Question

Hydrochloric acid (HCl) is considered a strong acid. For many problems, it is convenient to assume that it completely dissociates to H+ ions and Cl− ions. But how good is this assumption? As a way to find out, calculate the relative error that results when one makes this assumption with a 0.1 M solution of HCl. Report your answer as a percent to one significant figure, and include the proper sign. Recall that relative error (in this context) is as follows: Er = ((xi – xt)/xt) × 100; where xi is the value under the assumption that complete dissociation occurs and xt is the true or actual value obtained when the pKa of the acid is taken into account. The pKa of hydrochloric acid is −7. For this problem, you can ignore the contribution of H+ ions due to the autoproteolysis of water. You may want to do this calculation with the aid of a spreadsheet so that you can adjust the format of the cells to retain several figures beyond the decimal point.

answer is NOT -99.99

Answer 1

first,

assuming it is 100% dissociation = 0.1 M of HCl = 0.1 M of H+

for strong acid:

HCl <-> H+ + Cl-

Ka = [H+][Cl-]/[HCl]

10^-pKa =  [H+][Cl-]/[HCl]

10^-(-7) = x*x/(0.1-x)

10^7 = x^2 / (0.1-x)

get x

x = 0.0999999

Now..

[H+] = x = 0.0999999

so

% error = (0.1-0.099999999)/(0.1)*100 = 9.97*10^-7 % ( 8 sig fig in calculator)

This depends on the max number of sig fig you add... my calcualtor does 8; for other computation systems might be up to 16... the point of this is to note that the assumption is valid... 0.1 M --> 100% dissociation