Instrumental acid-base titrations use a pH meter to monitor the changes in pH and volume. The equivalence point is found from the volume at which the curve has the steepest slope.

(a) Use Figure 19.7 to calculate the slope $\mathbf{\Delta pH}\mathbf{/}\mathbf{\Delta V}$ for all pairs of adjacent points and to calculate the average volume ${\mathbf{\text{(V}}}_{\mathbf{\text{avg}}}\mathbf{\text{)}}$ for each interval.

(b)Plot $\mathbf{\Delta pH}\mathbf{/}\mathbf{\Delta V}$vs. ${\mathbf{\text{V}}}_{\mathbf{\text{avg}}}$ to find the steepest slope, and thus the volume at the equivalence point. (For example, the first pair of points gives localid="1663707962429" $\mathbf{\Delta pH}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{22}\mathbf{,}\mathbf{\Delta V}\mathbf{=}\mathbf{10}\mathbf{.}\mathbf{00}\mathbf{mL}$; hence, localid="1663702845904" $\mathbf{\Delta pH}\mathbf{/}\mathbf{\Delta V}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{022}{\mathbf{mL}}^{\mathbf{-}\mathbf{1}}$, and localid="1663703054756" ${\mathbf{\text{V}}}_{\mathbf{\text{avg}}}\mathbf{\text{= 5.00 mL}}$).

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