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# pH of a solution

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

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

#### pH of a strong acid/base solution

pH

Digits after the decimal point: 3

#### pH of a weak acid/base solution

pH

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 these two are related? Of course ion activity depends on ion concentration and this is described by the equation
$a_{H^+}=f \cdot [H^+]$
where,
$a_{H^+}$ - 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 which assume ideal solutions we can use 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 STP has pH of 7. Acids release hydrogen ions, so their aqueous solutions contain more hydrogen ions than neutral water and are considered acidic with 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 case of 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. Calculation of pH becomes straightforward
$pH=-log_{10}[H^+]$

For basic solutions you have the concentration of the base, thus, the concentration of the hydroxide ions OH-. You can calculate pOH.
$pOH=-log_{10}[OH^-]$

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 case of basic solution
$pH=14 - pOH=14 + log_{10}[OH^-]$

There are only 7 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 as well, and some of them not very soluble in water. Those 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 1M (1 mol/L) has a pH of 0. A solution of a strong alkali at concentration 1M (1 mol/L) has a pH of 14. Thus, in most problems you will deal with 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:

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

where:
$[H^+]$ - 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 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 Ka formula:

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

After re-arrangement, we get quadratic equation:

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

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

Finally, plug x to pH formula to find 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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