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pH Calculations

By Luis Martinez and Malik Harris

pH Calculations are when water undergoes different types of reaction to produce hydronium and hydroxide ions.  When doing these types of calculations you will be using logs to solve and get the answer to the equations. Their are different ways to solve the equation and I will show all four equations to solve but you still need to use two to get the answer.

Standard equation is pH = - log [H3O+].

pH of Aqueous solutions

• pH solutions range from from 0-14.
• 7 is the neutral
• 0-7 is acidic
• 7-14 is basic

Some Examples and problems for pH Calculations

Example 1

Find the pH of a 0.0025 M HCl solution. The HCl is a strong acid and is 100% ionized in water. The hydronium ion concentration is 0.0025 M.

• So first you set the equation to pH=-log[H30+]
• Then you plug in the numbers and solve.

pH = - log (0.0025) = - ( - 2.60) = 2.60

Example 2 What is the [OH–] of an aqueous solution with a pH of 2.35?

First way to solve the equation

[H3O+] = 10–pH

[H3O+] = 10–2.35

[H3O+] = 0.00447 M

Kw = 10–14 M2 = [H3O+][OH–]

10–14 M2 = [0.00447 M][OH–]

2.24 ´ 10–12 M = [OH–]

OR

pH + pOH = 14

2.35 + pOH = 14

pOH = 11.65

[OH–] = 10–pOH

[OH–] = 10–11.65

[OH–] = 2.24 ´ 10–12 M

Short quiz

1.Find the pH of a 10–4 M NaOH solution.

• Again, recall that strong bases like NaOH ionize completely into OH–, so you can assume that the [NaOH] = [OH–]. However, to use this particular pH calculation equation, you need to know the [H3O+]. So, we’ll need to use the Kw formula first:

Kw = 10–14 M2 = [H3O+][OH–] pH = –log [H3O+]

10–14 M2 = [H3O+][10–4 M] pH = –log [10–10]

10–10 M = [H3O+] pH = 10

2. What is the pH of a 0.00450 M KOH solution?

Kw = 10–14 M2 = [H3O+][OH–] pH = –log [H3O+]

• 10–14 M2 = [H3O+][0.00450 M] pH = –log [2.22 ´ 10–12]
• 2.22 ´ 10–12 M = [H3O+] pH = 11.7

3. What is the pOH of a 10–5 M LiOH solution?

• i. pOH = –log [OH–]
• ii. pOH = –log [10–5]
• iii. pOH = 5

4. What is the pOH of a solution whose pH is 9.45?

• pH + pOH = 14
• 9.45 + pOH = 14
• i. pOH = 4.55

5. What is the pH of a solution whose pOH is 11?