Many students often approach the concept of pKa with dread because it requires significantly more math than most other aspects of chemistry. However, students need to familiarize themselves with pKa because most AP Chemistry and inorganic chemistry exams will test pKa calculations and concepts. The pKa of a solution describes the acidity of that solution, based on the inherent properties of the acid involved and the concentration of that acid. The pKa should not be confused with the pH; they are separate but related concepts.
Define the acid and its conjugate base in the relevant reaction. The acid is the compound with the extra hydrogen, and its conjugate base is the compound without that hydrogen. For instance, acetic acid has a formula of HC2H3O2; its conjugate base loses the initial hydrogen to get a chemical formula of C2H3O2.
Write down all of the information that the problem gives you. To successfully solve for the pKa, the problem should include the pH of your solution, the concentration of the relevant acid and the concentration of its conjugate base. You should already have identified the acid and its conjugate base in Step 1.
Divide the concentration of acid by the concentration of the conjugate base. For a solution that contains 1M acetic acid and 0.5M acetate, you would divide 1 by 0.5 to get 2.
Take the log of the number that you got in Step 3. Log is short for logarithm, which is a math function just like addition or subtraction. However, you will almost always need a calculator to find logs. In this example, you would use a calculator to take the log of 2 and get 0.30.
Add the number that you got in Step 4 to the pH given to you in the problem. If your solution has a given pH of 1.3, add 0.3 to 1.3 to get a pKa of 1.6.
Check your work. The most important formula to remember is that the pKa = pH + log(Acid/Base), better known as the Henderson-Hasselbalch equation. As long as your numbers do not contradict the Henderson-Hasselbalch equation, you have correctly calculated the pKa of your solution.
Make sure that you correctly identify the acid and its conjugate base. Switching these will give you a completely wrong answer.