Chapter 16, Problem 116DIA

Data Interpretation and Analysis

We can use electrochemical cells to measure the concentrations of certain species in solution because the voltage of the cell is sensitive to the concentrations of the reactants and products in the redox reaction associated with the cell. For example, the voltage of electrochemical cell based on the reaction ${\text{H}}_{\text{2}}(g)+{\text{Cu}}^{2+}(aq)\to 2{\text{H}}^{+}(aq)+\text{Cu}(s)$ is sensitive to both the ${\text{Cu}}^{2+}$

concentration and the ${\text{H}}^{+}$ concentration in solution. If the ${\text{H}}^{+}$ concentration is held constant, then the voltage only depends on the ${\text{Cu}}^{2+}$ concentration, and we can use the cell to measure the ${\text{Cu}}^{2+}$ concentration in an unknown solution.

When using an electrochemical cell for this purpose, chemists often make voltage measurement of several ${\text{Cu}}^{2+}$ solutions of known concentrations and construct a calibration curve, a graph that shows the relationship between voltage and concentration. The calibration curve can be used to determine the concentration of an unknown solution based on the voltage associated with that solution. The tabulated data show the measured voltage in the hydrogen/copper electrochemical cell just discussed for several different ${\text{Cu}}^{2+}$ concentrations. Examine the data and answer the questions that follow.

${\text{Cu}}^{2+}$	Voltage (V)
0.100	0.310
0.200	0.319
0.300	0.325
0.400	0.328
0.500	0.331
0.700	0.335
1.00	0.340

a. Construct a graph of the measured voltage versus the log of the copper concentration. Is the graph linear?

b. Determine the slope and $y$

-intercept of the best fitting line to the points in your graph from part a.

c. The voltage of two unknown solutions are measured and recorded. Use the slope and intercept from part b, together with the equation, $\text{voltage}=\text{slope}\times \log \left[{\text{Cu}}^{2+}\right]+y-\text{intercept}$, to determine the ${\text{Cu}}^{2+}$ concentrations of the unknown solutions.

Unknown ${\text{Cu}}^{2+}$ Solution	Voltage (V)
i	0.303
ii	0.338