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We can perform calculations involving pH, pOH, and other quantities for pure water when we’re not at 25°C. We’ll do one example here.
Calculations Involving Water at
Temperatures Other Than 25°CExample 1
Before we start the example, it’s very important to remember that when we’re not at 25°C
When we’re NOT at 25°C,
We CANNOT use
When we’re NOT at 25°C,We CANNOT use:
[H3O+][OH–]= 1.00 × 10–14
When we’re NOT at 25°C,We CANNOT use:
[H3O+][OH–]= 1.00 × 10–14
When we’re NOT at 25°C,We CANNOT use:
[H3O+][OH–]= 1.00 × 10–14
And we cannot use pH + pOH = 14.00
When we’re NOT at 25°C,We CANNOT use:
[H3O+][OH–]= 1.00 × 10–14
pH + pOH = 14.00
When we’re NOT at 25°C,We CANNOT use:
[H3O+][OH–]= 1.00 × 10–14
pH + pOH = 14.00
Here’s the example question. We’re given that the value of Kw at 20°C is 6.81 × 10–
15.
The value of Kw at 20°C is 6.81 × 10–15.
a) What is the [H3O+] in water at 20°C?
Question “a” asks us to find the hydronium ion concentration in water at 20°C
The value of Kw at 20°C is 6.81 × 10–15.
b) What is the pH in water at 20°C?
c) What is the [OH–] in water at 20°C?
e) Is water at 20°C acidic, basic, or neutral?
2 153 3
15 83
H O OH H O 6.81 10
H O 6.81 10 8.25 10 M
d) What is the pOH in water at 20°C?
83H O OH 8.25 10 M
a) What is the [H3O+] in water at 20°C?
The Kw, which is hydronium concentration times hydroxide concentration is 6.81 x 10-15
The value of Kw at 20°C is 6.81 × 10–15.
b) What is the pH in water at 20°C?
c) What is the [OH–] in water at 20°C?
e) Is water at 20°C acidic, basic, or neutral?
2 153 3
15 83
H O OH H O 6.81 10
H O 6.81 10 8.25 10 M
d) What is the pOH in water at 20°C?
83H O OH 8.25 10 M
a) What is the [H3O+] in water at 20°C?
Because water is neutral, [OH–]=[H3O+]
The value of Kw at 20°C is 6.81 × 10–15.
b) What is the pH in water at 20°C?
c) What is the [OH–] in water at 20°C?
e) Is water at 20°C acidic, basic, or neutral?
2
3 3
15 83
15H O OH H O
H O
6.
6.81 10 8
81 1
.25
0
10 M
d) What is the pOH in water at 20°C?
83H O OH 8.25 10 M
Because water is neutral
[OH–]=[H3O+]
a) What is the [H3O+] in water at 20°C?
So we can substitute [H3O+] in for [OH–], and get [H3O+]2 = 6.81 × 10–15
The value of Kw at 20°C is 6.81 × 10–15.
b) What is the pH in water at 20°C?
c) What is the [OH–] in water at 20°C?
e) Is water at 20°C acidic, basic, or neutral?
2 153
153
3
8
H O 6.81 10
H O 6.81 10 8.25 10
H OH
M
O
d) What is the pOH in water at 20°C?
83H O OH 8.25 10 M
Substitute [H3O+] for [OH–]
a) What is the [H3O+] in water at 20°C?
So [H3O+] is the square root of 6.81 × 10–15
The value of Kw at 20°C is 6.81 × 10–15.
b) What is the pH in water at 20°C?
c) What is the [OH–] in water at 20°C?
e) Is water at 20°C acidic, basic, or neutral?
15 8
53
3
2 13
H O 6.8
H O OH H O 6.81 1
1 10 8.25 1
0
0 M
d) What is the pOH in water at 20°C?
83H O OH 8.25 10 M
a) What is the [H3O+] in water at 20°C?
Which is 8.25 × 10–8 M
The value of Kw at 20°C is 6.81 × 10–15.
b) What is the pH in water at 20°C?
c) What is the [OH–] in water at 20°C?
e) Is water at 20°C acidic, basic, or neutral?
2 153 3
15 83
H O OH H O 6.81 10
H O 6 8.25.81 10 10 M
d) What is the pOH in water at 20°C?
83H O OH 8.25 10 M
a) What is the [H3O+] in water at 20°C?
The second question asks us the pH in water at 20°C
The value of Kw at 20°C is 6.81 × 10–15.
b) What is the pH in water at 20°C?
c) What is the [OH–] in water at 20°C?
e) Is water at 20°C acidic, basic, or neutral?
2 153 3
15 83
H O OH H O 6.81 10
H O 6.81 10 8.25 10 M
d) What is the pOH in water at 20°C?
83H O OH 8.25 10 M
a) What is the [H3O+] in water at 20°C?
pH is the negative log of the hydronium ion concentration,
The value of Kw at 20°C is 6.81 × 10–15.
b) What is the pH in water at 20°C? c) What is the [OH–] in water at 20°C?
e) Is water at 20°C acidic, basic, or neutral?
