Question

Verify the derivative in cell D7 of Figure 11-6.

Short answer

The value 0.226 in cell D7 is verified.

Step-by-step solution

Information given

The derivative in cell D7=0.226. We need to verify the value. All the information must be taken from the following table

The second number in the third column, 86.5, is the average of the second and third volumes (86.0 and 87.0) in the first column.

Derivation

To compute the first derivative, each pair of volumes need to be averaged and the quantity ΔpH/ΔV will be calculated. Between consecutive readings the change in pH is ΔpH and the change in volume is ΔV.

Calculation

The derivative ΔpH/ΔV is calculated using the above-mentioned values.

$\begin{array}{rcl}\frac{∆pH}{∆V}& =& \frac{4.626-4.400}{87-86}\\ & =& \frac{0.226}{1}\\ & =& 0.226\end{array}$