http://www.ck12.org Chapter 21. Acids and Bases
Known
- initial [HCOOH] = 0.500 M
- pH = 2.04
Unknown
- Ka=?
First, the pH is used to calculate the value of [H+] at equilibrium. An ICE table is set up in order to determine
the concentrations of HCOOH and HCOO−at equilibrium. All concentrations are then substituted into the Ka
expression, and the Kavalue is calculated.
Step 2: Solve.
H+ = 10−pH= 10−^2.^04 = 9.12× 10 −^3Since each formic acid molecule that ionizes yields one H+ion and one formate ion (HCOO−), the concentrations
of H+and HCOO−are equal at equilibrium. We assume that the initial concentrations of each ion are zero, resulting
in the following ICE table (Table21.7). Although the concentration of H+would technically be 1.0× 10 −^7 before
any dissociation occurs, we can ignore this very small amount because, in this case, it does not make a noticeable
contribution to the final value of [H+].
TABLE21.7:ICE Table
Concentrations [HCOOH] [H+] [HCOO−]
Initial 0.500 0 0
Change −9.12× 10 −^3 +9.12× 10 −^3 +9.12× 10 −^3
Equilibrium 0.491 9.12× 10 −^3 9.12× 10 −^3Substituting the equilibrium values into the Kaexpression gives the following:
Ka=[H+][HCOO−]
[HCOOH]
=
( 9. 12 × 10 −^3 )( 9. 12 × 10 −^3 )
0. 491
= 1. 7 × 10 −^4
Step 3: Think about your result.
The value of Kais consistent with that of a weak acid. Two significant figures are appropriate for the answer, since
there are two digits after the decimal point in the reported pH.
Practice Problems- Hypochlorous acid (HClO) is a weak acid. What is its Kaif a 0.250 M solution of hypochlorous acid has a pH
of 4.07?
Similar steps can be taken to determine the Kbof a base. For example, a 0.750 M solution of the weak base
ethylamine (C 2 H 5 NH 2 ) has a pH of 12.31.