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>>
View the other Key Equations and Concepts in this
chapter
Autoionization of Water
>> Parts of this equation/concept include:
Because of the autoionization of water, the concentration of H3O+
and the concentration of OH– are inversely related
in any aqueous solution. Either of the following equations can be
used.
Kw = 1.0 x 10–14 = [H3O+][OH–] at
25 °C (Example
16.11)
pKw = 14.00 = pH + pOH (Example
16.14)
>> Example 1
What is the hydroxide ion concentration if [H+] =
3.8 x 10–4 M?
Solution:
Kw = 1.0 x 10–14 = [H3O+][OH–]
1.0 x 10–14 = [3.8 x 10–4][OH–]
2.6 x 10–11 M = [OH–]
>> Example 2
What is the H3O+ concentration if [OH–]
= 0.011 M?
Solution:
Kw = 1.0 x 10–14 = [H3O+][OH–]
1.0 x 10–14 = [H3O+][0.011]
9.1 x 10–13 M = [H3O+]
>> Example 3
At 0 °C, Kw = 1.14 x 10–15,
what is the [H3O+] in pure water?
Solution:
The equation is the same, but the constant (Kw)
is different.
Kw = 1.14 x 10–15 = [H3O+][OH–]
Because water is the only source of H3O+
and OH–, [H3O+] = [OH–].
Therefore
1.14 x 10–15 = [H3O+][OH–]
= x2
3.38 x 10–8 M = x = [H3O+]
The equation for pH is
pH = –log[H3O+] (Example
16.12)
The keys to working with this equation correctly are using your
calculator correctly and using the significant–figure rule
for logarithms. (Just as the rules for addition and multiplication
are different, so is the one for logarithms.)
>> Significant Figures for Logs
The number of significant figures in the regular number ([H3O+]
in this case) becomes the number of decimal places in the log term
(pH). For the log term, all digits to the right of the decimal are
counted, regardless of whether or not the digit is zero. None of
the digits to the left of the decimal count as significant figures.
>> Determining pH from [H3O+]
For most nonprogrammable scientific calculators, enter the concentration
using the appropriate scientific notation key (see Chapter 1). Enter
the "log" key, then the +/– key. To check your answer, compare
the exponent from the concentration term to the number to the left
of the decimal of the pH term. These two values should be opposite
in sign, but have a value that differs by no more than one.
>> Example 4
What is the pH of solutions with the following concentrations of H3O+?
- 0.023 M
- 5.74 x 10–6 M
Solution:
- 1.63 = pH. The concentration has two significant figures,
so the answer is reported to two decimal places.
- 5.241 = pH. The concentration has three significant figures,
so the answer is reported to three decimal places.
>> Determining [H3O+] from pH
For most nonprogrammable scientific calculators, enter the pH value.
Change the sign by pressing the +/– key. Then use the 10x
key (usually "shift log") to convert to concentration.
>> Example 5
What is the H3O+ for the following pH values?
- 8.1
- 9.13
Solution:
- 8 x 10–9 = [H3O+]. Since
there is one digit to the right of the decimal, the concentration
has one significant figure.
- 7.4 x 10–10 = [H3O+].
Since there are two digits to the right of the decimal, the
concentration value has two significant figures. Also note that
the power on the 10 (–10) is within one of the number to
the left of the decimal.
>> back
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pOH is determined in the same manner as pH, with the concentration
of OH– instead of H3O+.
>> Example 6
What is the pOH of a solution with [OH–] = 5.7
x 10–10 M?
Solution:
The pOH has two decimal places to match the significant figures
in the concentration
pOH = 9.24
>> Example 7
What is the hydroxide ion concentration in a solution with pOH
= 4.7?
Solution:
The concentration has one significant figure. [OH–]
= 2 x 10–5 M.
Because of the autoionization of water, hydroxide ion concentration
can be expressed as pH.
>> Example 8
What is the hydroxide ion concentration in a solution with pH
= 5.82?
Solution:
Using Equation 16.14, if pH = 5.82, then pOH = 14.00 – 5.82
= 8.18. Using the antilog (10x) of pOH, the
concentration is determined 6.6 x 10–9 M
= [OH–]
>> Example 9
What is the pH if the hydroxide ion concentration is 2.4 x 10–4
M?
Solution:
If the [OH–] = 2.4 x 10–4 M,
pOH = 3.62. Since pH + pOH = 14.00, so 14.00 – 3.62 = 10.38
>> View
the other Key Equations and Concepts in this chapter
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