Question

Design a device that uses an electrochemical cell to determine the amount of Cu2+ in a sample of water. Describe, in detail, the construction and the theory of operation of your device. If you areable to measure voltage with one-millivolt accuracy, what will the uncertainty in your measured concentration?

Answer 1

An electrochemical (or galvanic) cell, also known as a battery, is a device that produces an electric current as the result of an electron transfer reaction. Such electron transfer reactions are also known as oxidation-reduction, or redox, reactions. Electron transfer occurs as one substance is oxidized, or loses electrons, while another substance is reduced, or gains electrons. For example, if a piece of zinc metal were immersed in a solution containing copper(II) ions, the zinc would spontaneously lose electrons while the Cu(II) would spontaneously gain electrons. This process can be expressed as two half-reactions that sum to yield the overall reaction: 1st half rxn. Zn (s) --> Zn+2 (aq) + 2 e2nd half rxn. Cu+2 (aq) + 2 e- --> Cu (s) overall net rxn. Zn (s) + Cu+2 (aq) --> Cu (s) + Zn+2 (aq) Any spontaneous redox reaction can be harnessed to produce electrical energy under the right conditions. The problem with simply dropping a piece of zinc metal into a solution of Cu(II) is that the electrons provided by the zinc move directly to the aqueous Cu(II) ions without doing any work. In order to create a useful battery, the two half reactions must be physically separated so that the electrons will flow through an external circuit as shown in Figure 1. A salt bridge is necessary for charge balance: in this case sulfate ions flow from the copper to the zinc compartment. The electrochemical cell shown in Figure 1 can be represented by the following shorthand: Zn (s) !Zn+2 (aq) !! Cu+2 (aq) ! Cu (s)

In this type of “line notation”, the components at the site of oxidation (the anode) are listed on the left; at the site of reduction (the cathode), on the right; and central double vertical lines represent the salt bridge. A single vertical line indicates a phase difference.

Electrons that are generated at the anode of an electrochemical cell are driven toward the cathode by a thermodynamic tendency called the electromotive force (emf), measured in volts. The emf is also called the cell potential and depends on both the identities of the substances involved in the redox reactions as well as their concentrations. By convention, the standard cell potential Eo cell corresponds to cell voltages under standard state conditions- gases at 1 atm pressure, solutions at 1 M concentrations, and temperatures at 25o C. The overall cell potential can be regarded as the sum of the two half-cell potentials: Ecell = Ecathode – Eanode (1) Half-cell potentials are assigned relative to a reference, the standard hydrogen half-reaction that by convention has a standard reduction potential of exactly 0.000 Volts: 2 H+ (1 M) + 2 e- --> H2 (1 atm) Eo red= 0.000 V Thus, creation of a voltaic cell that has the following half-reactions allows calculation of the Eox of Zn via the measured Eo cell: Zn (s) --> Zn+2 (aq) + 2 e- Eo anode =? 2 H+ (1 M) + 2 e- --> H2 (1 atm) Eo cathode= 0.000 V net rxn: Zn (s) + 2 H+ (aq) --> H2 (g) + Zn+2 (aq) Eo cell= 0.76 V

Equation (1) above allows calculation of the standard reduction potential of Zn as follows: Ecell = 0.76 V = Ecathode – Eanode = 0 V – (Eanode) Note that by convention, half-cell potentials are listed as reductions. Thus, Zn+2 (aq) + 2 e- --> Zn (s) Eo red= -0.76 V By measuring other standard-cell emf values containing the standard hydrogen half-reaction, we can establish a series of standard potentials for other half-reactions. Cell potentials for product-favored electrochemical reactions are positive. The exact relationship between the Gibbs free energy and the cell potential is as follows: ΔGo rxn = -nFEo (2) where n is the number of electrons transferred in the balanced redox reaction and F is the Faraday constant (96,500 J/V-mol), the charge on a mole of electrons. Thus, to achieve a favorable free energy change (a negative value), the cell potential must be positive.