EMF of Galvanic Cells
EMF of Galvanic Cells
Electromotive force (EMF) is a measure of the energy that causes current to flow through a circuit. In the context of electrochemistry, the EMF of a galvanic cell (also known as a voltaic cell) is the voltage developed by the chemical reaction occurring in the cell. A galvanic cell harnesses the energy from a spontaneous redox reaction to generate electrical energy.
Understanding Galvanic Cells
A galvanic cell consists of two half-cells, each containing an electrode and an electrolyte. The two electrodes are connected by an external circuit, while the electrolytes are connected by a salt bridge that allows ions to flow between the half-cells to maintain charge balance.
The EMF of the cell is determined by the difference in reduction potentials of the two half-cell reactions. The electrode with the higher reduction potential acts as the cathode (where reduction occurs), and the electrode with the lower reduction potential acts as the anode (where oxidation occurs).
Standard Electrode Potentials
The standard electrode potential (E°) is the voltage that a half-cell, under standard conditions (1 M concentration, 1 atm pressure, and 25°C), develops when combined with the standard hydrogen electrode (SHE), which is assigned a potential of 0.00 V. The standard EMF of a galvanic cell can be calculated using the standard electrode potentials of the two half-cells.
Calculating EMF
The EMF of a galvanic cell can be calculated using the Nernst equation, which relates the EMF of the cell to the standard electrode potentials and the activities (or concentrations) of the reactants and products.
For a cell reaction represented as: [ aA + bB \rightarrow cC + dD ]
The Nernst equation is given by: [ E = E^\circ - \frac{RT}{nF} \ln Q ]
Where:
- ( E ) is the EMF of the cell.
- ( E^\circ ) is the standard EMF of the cell.
- ( R ) is the universal gas constant (8.314 J/mol·K).
- ( T ) is the temperature in Kelvin.
- ( n ) is the number of moles of electrons transferred in the reaction.
- ( F ) is the Faraday constant (96485 C/mol).
- ( Q ) is the reaction quotient, which is the ratio of the activities of the products to the reactants.
Differences and Important Points
| Feature | Anode | Cathode |
|---|---|---|
| Reaction Type | Oxidation | Reduction |
| Electron Flow | Electrons flow away from the anode | Electrons flow towards the cathode |
| Sign of Electrode Potential | Negative | Positive |
| Connection to External Circuit | Negative terminal | Positive terminal |
Important Points:
- The EMF of a galvanic cell is positive for spontaneous reactions.
- The greater the difference in standard electrode potentials, the higher the EMF of the cell.
- The EMF decreases as the cell operates because the concentrations of reactants decrease and products increase, affecting the reaction quotient ( Q ).
Examples
Example 1: Standard EMF Calculation
Consider a galvanic cell made of a zinc electrode in a ZnSO₄ solution and a copper electrode in a CuSO₄ solution. The standard electrode potentials are:
- ( E^\circ_{\text{Zn}^{2+}/\text{Zn}} = -0.76 ) V
- ( E^\circ_{\text{Cu}^{2+}/\text{Cu}} = +0.34 ) V
The standard EMF of the cell is: [ E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}} ] [ E^\circ_{\text{cell}} = 0.34 \, \text{V} - (-0.76 \, \text{V}) ] [ E^\circ_{\text{cell}} = 1.10 \, \text{V} ]
Example 2: Nernst Equation Application
For the same zinc-copper cell, if the concentrations are not standard (1 M), we can use the Nernst equation to calculate the EMF. Suppose the concentrations are 0.01 M Zn²⁺ and 0.1 M Cu²⁺, and the temperature is 298 K (25°C).
The reaction quotient ( Q ) is: [ Q = \frac{[\text{Cu}^{2+}]}{[\text{Zn}^{2+}]} = \frac{0.1}{0.01} = 10 ]
Using the Nernst equation: [ E = E^\circ - \frac{RT}{nF} \ln Q ] [ E = 1.10 \, \text{V} - \frac{(8.314 \, \text{J/mol·K})(298 \, \text{K})}{(2)(96485 \, \text{C/mol})} \ln 10 ] [ E = 1.10 \, \text{V} - \frac{(8.314)(298)}{(2)(96485)}(2.303) ] [ E \approx 1.10 \, \text{V} - 0.059 \, \text{V} ] [ E \approx 1.04 \, \text{V} ]
The EMF of the cell under these non-standard conditions is approximately 1.04 V.
Understanding the EMF of galvanic cells is crucial for predicting the voltage output of batteries and for designing electrochemical cells for various applications. The Nernst equation is a powerful tool for calculating the EMF under any conditions, taking into account the effect of temperature and concentration on the cell's potential.