Final answer:
To calculate the pH of a 0.100 M NaCH3CO2 solution, the Henderson-Hasselbalch equation is used, along with the given Ka value for acetic acid. The pKa is calculated from the Ka, and the concentration of the acetate ion is considered given the 0.100 M concentration of sodium acetate.
Step-by-step explanation:
To calculate the pH of a 0.100 M NaCH3CO2 solution, we can use the formula for the ionization of acetic acid in water, understanding that sodium acetate (NaCH3CO2) will dissociate completely into Na+ and CH3CO2− in solution. Since acetic acid (CH3CO2H) is a weak acid, we can assume its salt (sodium acetate) will hydrolyze to form the weak acid and hydroxide ions (OH−).
Utilizing the hydrolysis of the acetate ion and the given Ka value for acetic acid, we will use the Henderson-Hasselbalch equation to calculate the solution's pH:
pH = pKa + log([A−]/[HA])
First, we find the pKa from the given Ka value:
a = −log(Ka)
pKa = −log(1.8 × 10−5)
Since the solution is 0.100 M sodium acetate, we can consider this to be the concentration of the acetate ion ([CH3CO2−]), while the concentration of acetic acid ([CH3CO2H]) is negligible due to the common ion effect. Subtituting into the equation:
pH = pKa + log([CH3CO2−])
pH = pKa + 0 since log of 1 is 0
pH = pKa