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pH calculation questions » finding pKa of weak acid

20 mL of 0.1 M solution of weak acid was mixed with 8  mL 0.1 M solution of NaOH. Measured pH was 5.12. Calculate pKa.

In the case of not-so-weak acids you can assume the neutralization reaction is quantitative (all of the strong base reacts with the weak acid) and the pH of the solution is described by Henderson-Hasselbalch equation:

Henderson-Hasselbalch equation, eq. 15.215.2

All you have to do is to find out concentrations of A- and HA. However, it is worth of noting here, that you can save part of the calculations, replacing concentrations with numbers of moles - volume is the same for both substances so it cancels out.

Solution was prepared using 20×0.1=2 mmol of acid and 8×0.1=0.8 mmol of strong base. If the reaction was quantitative after the neutralization there was 1.2 mmol of acid HA left and 0.8 mmol of A-. Inserting these values into Henderson-Hasselbalch equation gives 5.12=pKa+log(0.8/1.2). Solving for pKa you get pKa=5.12-log(0.8/1.2)=5.12+0.18=5.30.

pH calculator can help you check this result. Enter 5.3 as pKa, 0.1 as concentration of acid, select sodium hydroxide as a base, enter 0.1 as its concentration, finally select Ca+Cb+Va+Vb as a way of expressing solution composition and enter 20 and 8 as acid and base solutions volumes - and the pH displayed will be 5.12, confirming the result.

Note that for strong or very weak acids and/or for very diluted solutions this method may give wrong results - when pH is further changed by dissociation or hydrolyzis or when the water autodissociation can't be neglected.

If you want to check your skill at solving similar questions, please visit www.chemistry-quizzes.info and select problems from the Acid/base equilibrium section. To check your answers you will need to register - for free.

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