Question

Consider a buffered solution was (weak acid] > [conjugate base). How is the pH of the solution related to the pK_avalue of the weak acid? If (conjugate base] > (weak acid), how is pH related to pK_a?

Short answer

When $\mathbf{\left[}\mathit{W}\mathit{e}\mathit{a}\mathit{k}\mathit{a}\mathit{c}\mathit{i}\mathit{d}\mathbf{\right]}\mathbf{>}\mathbf{\left[}\mathit{C}\mathit{o}\mathit{n}\mathit{j}\mathit{u}\mathit{g}\mathit{a}\mathit{t}\mathit{e}\mathit{b}\mathit{a}\mathit{s}\mathit{e}\mathbf{\right]}\mathbf{-}\mathit{p}\mathit{H}\mathbf{<}\mathit{p}{\mathit{K}}_{\mathbf{a}}$

When $\mathbf{\left[}\mathit{W}\mathit{e}\mathit{a}\mathit{k}\mathit{a}\mathit{c}\mathit{i}\mathit{d}\mathbf{\right]}\mathbf{<}\mathbf{\left[}\mathit{C}\mathit{o}\mathit{n}\mathit{j}\mathit{u}\mathit{g}\mathit{a}\mathit{t}\mathit{e}\mathit{b}\mathit{a}\mathit{s}\mathit{e}\mathbf{\right]}\mathbf{-}\mathit{p}\mathit{H}\mathbf{>}\mathit{p}{\mathit{K}}_{\mathbf{a}}$

Step-by-step solution

Equation of Henderson-Hasselbalch equation 

The equation of Henderson-Hasselbalch equation can be denoted as,

$pH=p{K}_a+\log \frac{\left[conjugatebase\right]}{\left[acid\right]}$

Log term is negative and positive 

When $\left[weakacid\right]>\left[conjugatebase\right]$then $\frac{\left[base\right]}{\left[acid\right]}<1,\log \frac{\left[base\right]}{\left[acid\right]}<0$

When the log term is negative $pH<p{K}_a.$

When $\left[weakacid\right]<\left[conjugatebase\right]$then $\frac{\left[base\right]}{\left[acid\right]}>1,\log \frac{\left[base\right]}{\left[acid\right]}>0$

When the log term is positive $pH>p{K}_a.$