Calculate pH of Strong Bases | NaOH, KOH

Strong bases dissociate completely to hydroxyl ions and related cations in the water. Strong bases may show higher pH values than weak bases (such as aqueous ammonia solution).


In this tutorial, we will learn following sections of chemistry of bases (alkali)

  1. Calculate pOH, pH when concentration is known
  2. Calculate concentration when pH or pOH is known

What are the strong bases or alkalis?

Strong bases dissociate completely in water. Some of strong bases are NaOH, KOH, Ba(OH)2. In water, these bases dissociate into metal ion and OH- ion. As an example, NaOH dissociate completely to Na+ and OH- ions.


General equation of strong acid dissociation

MOH(aq) → M+(aq) + OH-(aq)


NaOH(aq) → Na+(aq) + OH-(aq)

KOH(aq) → K+(aq) + OH-(aq)



Strong Bases

Following metal hydroxides dissolve very well in water and give strong alkaline solution.


Calculate pH of NaOH solution

pH is mainly changed due to change of concentration of the solution. The concentration of the base increases, it results increase of pH.


pH and pOH

pH is defined for expressing H3O+ concentration and pOH is defined for expressing OH- concentration.


In calculating pH of NaOH solution, first, we have to calculate the pOH value. We have a relationship between pH and pOH as below.

pH + pOH = pKa

pKa is a constant to a certain temperature and pKa = 14 at 250C. So at 250C,

pH + pOH = 14



We can use two methods to calculate pH of basic solution.

  1. Calculate pOH of the base and then pH
  2. Calculate [H3O]+(aq), then calculate the pH


How about the pH of aqueous ammonium hydroxide and sodium hydroxide?

Ammonium hydroxide is a weak base give less hydroxyl ion concentration. But sodium hydroxide is a strong acid and completely dissociate to sodium ion and hydroxyl ions.

When hydroxyl ion concentration is high, its basic strength is higher and has a high pH value.



Method 1

Calculate pOH of strong base and pH

The formula of pOH,

pOH = -log10[OH-(aq)]

calculating pOH is a logarithmic one.


Then use the expression of

pH + pOH = pKw

to calculate pH. The sum of pH + pOH become 14 when room temperature is 250C. In other temperatures, we have to give the related value of that temperature.



Method 2

Calculate [H3O]+(aq) and then pH

There is a relation between [H3O]+(aq) and [OH]-(aq) in aqueous solution.


Relationship of [H3O]+(aq) and [OH]-(aq)

[H3O]+(aq) * [OH]-(aq) = Kw

Kw = constant

At 250Kw,
Kw = 1.0 * 10-14mol2 dm-6

When we know [OH]-(aq), using this equation, we can easily calculate the [H3O]+(aq).

Then, we can use pH equation, to calculate pH.

pH = -log10[H3O+(aq)]


NOTE

pKw = -log10[Ka]



Calculate pH of strong base examples


Example 1

Calculate pH of 0.1 moldm-3 NaOH solution

The room temperature is 250C.
Note : M = mol dm-3


We solve this example according to method 1.

NaOH dissociate completely into Na+(aq) & OH-(aq) ions in water.

NaOH dissiciation in water

We have to calculate concentration of OH-(aq) to calculate pH.

strong alkaline dissociation table

First we calculate pOH and then calculate the pH using the relationship of pH and pOH

Calculate pOH

pOH = -log(OH-(aq))
pOH = -log ( 0.1)
pOH = 1

relation of pH and pOH

pH + pOH = 14 (at 250C)
pH + 1 = 14
pH = 13


Let's solve example 1 according to method 2.


We know the concentration of OH- ions

[OH-(aq)] = 0.1 moldm-3

Use the relation of,

[H3O]+(aq) * [OH]-(aq) = Kw

at 250C, Kw = 1.0 * 10-14mol2 dm-6

[H3O]+(aq) * 0.1 = 1.0 * 10-14

[H3O]+(aq) = 1.0 * 10-13

Now, we know the concentration of [H3O]+(aq), therefore we can use pH equation,


pH = -log10[H3O+(aq)]

pH = -log10(1.0 * 10-13)

pH = 13



Example 2

Calculate pH of 0.01 moldm-3 NaOH solution

Here only changes the concentration of NaOH. We studied, NaOH completely dissociate in the water. Therefore,
[OH]-(aq) = 0.01 moldm-3

Then substitute [OH]-(aq) to the pOH equation.

pOH = -log(OH-(aq))
pOH = -log ( 0.01)
pOH = 2

relation of pH and pOH

pH + pOH = 14 (at 250C)
pH + 2 = 14
pH = 12


pH variation against concentration of base

When OH- concentration of aqueous solution is reduced by 10 times, pH is increased by a 1.

At 250C, pH + pOH = 14

pH variation against concentration of base


Example 3

Calculate pH of 0.1 moldm-3 of Ba(OH)2

Ba(OH)2 is a strong base. Therefore it dissociate completely in water to Ba2+(aq) and OH- ions.

barium hydroxide dissociation

Dissociation of Ba(OH)2

When one Ba(OH)2 molecule dissociate, one Ba2+ ion and two OH- ions are given. See the stoichiometry ratio.

Dissociation of Ba(OH)2

[OH-(aq)] = 0.2 moldm-3


Then substitute [OH]-(aq) to the pOH equation.

pOH = -log(OH-(aq))

pOH = -log ( 0.2)

pOH = 0.7


relation of pH and pOH

pH + pOH = 14 (at 250C)

pH + 0.7 = 14

pH = 13.3



Example 4

Calculate concentration and pH of NaOH solution

4g of solid NaOH are dissolved in water and then diluted the mixture upto 250cm3. Calculate the concentration of OH- ions and pH of solution.

NaOH solution diluting

First, number of moles(n) of dissolved NaOH should be calculated.

Molecular weight of NaOH

NaOH = 23 + 16 + 1
NaOH = 40 g mol-1


number of moles of dissolved NaOH, nNaOH

nNaOH = 4 g / 40 gmol-1
nNaOH = 0.1 mol


Calculate the concentration now


[NaOH(aq)] = 0.1mol / 0.25 dm3
[NaOH(aq)] = 0.4 mol dm-3
[OH-(aq)] = 0.4 mol dm-3

pOH = -log(OH-(aq))
pOH = -log ( 0.4)
pOH = 0.4

pH = 13.6



Questions



If pH of a solution of the strong base NaOH is known, which property of the solution can be calculated?

If pH value is high, we know, pH value will completely depend on the concentration of NaOH. Otherwise we have to consider dissociation of water to calculate OH- concentration.

  • If pH is higher (above 9), we can directly calculate OH- concentration from pOH = -log10[(OH-)].
  • To find the pOH, use the relationship of pH + pOH = pKa.
  • Also you can calculate concentration of [H3O+] from pH value.


Is pH value of different NaOH and KOH solutions equal or not when their concentrations are equal.?

Both NaOH and KOH are strong bases and dissociate completely in the water. So when NaOH and KOH concentrations are equal, after the dissociation, hydroxyl ion concentration is also equal. Therefore pH of both solution is equal.

But, basic strength of KOH is much higher than NaOH.



NaOH ph level

pH of dilute NaOH solutions are usually above 10 if concnetration of NaOH is higher than 0.0001 mol dm-3

Is KOH a strong base

Yes. KOH is a strong base and it completely dissociates to K+ and OH- ions in the water.



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