Hydrochloric acid (HCl) is considered a strong acid. For many problems, it is co

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.

Explanation / Answer

complete dissociation :

HCl ---------------------> H+ + Cl-

0.1 0.1 0.1 M

[H+] = 0.1 M

true value

pKa = -7

Ka = 10^-pKa = 10^-(-7) = 10^7

C = 0.1

[H+] = sqrt (Ka x C) = sqrt (10^7 x 0.1)

[H+] = 1000 M

Er = ((xi – xt)/xt) × 100

= (0.1 -1000 / 1000) x 100

= -99.99

the relative error =   - 99.99

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