# How to Calculate Hydrogen Ion Concentration

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A hydrogen ion concentration in a solution results from the addition of an acid. Strong acids give a higher concentration of hydrogen ions than weak acids, and it is possible to calculate the resulting hydrogen ion concentration either from knowing the pH or from knowing the strength of the acid in a solution. Solving with a known pH is easier than solving from the acid dissociation constant and the initial concentration.

## Solving With a Known pH or pOH

Check to determine whether the information provided contains the pH or the pOH of the solution.

Calculate hydrogen ion concentration by taking 10 to the power of the negative pH. For example, for a solution of pH 6.5, the hydrogen ion concentration would be 1 * 10^-6.5, which equals 3.16 * 10^-7. Scientists have defined pH as a logarithmic shortcut for hydrogen ion concentration. This means that pH equals the negative logarithm of the hydrogen ion concentration.

Subtract the pOH from 14 (pH and pOH always add up to 14) to arrive at the pH, if faced with a pOH number only, then complete the above calculation, since the pOH is the negative logarithm of the OH ion concentration in a solution.

## Solving From Acid Dissociation Constant (Ka) and Amount

Translate from grams to moles, if necessary, by using the molar mass of the acid. Clackamas Community College offers a great tutorial on how to do this (see Resources). Every chemistry student should be sure to understand units conversions and practice with them consistently.

Find the molar concentration of the acid by calculating moles divided by liters: for example, 0.15 moles of acid in 100mL would equal 0.15 divided by 0.100, which equals a 1.5 M solution.

Use the original concentration of the acid as the hydrogen ion concentration for a strong acid in solution: all of the acid ionizes. The following are the only strong acids: HCl (hydrochloric), HBr (hydrobromic), HI (hydroiodic), H2SO4 (sulfuric), HNO3 (nitric) and HClO4 (perchloric) acids.

Use the acid dissociation constant and a calculator to find the concentration of hydrogen ions for a weak acid. Write out this equation: Ka = ([H+]*[A-]) / [HA] where [HA] is the concentration of the acid at equilibrium, [H+] is the concentration of hydrogen ions, [A-] is the concentration of the conjugate base or anion, which will be equal to [H+] and Ka is the acid dissociation constant.

Plug in the known value for Ka. The equation then looks like this: Ka = x^2 / [HA] Now, since the acid splits into ions, the molar concentration of each ion at equilibrium equals the same amount missing from the original acid. So that equation equals: Ka = x^2 / (Original concentration minus x).

Convert this to a quadratic equation: X^2 + Ka x - (original concentration * Ka) = 0 Use the quadratic formula to solve for the final value of x.