2 153 3
15 83
H O OH H O 6.81 10
H O 6.81 10 8.25 10 M
d) What is the pOH in water at 20°C?
83H O OH 8.25 10 M
83pH log log 8.25 10 7.084H O
a) What is the [H3O+] in water at 20°C?
Which is the negative log of 8.25 x 10-8,
The value of Kw at 20°C is 6.81 × 10–15.
b) What is the pH in water at 20°C? c) What is the [OH–] in water at 20°C?
e) Is water at 20°C acidic, basic, or neutral?
2 153 3
15 83
H O OH H O 6.81 10
H O 6 8.25.81 10 M10
d) What is the pOH in water at 20°C?
83H O OH 8.25 10 M
38log 8pH lo .25 10 7.084g H O
a) What is the [H3O+] in water at 20°C?
Which comes out to 7.084
The value of Kw at 20°C is 6.81 × 10–15.
b) What is the pH in water at 20°C? c) What is the [OH–] in water at 20°C?
e) Is water at 20°C acidic, basic, or neutral?
2 153 3
15 83
H O OH H O 6.81 10
H O 6.81 10 8.25 10 M
d) What is the pOH in water at 20°C?
83H O OH 8.25 10 M
83pH log log 8.25 10H O 7.084
a) What is the [H3O+] in water at 20°C?
Question “c” asks for the hydroxide ion concentration in water at 20°C
The value of Kw at 20°C is 6.81 × 10–15.
b) What is the pH in water at 20°C? c) What is the [OH–] in water at 20°C?
e) Is water at 20°C acidic, basic, or neutral?
2 153 3
15 83
H O OH H O 6.81 10
H O 6.81 10 8.25 10 M
d) What is the pOH in water at 20°C?
83H O OH 8.25 10 M
83pH log log 8.25 10 7.084H O
a) What is the [H3O+] in water at 20°C?
We know that the hydronium ion concentration is 8.25 x 10-8 M, and we need to find the hydroxide ion concentration. But be careful, we Cannot use 1.0 x 10-14 divided by hydronium concentration here, because we’re not at 25°C!
The value of Kw at 20°C is 6.81 × 10–15.
b) What is the pH in water at 20°C? c) What is the [OH–] in water at 20°C?
e) Is water at 20°C acidic, basic, or neutral?
2 153 3
15 83
H O OH H O 6.81 10
H O 6 8.25.81 10 10 M
d) What is the pOH in water at 20°C?
83H O OH 8.25 10 M
[H3O+]
83pH log log 8.25 10 7.084H O
a) What is the [H3O+] in water at 20°C?
However, because we’re dealing with pure water, we know that it is neutral.
The value of Kw at 20°C is 6.81 × 10–15.
b) What is the pH in water at 20°C? c) What is the [OH–] in water at 20°C?
e) Is water at 20°C acidic, basic, or neutral?
2 153 3
15 83
H O OH H O 6.81 10
H O 6 8.25.81 10 10 M
d) What is the pOH in water at 20°C?
83H O OH 8.25 10 M
[H3O+]
83pH log log 8.25 10 7.084H O
Neutral
a) What is the [H3O+] in water at 20°C?
Therefore hydroxide ion concentration is equal to hydronium ion concentration.
The value of Kw at 20°C is 6.81 × 10–15.
b) What is the pH in water at 20°C? c) What is the [OH–] in water at 20°C?
e) Is water at 20°C acidic, basic, or neutral?
2 153 3
15 83
H O OH H O 6.81 10
H O 6 8.25.81 10 10 M
d) What is the pOH in water at 20°C?
83OH H O 8.25 10 M
[H3O+]
83pH log log 8.25 10 7.084H O
Neutral
a) What is the [H3O+] in water at 20°C?
Which is 8.25 x 10-8 M
The value of Kw at 20°C is 6.81 × 10–15.
e) Is water at 20°C acidic, basic, or neutral?
2 153 3
15 83
H O OH H O 6.81 10
H O 6 8.25.81 10 10 M
d) What is the pOH in water at 20°C?
83H OOH 8.25 10 M
[H3O+]
c) What is the [OH–] in water at 20°C?
b) What is the pH in water at 20°C?
83pH log log 8.25 10 7.084H O
a) What is the [H3O+] in water at 20°C?
Question “d” asks us to find the pOH in water at 20°C. Remember, we cannot use 14 minus pH to find pOH because we’re not at 25°C.
The value of Kw at 20°C is 6.81 × 10–15.
e) Is water at 20°C acidic, basic, or neutral?
2 153 3
15 83
H O OH H O 6.81 10
H O 6.81 10 8.25 10 M
d) What is the pOH in water at 20°C?
83OH H O 8.25 10 M
c) What is the [OH–] in water at 20°C?
b) What is the pH in water at 20°C?
83pH log log 8.25 10 7.084H O
a) What is the [H3O+] in water at 20°C?
However, because water is neutral, we know that the hydroxide concentration is equal to the hydronium concentration,
The value of Kw at 20°C is 6.81 × 10–15.
e) Is water at 20°C acidic, basic, or neutral?
