Question

Can the five percent approximation be applied in determining the pH of the following solutions?


A table of pKa values can be found here.


Yes No  5.94×10^-1 M dimethylammonium ion
Yes No  5.52×10^-1 M chloroacetic acid
Yes No  6.64×10^-4 M ammonium ion
Yes No  3.99×10^-4 M benzoic acid

Answer 1

Answer – We know the five percent approximation is used for calculating the pH of weak base and acids. Generally 5% approximation not applied when the value of Ka or Kb is too small mean it is more than ten ratio to -5. 5% approximation applied when there is more than ten ratio to -5.

We need to calculate the percent using the formula like Ka or Kb/ [initial acid or base]*100 and if it is more than 5% then we need to use 5% approximation and not to neglect x from the reactant at equilibrium.

First we need to look for the pKa values for the each one given and then need to convert the pKa to Ka using the Ka = 10^-pKa.

For 5.94*10^-1 M dimethylammonium ion , pKa = 10.7

So, Ka = 10^-10.7 = 2.0*10^-11

So, 2.11*10^-11 / 5.94*10^-1 M * 100 %   = 3.35*10^-9 % which is less than 5 %, so we don’t need apply for this one 5% approximation.

Using the same method for the chloroacetic acid, ammonium ion and benzoic acid we can determine the whether the need to apply for 5% rule approximation or not.

pKa value for chloroacetic acid is 2.87, so Ka is around 1.3*10^-3 , so it is approximately more for then 10 ratio to -5 , so we need to apply for this one 5% approximation.

pKa value for ammonium ion is 9.25 and Ka value around 5.60*10^-10 , so it is very less and don’t need apply for this one 5% approximation.

pKa value for benzoic acid is 4.87, so Ka is around 6.30*10^-5 , so it is approximately more for then 10 ratio to -5 , so we need to apply for this one 5% approximation.

No 5.94×10^-1 M dimethylammonium ion
Yes  5.52×10^-1 M chloroacetic acid
No   6.64×10^-4 M ammonium ion
Yes 3.99×10^-4 M benzoic acid