Q19.126CP - Chemistry: Molecular Nature Of Matter And Change

Question

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 $\mathbf{\Delta pH}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{22}\mathbf{,}\mathbf{\Delta V}\mathbf{=}\mathbf{10}\mathbf{.}\mathbf{00}\mathbf{mL}$; hence, $\mathbf{\Delta pH}\mathbf{/}\mathbf{\Delta V}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{022}{\mathbf{mL}}^{\mathbf{-}\mathbf{1}}$ , and ${\mathbf{\text{V}}}_{\mathbf{\text{avg}}}\mathbf{\text{ = 5.00 mL}}$).

Step-by-Step Solution

Answer

(a) The slope $\left(\frac{\Delta pH}{\Delta V}\right)$  and average volume $\left({\text{V}}_{\text{avg}}\right)$ is plotted in a table given below.

(b) The graph for $\left(\frac{\mathrm{\Delta pH}}{\mathrm{\Delta V}}\right)$ vs. $\left({\text{V}}_{\text{avg}}\right)$ is as follows –

Concept Introduction

A  pH meter is used in instrumental acid-base titration to track changes in pH  and volume. The volume at which the curve has the sharpest slope is used to find the equivalency.

Calculation for slope and volume

(a) A table is prepared for recording the values of $\left(\frac{\Delta pH}{\Delta V}\right)$  and ${\text{V}}_{\text{avg}}$. The table for volume and slope is as follows –

Therefore, the volume and slope are obtained.

Plotting the graph

(b)

The graph is plotted by taking  $\left(\frac{\mathrm{\Delta pH}}{\mathrm{\Delta V}}\right)$on the y-axis and average volume on the x axis.

The graph is as follows –

Therefore, the graph for sharpest slope and volume is obtained.