The electrochemical cell shown below is a concentration cell.M | M2+ (...
-3 solution of Mx2) | M
Explanation:
A concentration cell is a type of electrochemical cell where the same material is present in both half-cells, but at different concentrations. In this case, the material is M2, and it is present in both half-cells, but at different concentrations.
The anode half-cell is M | M2 (saturated solution of a sparingly soluble salt, Mx2). This means that M is the anode, and it is in contact with a saturated solution of Mx2, which means that the concentration of M2 ions is very high. At the anode, M undergoes oxidation and loses electrons to become M2+. This reaction is represented as:
M → M2+ + 2e-
The cathode half-cell is M2 (0.001 mol dm-3 solution of Mx2) | M. This means that M2 is the cathode, and it is in contact with a solution of Mx2, which has a concentration of 0.001 mol dm-3. At the cathode, M2+ undergoes reduction and gains electrons to become M. This reaction is represented as:
M2+ + 2e- → M
Overall, the cell reaction is:
M → M2+ + 2e- (anode half-cell)
M2+ + 2e- → M (cathode half-cell)
-----------------------
M → M (cell reaction)
The cell potential can be calculated using the Nernst equation:
Ecell = E°cell - (RT/nF) ln Q
where E°cell is the standard cell potential, R is the gas constant, T is the temperature, n is the number of electrons transferred in the cell reaction, F is the Faraday constant, and Q is the reaction quotient.
Since this is a concentration cell, the standard cell potential is zero, so E°cell = 0. The reaction quotient can be calculated using the concentrations of M2+ in the two half-cells:
Q = [M2+]cathode / [M2+]anode
= (0.001 mol dm-3) / (very high concentration)
Since the concentration of M2+ in the anode half-cell is very high, we can assume that it is constant and equal to the solubility product of Mx2. Therefore, Q = Ksp.
The solubility product of Mx2 is not given, so we cannot calculate Q or the cell potential. However, we can say that the cell potential will be negative, since the reaction is non-spontaneous (E°cell = 0) and the anode half-cell has a higher concentration of M2+. The cell will therefore require an external voltage source to operate.
The electrochemical cell shown below is a concentration cell.M | M2+ (...
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