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Calculate the pH of a liter of solution that contains 0.1 mole of acetic acid and 0.1 mole of sodium acetate. If sodium hydroxide pellets is added to the solution that would make the solution 0.02 M in NaOH if the buffer was not present, what is the new pH of the solution?
Solution:
A buffer solution is a solution of weak acid and its salt or a solution of weak base and its salt. The purpose of making a buffer solution is to prevent the rapid change of pH if more acid or base is added to the solution.
Since acetic acid is a weak acid, then it is partially ionized into acetate ion and hydrogen ion as follows
In a liter of solution at equilibrium,
where x is moles of HC2H3O2 that partially ionized. The ionization constant for HC2H3O2 is given by the equation
From Table of Ionization Constants of Acids and Bases, Ka = 1.8 x 10-5 for acetic acid. The amount of HC2H3O2 that partially ionized is
If 0.1 moles of sodium acetate which is completely ionized into 0.1 moles of sodium ion and 0.1 moles of acetate ion is added to the solution, then the above equation becomes
The acetate ion from sodium acetate will be added to the acetate ion from acetic acid. Since the value of Ka is less than 1 x 10-3, then we can neglect x at the numerator and denominator as follows
Hence, the concentration of hydrogen ion is
Therefore, the pH of a buffer solution is
If sodium hydroxide pellets is added to buffer solution, then acetic acid will react with sodium hydroxide to form sodium acetate. The amount of acetic acid will decrease while the amount of acetate ion will increase. From the equation of buffer solution
if 0.02 M NaOH solution or 0.02 moles of NaOH pellets is added and assuming that the increase in volume of solution is negligible, then the above equation becomes
Since the value of Ka is less than 1 x 10-3, then we can neglect x at the numerator and denominator as follows
Hence, the concentration of hydrogen ion is
Therefore, the pH of final solution is
As you can see that there's a slight change of pH of buffer solution after the addition of sodium hydroxide pellets. Without buffer solution, the pH of 0.02 M NaOH solution is 12.30.