READ: pH

READ: pH

Relationship Between [H⁺] and [OH^-]

Even totally pure water will contain a small amount of H⁺ and OH^-. This is because water will break apart into two ions in the following equation:

H2O(l)→H++OH−

In pure water, the concentration of H⁺ and OH^- will be equal because one H⁺ is made for each OH^- ion in the balanced equation. We previously learned that acids form H⁺ ions in water. This means that if an acid is added to water, there will be a greater concentration of H⁺ ions than OH^- ions. Bases form hydroxide, OH^-, ions in water. If a base is added to water, there will be a greater concentration of OH^- than H⁺ ions. A further definition of acids and bases can now be made:

When H+=OH− (as in pure water), the solution is neutral.

When H+>OH−, the solution is an acid.

When H+<OH−, the solution is a base.

The pH scale was created in order to communicate the how acidic or basic a substance is. Most of the acids and bases dealt with in laboratory situations have hydrogen ion concentrations between 1.0 M and 1.0×10−14 M. Expressing hydrogen ion concentrations in exponential numbers can become tedious, so a Danish chemist named Søren Sørensen developed pH (a shorter method for expressing acid strength or hydrogen ion concentration with a non-exponential number). pH is determined by the formula below, where [H⁺] means molar concentration of hydrogen ion: If the hydrogen ion concentration is between 1.0 M and 1.0×10−14 M, the value of the pH will be between 0 and 14.

The pH scale developed by Sørensen is a logarithmic scale. Not only is the pH scale a logarithmic scale but by defining the pH as the negative log of the hydrogen ion concentration, the numbers on the scale get smaller as the hydrogen ion concentration gets larger. For example, pH=1 is a stronger acid than pH=2 and, it is stronger by a factor of 10. A solution whose pH=1 has a hydrogen ion concentration of 0.10 M while a solution whose pH=2 has a hydrogen ion concentration of 0.010 M. You should note the relationship between 0.10 and 0.010, 0.10 is 10 times 0.010. This is a very important point when using the pH scale.

The pH scale found in Figure above shows that acidic solutions have a pH within the range of 0 up to but not including 7. The closer the pH is to 0 the greater the concentration of H⁺ ions and therefore the more acidic the solution. The basic solutions have a pH with the range from 7 to 14 (Table above). The closer the pH is to 14, the higher the concentration of OH^- ion and the stronger the base. For 25ºC, a pH of 7 is neutral which means that [H+]=[OH−]=1×10−7 M.

Sørensen’s idea that the pH would be a simpler number to deal with in terms of discussing acidity level led him to a formula that relates pH and [H⁺]. This formula is:

pH=−log[H+]

The p from pH comes from the German word potenz meaning power or the exponent of. In this case the exponent is 10. Therefore, [H+]=10−pH.

When the [H+]=0.01 mol/L, the pH will be

pH=−log(0.01)=−log(1×10−2)=2

Since we are talking about negative logarithms (-log), the more hydrogen ions that are in solution, the more acidic the solution and the lower the pH.

Since pH is a logarithmic scale, an acid with pH=1 is stronger than an acid with pH=2 by a factor of 10. Simply put, lower pH values correspond to higher H⁺concentrations and more acidic solutions, while higher pH values correspond to higher OH^- concentrations and more basic solutions. This is illustrated in the figure below. It should be pointed out that there are acids and bases that fall outside the pH range depicted. However, we will confine ourselves for now to those falling within the 0-14 range, which covers H⁺ values from 1.0 M all the way down to 1×10−14 M.

Have you ever cut an onion and had your eyes water up? This is because of a compound with the formula C₃H₆OS that is found in onions. When you cut the onion, a variety of reactions occur that release a gas. This gas can diffuse into the air and eventfully mix with the water found in your eyes to produce a dilute solution of sulfuric acid. This is what irritates your eyes and causes them to water. There are many common examples of acids and bases in our everyday lives. Look at the pH scale above to see how these common examples relate in terms of their pH.

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