When chemists need to find the concentration of a substance dissolved in a solution, they often use a technique called titration. By adding a chemical that reacts with the solute until all of the solute has been neutralized, the chemist can determine how much was originally present -- and hence the concentration of the solution. Titration problems with acids and bases are common assignments on homework and tests in chemistry class.
Determine whether the analyte (the chemical dissolved in the solution) and the titrant (the chemical added to neutralize the solute) are strong acids or bases. An acid is a substance that gives away protons, while a base is a substance that takes up protons. If the solute is a base, the titrant will be an acid and vice versa. Hydrochloric acid, nitric acid, sulfuric acid, perchloric acid, hydrobromic acid and hydroiodic acid are the common strong acids, while lithium, sodium, potassium, rubidium, calcium, strontium and barium hydroxides are strong bases. For a list of common acids and bases, see the link in the Resources section.
Determine whether the product of the titration reaction will be a neutral salt or a basic/acidic salt. When a strong base and a strong acid react, the product is a neutral salt (a salt with pH 7); the reaction between hydrochloric acid and sodium hydroxide, for example, yields sodium chloride, which is neither basic nor acidic. A strong acid reacting with a weak base, however, produces an acidic salt, while a strong base reacting with a weak acid produces a basic salt. Titrations are hardly ever performed with a combination of a weak acid and a weak base, because it would be more difficult to find the equivalence point for this kind of titration.
Write down what you know and figure out what the problem is asking for. Usually a homework or test problem of this kind will give you the identities of the titrant and analyte, the volume of analyte and the concentration of the titrant. The problem might give you the amount of titrant needed to reach equivalence (the point where all the solute has been neutralized) and ask you to find the pH at equivalence and the concentration of the original solution, or it might give you the concentration of both titrant and solute then ask you to find the pH at each stage of the reaction. Each type of problem will require a different strategy.
Write down the balanced chemical equation for the reaction between the acid and the base (this will typically be given to you in the problem as well). Determine the ratio of the reactants using the chemical equation, i.e. how many molecules of one chemical are needed to react with one molecule of the other.
Use the data you've been given to calculate pH at each step of the reaction if the problem asks you to do so (if not, skip this step and proceed to Step 6). Depending on the identities of analyte and titrant, there are four possibilities.
1) If the analyte is a strong acid and the titrant is a strong base, the pH is just the negative log of the analyte concentration. To find the analyte concentration, subtract the number of moles of titrant added up to this point, then divide by the total volume (initial volume of analyte + volume of titrant added).
2) If the analyte is a strong base and the titrant is a strong acid, the steps you follow are the same as in (1) except that the negative log of the analyte concentration will give you the pOH instead of pH. To convert pOH to pH, subtract it from 14.
3) If the analyte is a weak acid and the titrant is a strong base, use the Henderson-Hasselbalch equation, pH = pKa + log ( [conjugate base concentration] / remaining weak acid concentration ). The amount of conjugate base is equal to the amount of titrant you've added so far; divide it by total volume to find concentration. The pKa values for many weak acids are listed in the table linked to in the Resources section.
4) If the analyte is a weak base and the titrant is a strong acid, use the other form of the Henderson-Hasselbalch equation, pOH = pKb + log ( [conjugate acid concentration] / remaining weak base concentration ). Then convert from pOH to pH by subtracting from 14.
Find the pH at equivalence if the problem asks you to do so. For a strong acid paired with a strong base, the pH at equivalence is 7. For a strong acid titrant and weak base analyte, take the number of moles of weak base originally present and divide by the new total volume (original volume of analyte + volume of titrant added to reach equivalence) to find concentration, then take the negative log of this concentration. The procedure for a strong base titrant with a weak acid analyte is the same, except that once you've taken the negative log you'll have the pOH rather than the pH, so you need to convert it to pH by subtracting it from 14.
Find the original concentration of the analyte if the problem asks you to do so. The volume of titrant added to reach equivalence multiplied by the molarity or concentration of the titrant will give you the number of moles of titrant added. The number of moles of titrant added, multiplied by the ratio between the reactants that you found in Step 4, is equal to the number of moles of analyte originally present. Divide the number of moles of analyte by original volume of analyte to find the analyte concentration.
TL;DR (Too Long; Didn't Read)
This procedure assumes a 1-to-1 ratio between acid and base in the neutralization reaction -- which is typically the kind of problem you'll see on a general chemistry quiz.
When finding concentrations at or before equivalence, take the volume of the titrant you've added into account.