We know the pH, so the formula we use to find hydronium concentration is the concentration of H3O+ is 10 to the negative pH. [H 3 O + ] [OH – ] pH pOH The pOH of a solution of HCl is Find the [HCl]. ([HCl] = [H 3 O + ]) pOH  pH  [H 3 O + ]

Which is 10 to the negative [H 3 O + ] [OH – ] pH pOH The pOH of a solution of HCl is Find the [HCl]. ([HCl] = [H 3 O + ]) pOH  pH  [H 3 O + ]

Which comes out to M. This has 3 significant figures because the given pOH was expressed to three decimal places. [H 3 O + ] [OH – ] pH pOH The pOH of a solution of HCl is Find the [HCl]. ([HCl] = [H 3 O + ]) pOH  pH  [H 3 O + ]

So the final answer is the concentration of HCl is equal to M [H 3 O + ] [OH – ] pH pOH The pOH of a solution of HCl is Find the [HCl]. ([HCl] = [H 3 O + ]) pOH  pH  [H 3 O + ]

Or, in Scientific notation, 6.59 × 10 –3 M [H 3 O + ] [OH – ] pH pOH The pOH of a solution of HCl is Find the [HCl]. ([HCl] = [H 3 O + ]) pOH  pH  [H 3 O + ]