pH Scale

Logarithms and pH Calculations

pH is the negative base-ten log of the hydronium ion concentration in a fluid, measured in moles per liter. Hydronium ion concentration is normally represented with this notation: [H3O+].

pH = -log[H3O+]

pH is value between 0 and 14 indicating the acidity of a fluid. Values less than 7 indicate a fluid is acidic. Values greater than 7 indicate the fluid is basic. A pH of 7 means the solution is neutral.

pH is imortant because water has a tendency to autoionize. This means water molecules (H2O) produce hydronium (H3O+) and hydroxide (OH-) ions. Greater concentrations of impurity in water triggers more autoionization. The more pure the water, the lower the ion concentration. Adding an acid to pure water disturbs the equilibrium and raises the H3O+ concentration.

• In a neutral solution:  [H3O+]  =  [OH-]
• In an acidic solution:  [H3O+]  >  [OH-]
• In a basic solution:     [H3O+]  <  [OH-]

Pure water is said to be pH neutral. In it, the Hydronium ([H30+]) and hydroxide ([OH-]) ion concentrations are equal at about 1.0 * 10^-7 moles per liter. The negative base 10 log of 1.0 * 10^-7 is positive 7.

H3O+ is an extra hydrogen ion bonded to a water molecule

Two Key Equations:

The most important equation is that pH is the negative base ten logarithm of the hydronium ion concentration. From that the hydronium ion can be determined, explained as follows:

pH is computed as the negative base 10 logarithm of the hydronium ion concentration [H30+], in moles per liter, in a liquid:

pH = -log[H30+]

This means the hydronium ion concentration, in moles per liter, is equal to 10 to the power of the negative pH. Conversion from the previous equation is as follows:

pH = -Log([H3O+])
-pH = Log([H3O+])
10^-(pH) = 10^(Log[H3O+])
10^-(pH) = [H3O+]
[H30+] = 10^-(pH)

With the Richter scale, earthquake magnitude is a computed value based on an empirical measured value, which is the intensity of an earthquake. Intensity is the wave height on a seismograph that records earth movement during an earthquake.

Similarly, with the pH scale, pH is a computed value based on an empirical measured value, which is the molar concentration of hydronium ions [H30+] in a fluid. Hydronium ion concentration is the number of moles per liter of [H30+] in a fluid.

pH math problems will usually present either pH and ask for computation of [H3O+], or will present a value for [H3O+] and ask for the pH.

Example:

If the hydronium ion concentration in water is 2.5 * 10^-6 moles per liter then what is the pH?

[H3O+] = 2.5 * 10^-6 M/L
pH = -Log([H3O+])
pH = -Log(2.5 * 10^-6)
pH = -[Log(2.5) + log(10^-6)]
pH = -[0.398 - 6] ~= + 5.6

Example:

If the pH of diet soda is 3.12 then what is the hydronium concentration [H3O+]?

pH = -Log[H3O+]
3.12 = -Log[H3O+]
10^3.12 = 10^(-Log[H3O+])
10^-3.12 =[H3O+]                  Careful handling the negative sign
[H3O+] = 7.57 * 10^-4 moles/liter             Do this on a calculator

The hydronium concentration is .000757 moles/liter

Example:

If the Hydronium ion concentration [H3O+] is 0.0032 moles per liter then what is the pH?

[H3O+] - 0.0032
pH = -log[H3O+]
pH = -[(Log (3.2 * 10^-3))]
pH = -[log(3.2) + log(10^-3)]
pH = -[0.505 - 3] = 2.49

This means that pH is ~2.5

Example:

If the pH of a fluid is 8.3 then what is the Hydronium ion concentration?

pH = -Log[H3O+]
pH = 8.3
8.3 = -Log[H3O+]
10^8.3 = -[10^(Log([H3O+]))]
10^-8.3 = [H3O+]
5.01 * 10^-9 = [H3O+]

Hydronium ion concentration [H3O+] is 5.01 * 10^-9 moles per liter.

Example:

If a fluid sample has a Hydronium ion concentration [H3O+] of 2.5 * 10^-6 moles per liter then what is the pH?

[H3O+] = 2.5 * 10^-6
[H3O+] = 10^-pH
Log([H3O+]) = Log(10^-pH)
Log([H3O+]) = -pH
pH = -Log ([H3O+)] = -log(2.5 * 10^-6) = -(Log(2.5) + Log (10^-6))
pH = -0.3979 + 6 = +5.6

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