# pH calculations for buffers, mixtures of acids and bases

Part 1: What is the pH of a solution of 1M HCO3 and 1M CO3?

Part 2: What is the pH if it was mixed with an equal volume of water?

Part 3: What is the pH if it was mixed with an equal volume of 0.001 M HCl?

Part 4: What is the pH if it was mixed with an equal volume of 0.001 M NaOH?

#### Solution Preview

PART ONE:

"What is the pH of a solution of 1M HCO3 and 1M co3?"

Step 1:

To calculate the pH of the solution, you will need to understand the Henderson-Hasselbach equation, and how buffers work, in general. You have probably learned that a "buffer" is a solution that is composed of a mixture of weak acid and weak base. The pH of the solution is determined by (a) the ratio of weak acid and weak base in the solution, and (b) the pKa of the weak acid. The relation of these factors to one another is defined by the "Henderson-Hasselbach equation" (for convenience, I will call this the "HH equation" from now on.)

The HH equation is useful in calculations involving situations such as (i) titrations of weak acids or bases with strong acids or bases, (ii) preparation of buffers in the laboratory, (iii) calculating the theoretical pH of solutions of weak acids/bases, (iv) etc. The equation is as follows:

pH = pKa + log ([A-]/[HA]), where

pH = the pH of the solution

pKa = -log (Ka)

[A-] = the concentration of weak base in the

solution

[HA]=the concentration of weak acid in the

solution

Step 3: Identify which species is the "weak acid", and which is the "weak base". Write a chemical equation to describe the relationship between the two. (Writing the chemical equation helps out with answering PART THREE, below, and also helps you understand which species is acid vs. base.)

In the problem you have given, the species HCO3(1-) is the "weak acid", and

CO3(2-) is the "weak base".

The chemical equation for the equilibrium between weak acid and weak base would be:

HCO3(1-) * H(1+) + CO3(2-)

Step 4: Look up the pKa of your weak acid.

pKa values can be found in textbooks. Many professors will provide pKa (or Ka) values/tables ...

#### Solution Summary

This solution walks you through the answer to a type of "buffer" problem commonly found on chemistry, biology, and biochemistry exams and laboratory assignments. The solution is laid out in a step by step fashion and includes both a long answer and a time-saving short-cut that you can use when the buffer is to made at a a certain pH. After reading and trying this problem, you should be better able to understand buffer calculations, find pKa values, understand and use the Henderson-Hasselbach equation, and calculate the pH of buffers under different situations. Take the steps shown and apply them to a problem from your textbook or assignment.