Acid-Base Calculations
The Ion-Product Constant for Water, Kw
Water undergoes ionization to a small extent:
H20(l) ↔ H+(aq) + OH–(aq)
The equilibrium constant for the reaction is the ion-product constant for water Kw:
K w  [H  ][OH ] 1.0 1014
(1)
This is a key equation in acid-base chemistry. Note that the product of [H+] and [OH–] is a constant at a
given temperature (Eq(1) value is for 25oC). Thus as the hydrogen ion concentration of a solution increases,
the hydroxide ion concentration decreases (and vice versa).
The pH scale is widely used to report the molar concentration of hydrogen ion H+(aq) in aqueous solution.
The pH of a solution is defined as
pH   log 10[H  ]
(2)
pOH   log10 [OH ]
pK w   log10 (K w )  14.00
(3)
(4)
Similarly, pOH and pKw are defined as
If you take the log10 of both sides of Eq(1), multiply the resulting equation by (-1), and use the definitions of
pH, pOH and pKw above, the result is the very useful equation
pH + pOH = pKw = 14.00
(5)
Equations (2) and (3) above may be solved for [H+] and [OH–] respectively to give
[H ] 10pH
[OH ] 10 pOH
(6)
(7)
x
(Here we use the well known rule that if log 10 y  x , then y 10 .) In practice, the pH scale is only used
when [H+(aq)] is less than 1.0 M.
Acidic, basic, and neutral solutions can be distinguished as shown below:
Type of Solution
Acidic
Neutral
Basic
pH
< 7.00
= 7.00
> 7.00
[H+]
7
> 1.0  10
= 1.0  10 7
< 1.0  10 7
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Color of litmus
pink
in between
blue
Example. You have a 1.5 M solution of HCl. Calculate the pH. Calculate the pOH and [OH-].
pH and [H+] Calculations for Strong Acids and Bases
By definition, strong acids and bases are 100% ionized in water solution. Ionization of a strong acid gives
rise to H+ ions, and ionization of a strong base produces OH– ions. The equilibrium constant for a strong acid or
strong base is undefined, since the reaction the ionization is complete. There is no equilibrium!
In nearly all cases of practical interest the [H+] for a strong acid (or the [OH–] for a strong base) is
determined completely by the stoichiometry of the reaction. Once the [OH–] or pOH is known for a base,
the [H+] or the pH of the base may be calculated using Eq(1) and/or Eq(5).
Exercises
1. Complete the following table:
pH
+
[H ]
pOH
7.8 x 10-10
(b)
(d)
[OH ]
5.4 x 10–4
(a)
(c)
–
10.75
5.00
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Acidic,
basic, or
neutral?
2. Calculate the pH of a 0.0430 M HNO3 solution. pOH. [OH-]
3. Calculate the pH of a 0.020 M Ba(OH)2(aq) solution. pOH. [OH-]
1. What is the hydrogen ion concentration of an aqueous HCl solution that has a pH of 3.0?
2. What is the pH of a 2.5 x 10-6 M solution of HCl?
3. Determine the pH of a 0.010 M HNO3 solution.
4. Calculate the pH of a 0.0010 M NaOH solution.
5. What is the pH of a 0.020M Sr(OH)2 solution?
6. What is the pH of a 0.0235 M HCl solution? pOH?
7. What is the pH of a 6.50 x 10-3 M KOH solution?
8. What is [H+] for a solution with a pH of 10.2? the pOH?
9. What is the pH of a 6.2 x 10-5 M NaOH solution?
10. 48.5 g of NaOH is dissolved to make a 0.500 L solution. What is the pH of the solution?
11. 35 mL of 0.75 M HCl is diluted to 2.00 L. What is the pH?
12. Find the [H+] and the [OH-] of a solution with a pH of 3.494.
13. What is the pH of 0.040 M HCl?
14. If the [OH-] = 4.0 x 10-9 M, what is the pH?
15. An aqueous solution of Na2CO3 has a pOH = 2.35. What are the pH and [H+]?
16. What is the pH if [H+] = 4.0 x 10-8M? What is the [OH-]?
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