Calculating Ka from pKa (and pKa from Ka) in Chemistry

Co-authored by Anne Schmidt and Christopher M. Osborne, PhD

Last Updated: October 23, 2024 Fact Checked

Ka ( $K_{a}$ )—the acid dissociation constant—tells you the strength of an acid in a different and more specific way than the better-known pH. Because Ka produces extremely wide-ranging values, pKa ( $pK_{a}$ )—the negative logarithm (base 10) of Ka—is often used to simplify the range of acid strength values. If all of this is twisting your brain a little, here’s some good news: it’s actually pretty easy to figure out Ka from pKa (or pKa from Ka) with a scientific calculator, or to get a decent estimate without a calculator. ^{[1]
X
Research source} And we’ll show you how to do it all!

Things You Should Know

Calculate Ka from pKa with the equation $Ka=10^{-pKa}$ .
Calculate pKa from Ka with the equation $pKa=-log(Ka)$ .
Estimate pKa from Ka (or vice versa) based on the pseudo-equation $n*10^{-m}=(m-1).(10-n)$ .

Section 1 of 4:

Calculating Ka from pKa

Download Article

1
Use the equation $Ka=10^{-pKa}$ for this conversion. pKa is defined as the negative logarithm (-log) of Ka, which means you calculate pKa with the calculation $pKa=-log(Ka)$ . Solving instead for Ka requires you to raise both sides of the equation by exponents of 10: ^{[2]
X
Research source}
- $10^{pKa}=10^{-log(Ka)}$
- $10^{-pKa}=10^{log(Ka)}$
- $10^{-pKa}=Ka$ → $Ka=10^{-pka}$
- For this example, we’ll say $pKa=14$ (which is in fact the pKa for plain water).
2
Enter the right side of the equation in your scientific calculator. Using a scientific calculator varies a bit by model and type (for both online and physical calculators ), but the buttons are generally similar. ^{[3]
X
Research source} For this article, we’ll use the online scientific calculator that appears when you Google “ scientific calculator .”
- Type in $10$ .
- Press the $x^{y}$ button.
- Type $-14$ in the superscript box.
- Press the $=$ button.
Advertisement
3
Translate the answer $1e-14$ . The result you get may not appear in the format you expect, but it is the right answer. Simply substitute $*10$ for $e$ and raise $-14$ to superscript:
- $1e-14$ equals $1*10^{-14}$ .
- So a pKa of $14$ equals a Ka of $1*10^{-14}$ .
- In some cases, your calculator may provide the answer in decimal form, such as $Ka=0.00072$ instead of its equivalent $Ka=7.2*10^{-4}$ . The latter format is typically how Ka is represented, however.

Section 2 of 4:

Calculating pKa from Ka

Download Article

1
Do this conversion with the equation $pKa=-log(Ka)$ . pKa exists largely as a matter of convenience, since the Ka of acids are unwieldy values like $1.54*10^{-2}$ and $1.34*10^{-5}$ . However, converting to the negative logarithm (-log) of these values creates much more manageable figures like $1.81$ and $4.87$ .
- Converting to the -log means that a lower pKa value indicates a stronger acid, as opposed to the Ka, in which a higher Ka value indicates a stronger acid.
- In this example, let’s make $Ka=4*10^{-4}$ (nitrous acid).
2
Input the right side of the equation in a scientific calculator. As with our pKa to Ka conversion, we’ll assume you’re using Google search’s scientific calculator :
- Press the $-$ button.
- Press the $log$ button.
- Enter $4*10$ inside the parentheses.
- Press the $x^{y}$ button.
- Enter $-4$ in the superscript box.
- Press the $=$ button.
For the example $-log(4*10^{-4})$ , your answer should be $3.4$ . So in this case $pKa=3.4$ .

Section 3 of 4:

Can I find Ka (or pKa) without a calculator?

Download Article

You can get a quick estimate that may help on a multiple-choice exam. The trick is to use the “equation” ^{[4]
X
Research source} $n*10^{-m}=(m-1).(10-n)$ :
- Finding an estimate of pKa from Ka is easier. Say, for example, Ka equals $2.33*10^{-11}$ :
  - Based on this Ka and the “equation” given above, $n=2.33$ and $m=11$ . Round $n$ to a single digit if needed (2 in this case), then plug these into the second half of the “equation.”
  - $(11-1).(10-2)$ → $10.8$ .
  - Your estimate of Ka is 10.8, while the actual answer is 10.63.
- Estimating Ka from pKa (let’s say it equals 10.63) is a bit trickier and less accurate:
  - Round to a single digit after the decimal as needed: 10.63 → 10.7
  - Based on the $(m-1).(10-n)$ half of the “equation,” add 1 to the 10 (from 10.7) to get $m$ and subtract the 7 (from 10.7) from 10 to get $n$ ; so $m=11$ and $n=3$ .
  - Plug the results (m=11 & n=3) into the first half of the “equation”: $3*10^{-11}$ is your estimate for Ka, while the actual answer is $2.33*10^{-11}$ .

Section 4 of 4:

Sample Problems

Download Article

1
What is Ka if pKa equals 3.14?
- $Ka=10^{-pKa}$
- $Ka=10^{-3.14}$
- $Ka=0.00072$ → $Ka=7.2*10^{-4}$
2
What is Ka if pKa equals 11.62?
- $Ka=10^{-pKa}$
- $Ka=10^{-11.65}$
- $Ka=2.2e^{-12}$ → $Ka=2.2*10^{-12}$ ^{[5]
  X
  Research source}
3
What is pKa if Ka equals $2.33*10^{-11}$ ?
- $pKa=-log(Ka)$
- $pKa=-log(2.33*10^{-11})$
- $pKa=10.63$ ^{[6]
  X
  Research source}
4
What is pKa if Ka equals $6.46*10^{-5}$ ?
- $pKa=-log(Ka)$
- $pKa=-log(6.46*10^{-5})$
- $pKa=4.19$
5
Estimate pKa if Ka equals $5.6*10^{-10}$ .
- Using $n*10^{-m}=(m-1).(10-n)$ , plug 5 (from 5.6) in as $n$ and 6 (from 5.6) in as $m$ in the second half of the “equation.” ^{[7]
  X
  Research source}
- (10-1).(10-6) → 9.4. The accurate result for PKa is 9.25.