\[ \text{pKa} = \text{pH} - \log\left(\frac{\text{CB}}{\text{WA}}\right) \]
Where:
pKa is a measure of the strength of an acid in solution. It represents the negative logarithm of the acid dissociation constant (Ka), which quantifies how easily an acid dissociates into its conjugate base and hydrogen ions in water. A lower pKa value indicates a stronger acid, which more readily dissociates, while a higher pKa value indicates a weaker acid. The pKa value is crucial in chemistry for understanding the behavior of acids and bases in various chemical reactions.
pH: 4.0
Concentration of Conjugate Base (CB): 0.01 M
Concentration of Weak Acid (WA): 0.1 M
pKa: \[
4.0 - \log\left(\frac{0.01}{0.1}\right) = 4.0 - \log(0.1) = 4.0 - (-1) = 5.0
\]
pH: 7.0
Concentration of Conjugate Base (CB): 0.2 M
Concentration of Weak Acid (WA): 0.5 M
pKa: \[
7.0 - \log\left(\frac{0.2}{0.5}\right) = 7.0 - \log(0.4) \approx 7.0 - (-0.398) \approx 7.4
\]