pH of a solution calculator

These online calculators calculate the pH of a solution. There are two calculators – one for either strong acid or strong base, and another for either weak acid or weak base.

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Karen Luckhurst

Created: 2020-08-31 13:01:50, Last updated: 2020-11-30 17:12:39

Below you can find two calculators that you can use to check answers to chemistry problems. The first one calculates the pH of a strong acid or strong base solution, and the second one calculates the pH of a weak acid or weak base solution. Some theory and an explanation of the calculations with formulas can be found below the calculators.

PLANETCALC, pH of a strong acid/base solution

pH of a strong acid/base solution

Digits after the decimal point: 3

PLANETCALC, pH of a weak acid/base solution

pH of a weak acid/base solution

Digits after the decimal point: 3

pH of a solution

pH means 'potential of hydrogen' or 'power of hydrogen'. pH is the negative of the base 10 logarithm of the hydrogen ion activity.
\ce {pH} = -\log_{10}(a_{\ce {H^+}})=\log _{10}\left({\frac {1}{a_{{\ce {H^+}}}}}\right)

In most chemistry problems, however, we do not use hydrogen ion activity, but molar concentration or molarity. How are these two related? Of course, ion activity depends on ion concentration and this is described by the equation
a_{H^+}=f \cdot [H^+]
a_{H^+} – hydrogen ion activity
f – hydrogen ion activity coefficient
[H^+] – hydrogen ion concentration

The activity coefficient is a function of the ion concentration and approaches 1 as the solution becomes increasingly dilute. For dilute (ideal) solutions, the standard state of the solute is 1.00 M, so its molarity equals its activity. That's why for most problems that assume ideal solutions we can use the base 10 logarithm of the molar concentration, not the activity.

Why do we need pH at all? pH is a measure used to specify acidity or basicity of an aqueous solution. Whether an aqueous solution reacts as an acid or a base depends on its hydrogen ion (H+) content.

However, even chemically pure, neutral water contains some hydrogen ions1 due to the auto dissociation of water.

H_2O \longleftrightarrow H^+ + OH^-

It is known that at equilibrium under standard conditions (750 mmHg and 25°C), 1 L of pure water contains 10^{-7} mol H^+ and 10^{-7} mol OH^- ions, hence, water at standard temperature and pressure (STP) has a pH of 7. Acids release hydrogen ions, so their aqueous solutions contain more hydrogen ions than neutral water and are considered acidic with a pH less than 7. Bases accept hydrogen ions (they bind to some of the hydrogen ions formed from the dissociation of the water), so their aqueous solutions contain fewer hydrogen ions than neutral water and are considered basic with pH more than 7. Note that the pH scale is logarithmic (difference by one means difference by order of magnitude, or tenfold) and inversely indicates the concentration of hydrogen ions in the solution. A lower pH indicates a higher concentration of hydrogen ions and vice versa.

The calculation of pH using molar concentration is different in the case of a strong acid/base and weak acid/base. More on this below.

Strong acid/base

Strong acids and bases are compounds that, for practical purposes, completely dissociate into their ions in water. Hence the concentration of hydrogen ions in such solutions can be taken to be equal to the concentration of the acid. The calculation of pH becomes straightforward

For basic solutions, you have the concentration of the base, thus, the concentration of the hydroxide ions OH-. You can calculate pOH.

Based on equilibrium concentrations of H+ and OH− in water (above), pH and pOH are related by the following equation
pH + pOH=14, which is true for any aqueous solution.

Hence, in the case of a basic solution
pH=14 - pOH=14 + log_{10}[OH^-]

There are only seven common strong acids:

– hydrochloric acid HCl
– nitric acid HNO3
– sulfuric acid H2SO4
– hydrobromic acid HBr
– hydroiodic acid HI
– perchloric acid HClO4
– chloric acid HClO3

There aren't very many strong bases either, and some of them are not very soluble in water. Those that are soluble are

– sodium hydroxide NaOH
– potassium hydroxide KOH
– lithium hydroxide LiOH
– rubidium hydroxide RbOH
– cesium hydroxide CsOH

A solution of a strong acid at concentration 1 M (1 mol/L) has a pH of 0. A solution of a strong alkali at concentration 1 M (1 mol/L) has a pH of 14. Thus, in most problems that arise pH values lie mostly in the range 0 to 14, though negative pH values and values above 14 are entirely possible.

Weak acid/base

Weak acids/bases only partially dissociate in water. Finding the pH of a weak acid is a bit more complicated. The pH equation is still the same: pH = -log[H^+], but you need to use the acid dissociation constant (Ka) to find [H+].

The formula for Ka is:

K_a =\frac{[H^+][B^-]}{[HB]}

[H^+] – concentration of H+ ions
[B^-] – concentration of conjugate base ions
[HB] – concentration of undissociated acid molecules
for a reaction HB \leftrightarrow H^+ + B^-

This formula describes the equilibrium. In order to deduce the formula for H+ from the formula above, we can use an ICE (initial – change – equilibrium) table. Let x represent the concentration of H+ that dissociates from HB, then we can fill the table like this:

HB H+ B-
Initial concentration C M 0 M 0 M
Change in concentration -x M +x M +x M
Equilibrium concentration (C-x) M x M x M

Now, plug these into the Ka formula:

K_a =\frac{x \cdot x}{(C - x)}

After re-arrangement, we get a quadratic equation:

x^2 - K_a(C - x) = 0 \\ x^2 + K_ax - K_aC = 0

To find x we need to solve the quadratic equation and pick the positive root.

Finally, plug x into the pH formula to find the pH value.

The same applies to bases, where you use the base dissociation constant Kb. Ka and Kb are usually given, or can be found in tables.

You may notice that tables list some acids with multiple Ka values. This means that acid is polyprotic, which means it can give up more than one proton. However, due to molecular forces, the value of the constant for each next proton becomes smaller by several orders of magnitude. For example, for phosphoric acid

K_1 = 7.2 \cdot 10^{-3} \\ K_2 = 6.3 \cdot 10^{-8} \\ K_3 = 4.6 \cdot 10^{-13}

So, usually only one proton is considered, and you use stoichiometric coefficient equals to one for all calculations.

  1. The hydrogen ion does not remain as a free proton for long, as it is quickly hydrated by a surrounding water molecule. The result is the hydronium ion H_2O + H^+ \longleftrightarrow H_3O^+ 

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PLANETCALC, pH of a solution calculator