pH and Titration: Assignment # 13
Relation between pH and Hydrogen Ion Concentration
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  ]
(1)
where [H+] = the molar concentration of H+(aq) in the solution. (In chemistry, square brackets around a
chemical symbol mean "the molar concentration of" whatever they enclose.) Equation (1) above may be solved
for [H+] to give

[H  ]  10pH
(2)
y
(Here we use the well known rule that if y  log10 x , then x  10 .) In practice, the pH scale is only used
when [H+(aq)] is less than 1.0 M. See Chang, pp. 631-633, for further information.
 can be distinguished as shown below:
Acidic, basic, and neutral solutions
Type of Solution
Acidic
Neutral
Basic
[H+]
> 1.0  10 7
= 1.0  10 7
< 1.0  10 7
pH
< 7.00
= 7.00
> 7.00
Color of litmus
pink
in between
blue
Titration
A titration is a procedure in which a solution of known concentration is used to determine the concentration
of another solution with which it reacts. The reaction must be rapid and should go to completion. It may be an
acid-base reaction, an oxidation-reduction reaction, or a precipitation reaction.
Typically a titration is conducted by filling a buret with one solution and transferring an exact amount of
the second solution to an Erlenmeyer (conical) flask with a pipet. Indicator is added to the flask, and the first
solution is added drop wise from the buret until the indicator changes color. The point of color change is called
the endpoint, the equivalence point, or the stoichiometric point of the titration: all of these terms are
synonymous. The indicator is chosen so the color change occurs when stoichiometric amounts of the reactants
have been added to the flask.
The concentration of the unknown solution is calculated as illustrated in the exercise 3 below.
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Exercises:
1. Use Eq (1) and the log10 button on your calculator to determine the pH of solutions with the specified
hydrogen ion concentrations [H+]:
(a)
(b)
(c)
(d)
(e)
(f)
[H+]
0.10 M
10-7 M
0.0010 M
5.0 x 10-10 M
6.0 M
1.0 M
pH
Acidic,
basic or
neutral?
2. Use Eq (2) and the +/- and 10x buttons on your calculator to determine the [H+] of solutions with the
following pH values:
(a)
(b)
(c)
(d)
(e)
pH
2.00
4.00
0.30
12.80
4.500
+
[H ]
Acidic,
basic or
neutral?
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pH and Titration: Assignment # 13
3. A 25.00 mL sample of a 0.5250 M H2SO4 solution is titrated with a NaOH solution using phenolphthalein as
the indicator. It is found that 22.07 mL of the NaOH solution is needed to reach the endpoint of the titration.
What is the molarity of the NaOH solution?
Notes: A good procedure is to divide the problem into the following steps:
•
Write the balanced overall equation for the reaction.
•
Determine the moles of the known solution available (in this case find the mol H2SO4 available).
•
Use your result from step 2 above and the stoichiometric ratio from the balanced equation to find the moles of the other solution (the
one of unknown concentration) needed for complete reaction (in this case use the mol H2SO4 and your balanced acid-base equation to
find the mol NaOH needed). (Alternatively, steps 2 and 3 can be combined into one step! Do you see how this could be
accomplished?)
•
Obtain the molarity (M) by dividing the moles obtained in step 3 by the volume of the same solution used in the titration, and
converting units to obtain mol/L (here begin by dividing mol NaOH by 22.07 mL).
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