pH of a strong acid – Examples | Chemistry Net

# pH of a strong acid – Examples

pH of a strong acid - Examples

# pH of a strong acid - Examples

In a previous post entitled “Strong Acids and Bases – Ionic Equilibrium – A general relation for the pH of a strong acid” the following equation was derived for the hydronium ion concentration [H+] for strong acids :

For strong acids at equilibrium :

[H+] = C  where C is the initial concentration of the strong acid            (1)

Let us see the following examples:

Example #1

Calculate the pH of a 0.1 M solution of  HCl.

HCl is considered to be a strong acid (Table I.1). It dissociates completely in water to produce 0.1 M of H+ and 0.1 M of Cl-.

HCl(aq) + H2O(l) → H3O+(aq) + Cl(aq)

STEPS
RESULTS
NOTES
I

 Data given [HCl] = 0.1 M Asked for pH = ?

Write down the data given and the   unknown.
II

pH = -log [H+]            (1)

HCl     H+      +        Cl-       (2)

 Initially 0.1 Μ 0 Μ 0 Μ Change -0.1 M 0.1 M 0.1 M Final (at equilibrium 0 0.1 M 0.1 M

Write down equations relating data given and unknowns. Write down the relevant chemical equation.
[H+] and pH’s are unknowns but they can be calculated.
III

From Step II above at equilibrium:  [H+] = 0.1 M    (3)

 IV From (1) at Step ΙΙ and (3):                                pH = -log [H+] = -log (0.1) = -log (10-1) = -(-1) = 1    pH = 1

Mathematical Approach

From equation (1) above and for strong acids:

[H+] = C

Since the concentration of a strong acid at equilibrium is given as:
[H+] = C = [HCl] = 0.1 M    (2)

The pH of the 0.1 M HCl solution would be:

pH = -log([H+]) = -log (0.1) = -log (10-1) = -(-1) = 1

Example #2

Calculate  the pH of a 10-7 M solution of  HCl

Since HCl is a strong acid dissociates completely in water to produce at equilibrium 10-7 M H+ and 10-7 M Cl- :

HCl(aq) + H2O(l) → H3O+(aq) + Cl(aq)
-10-7 M                  +10-7 M        +10-7 M

From the above reaction at equilibrium:

H3O+ = 10-7 M  and  pH = -log [H+] = -log (10-7) =  -(-7) = 7     (2)

However, we do know from theory that an acid solution has to have a pH less than 7. This erroneous result was obtained because we do not take into account the autoionazation of H2O. This autoionaziation of H2O becomes important when the initial concentration of an acid is lower or equal to 10-7.

STEP
RESULTS
NOTES

I

 Data given HCl solution  [HCl] = 10-7 M Asked for pH = ?

Write down the data given and the   unknown.

II
Write down equations relating data given and unknowns. Write down the relevant chemical equation.
[H+] and pH’s are unknowns but they can be calculated.

pH = -log([H3O+])  (1)

HCl dissociates in water according to:

ΗCl + H2O H3O+ + Cl-  (2)
10-7 mol/ℓ       10-7 mol/ℓ
From  (1) pH = -log([H3O+]) = -log([10-7]) = 7

However, it is known from theory that the pH of an acid must be pH<7. This erroneous result was obtained because the autoionization of water becomes important and must be taken into consideration where the concentration of an acid is [acid] ≤ 10-7 Μ.
Suppose that χ mol/ℓ water react and χ mol/ℓ H3O+ is produced:
H2O + H2O    H3O+ + OH-  (3)
-x mol/ℓ react          +x mol/ℓ is produced

From (2)+(3) :
[H3O+] = (10-7 + x) M   και [OH-] = x M   (4)

For kw at 25 °C:

kw = [H3O+].[OH-] = 10-14  (5)

III

By substituting in equation (5) the concentrations derived in (4) at step ΙΙ  χ can be calculated.

From (5) and (4):

kw  = [H3O+].[OH-] = (10-7 + x). x = 10-14
x2+(10-7).x-10-14 = 0  and
x = (6.2)*10-8 M  (6)

The quadratic equation has to be solved since x is appreciable at low concentrations of acids.

IV

From (4) and (6):
x = [H3O+] = (10-7 + x) = 10-7 + (6.2)*10-8 =  (1.6)*10-7 M  (7)
From (1) and (7):
pH = -log((1.6)*10-7) = -log(1.6)-log(10-7) = -0.2-(-7) 6.8

Relevant Posts

References

J-L. Burgot “Ionic Equilibria in Analytical Chemistry”, Springer Science & Business Media, 2012
J.N. Butler  “Ionic Equilibrium – Solubility and pH calculations”, Wiley – Interscience, 1998
Clayden, Greeves, Waren and Wothers “Organic Chemistry”, Oxford,
D. Harvey,  “Modern Analytical Chemistry”, McGraw-Hill Companies Inc., 2000
Toratane Munegumi, World J. of Chem. Education, 1.1, 12-16 (2013)
J.N. Spencer et al., “Chemistry structure and dynamics”, 5th Edition, John Wiley & Sons, Inc., 2012
L. Cardellini, Chem. Educ. Res. Pract. Eur., 1, 151-160, (2000)