2 153 3
15 83
H O OH H O 6.81 10
H O 6.81 10 8.25 10 M
d) What is the pOH in water at 20°C?
83OH H O 8.25 10 M
c) What is the [OH–] in water at 20°C?
b) What is the pH in water at 20°C?
83pH log log 8.25 10 7.084H O
Neutral
a) What is the [H3O+] in water at 20°C?
Therefore, the pOH is equal to the pH
The value of Kw at 20°C is 6.81 × 10–15.
e) Is water at 20°C acidic, basic, or neutral?
2 153 3
15 83
H O OH H O 6.81 10
H O 6.81 10 8.25 10 M
d) What is the pOH in water at 20°C?
83OH H O 8.25 10 M
c) What is the [OH–] in water at 20°C?
b) What is the pH in water at 20°C?
83pH log log 8.25 10 7.084H O
pOH = pH
Neutral
a) What is the [H3O+] in water at 20°C?
Which is 7.084.
The value of Kw at 20°C is 6.81 × 10–15.
e) Is water at 20°C acidic, basic, or neutral?
2 153 3
15 83
H O OH H O 6.81 10
H O 6.81 10 8.25 10 M
d) What is the pOH in water at 20°C?
83OH H O 8.25 10 M
c) What is the [OH–] in water at 20°C?
b) What is the pH in water at 20°C?
83pH log log 8.25 10H O 7.084
pOH = pH = 7.084
a) What is the [H3O+] in water at 20°C?
We could also have said that pOH is the negative log of [OH-]
The value of Kw at 20°C is 6.81 × 10–15.
e) Is water at 20°C acidic, basic, or neutral?
2 153 3
15 83
H O OH H O 6.81 10
H O 6.81 10 8.25 10 M
d) What is the pOH in water at 20°C?
83OH H O 8.25 10 M
c) What is the [OH–] in water at 20°C?
b) What is the pH in water at 20°C?
83pH log log 8.25 10 7.084H O
pOH = –log[OH–] =–log(8.25 × 10–8) = 7.084
a) What is the [H3O+] in water at 20°C?
Which is the negative log of 8.25 x 10-8
The value of Kw at 20°C is 6.81 × 10–15.
e) Is water at 20°C acidic, basic, or neutral?
2 153 3
15 83
H O OH H O 6.81 10
H O 6.81 10 8.25 10 M
d) What is the pOH in water at 20°C?
388.OH 2 1H 5O 0 M
c) What is the [OH–] in water at 20°C?
b) What is the pH in water at 20°C?
83pH log log 8.25 10 7.084H O
pOH = –log[OH–] = –log(8.25 × 10–8) = 7.084
a) What is the [H3O+] in water at 20°C?
Which is 7.084
The value of Kw at 20°C is 6.81 × 10–15.
e) Is water at 20°C acidic, basic, or neutral?
2 153 3
15 83
H O OH H O 6.81 10
H O 6.81 10 8.25 10 M
d) What is the pOH in water at 20°C?
83OH H O 8.25 10 M
c) What is the [OH–] in water at 20°C?
b) What is the pH in water at 20°C?
83pH log log 8.25 10 7.084H O
pOH = –log[OH–] = –log(8.25 × 10–8) = 7.084
a) What is the [H3O+] in water at 20°C?
The last question asks if water at 20°C is acidic, basic, or neutral.
The value of Kw at 20°C is 6.81 × 10–15.
e) Is water at 20°C acidic, basic, or neutral?
2 153 3
15 83
H O OH H O 6.81 10
H O 6.81 10 8.25 10 M
d) What is the pOH in water at 20°C?
83OH H O 8.25 10 M
c) What is the [OH–] in water at 20°C?
b) What is the pH in water at 20°C?
83pH log log 8.25 10 7.084H O
pOH = pH = 7.084
a) What is the [H3O+] in water at 20°C?
Here’s where we have to be careful. Notice the pH is above 7. We’re used to thinking that if the pH is above 7, then it is basic. However the 7 is only valid at 25°C.
The value of Kw at 20°C is 6.81 × 10–15.
e) Is water at 20°C acidic, basic, or neutral?
2 153 3
15 83
H O OH H O 6.81 10
H O 6.81 10 8.25 10 M
d) What is the pOH in water at 20°C?
83OH H O 8.25 10 M
c) What is the [OH–] in water at 20°C?
b) What is the pH in water at 20°C?
83pH log log 8.25 10H O 7.084
pOH = pH = 7.084
pH
a) What is the [H3O+] in water at 20°C?
Remember pure water is neutral, no matter what the temperature is.
The value of Kw at 20°C is 6.81 × 10–15.
e) Is water at 20°C acidic, basic, or neutral? Neutral
2 153 3
15 83
H O OH H O 6.81 10
H O 6.81 10 8.25 10 M
d) What is the pOH in water at 20°C?
83OH H O 8.25 10 M
c) What is the [OH–] in water at 20°C?
b) What is the pH in water at 20°C?
83pH log log 8.25 10 7.084H O
pOH = pH = 7.084
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