The pH of a solution is a measure of how acidic or basic it is. It is defined as the negative logarithm of the hydronium ion (H3O+) concentration in moles per liter (M):
��=−log[�3�+]pH=−log[H3O+]
The hydronium ion is formed when a water molecule (H2O) accepts a proton (H+) from an acid. The more hydronium ions are present in a solution, the more acidic it is. Conversely, the fewer hydronium ions are present, the more basic it is.
The pH Scale
The pH scale ranges from 0 to 14, with 7 being neutral. A solution with a pH less than 7 is acidic, and a solution with a pH greater than 7 is basic. The pH scale is logarithmic, which means that a change of one unit in pH corresponds to a tenfold change in hydronium ion concentration. For example, a solution with a pH of 4 has 10 times more hydronium ions than a solution with a pH of 5, and 100 times more than a solution with a pH of 6.
The following table shows some common substances and their approximate pH values:
Substance
pH
Battery acid
0
Lemon juice
2
Vinegar
3
Soda
4
Tomato juice
4
Black coffee
5
Milk
6
Pure water
7
Blood
7.4
Seawater
8
Baking soda
9
Ammonia
11
Bleach
12
Lye
13
Calculating pH from H3O+ Concentration
To calculate the pH of a solution from the hydronium ion concentration, we can use the formula:
��=−log[�3�+]pH=−log[H3O+]
For example, if we have a solution with [H3O+] = 0.001 M, we can plug it into the formula and get:
��=−log[0.001]pH=−log[0.001]
��=−(−3)pH=−(−3)
��=3pH=3
This means that the solution is acidic, with a pH of 3.
Alternatively, we can use a calculator that has a log function to find the pH. For example, on a scientific calculator, we can enter:
log(0.001)
and then multiply the result by -1 to get the pH.
Calculating H3O+ Concentration from pH
In some cases, we may know the pH of a solution and want to find the hydronium ion concentration. To do this, we can rearrange the formula to solve for [H3O+]:
��=−log[�3�+]pH=−log[H3O+]
−log[�3�+]=��−log[H3O+]=pH
log[�3�+]=−��log[H3O+]=−pH
[�3�+]=10−��[H3O+]=10−pH
For example, if we have a solution with a pH of 8, we can plug it into the formula and get:
[�3�+]=10−8[H3O+]=10−8
[�3�+]=0.00000001�[H3O+]=0.00000001M
This means that the solution is basic, with a very low hydronium ion concentration.
Alternatively, we can use a calculator that has an exponent function to find the [H3O+]. For example, on a scientific calculator, we can enter:
10^(-8)
and get the [H3O+].
Summary
The pH of a solution is related to the hydronium ion concentration by the formula:
��=−log[�3�+]pH=−log[H3O+]
The lower the pH, the higher the [H3O+], and vice versa. The pH scale ranges from 0 to 14, with 7 being neutral. A solution with a pH less than 7 is acidic, and a solution with a pH greater than 7 is basic.
According to wikiHow, Khan Academy, Chemistry LibreTexts, and other sources.
