A Cu/Cu2+ concentration cell has a voltage of 0.22 V at 25 ∘C. The concentration of Cu2+ in one of the half-cells is 1.6×10−3 M . What is the concentration of Cu2+ in the other half-cell? (Assume the concentration in the unknown cell to be the lower of the two concentrations.)
A Cu/Cu2+ concentration cell has a voltage of 0.22 V at 25 ∘C.
The concentration of Cu2+ in one of the half-cells is 1.6×10−3 M .
What is the concentration of Cu2+ in the other half-cell? (Assume the concentration in the unknown cell to be the lower of the two concentrations.)
E°cell = 0, sinc E Cu/Cu+2 is the same for both sides
When the cell is NOT under standard conditions, i.e. 1M of each reactants at T = 25°C and P = 1 atm; then we must use Nernst Equation.
The equation relates E°cell, number of electrons transferred, charge of 1 mol of electron to Faraday and finally, the Quotient retio between products/reactants
The Nernst Equation:
Ecell = E0cell - (RT/nF) x lnQ
In which:
Ecell = non-standard value
E° or E0cell or E°cell or EMF = Standard EMF: standard cell
potential
R is the gas constant (8.3145 J/mol-K)
T is the absolute temperature = 298 K
n is the number of moles of electrons transferred by the cell's
reaction
F is Faraday's constant = 96485.337 C/mol or typically 96500
C/mol
Q is the reaction quotient, where
Q = [C]^c * [D]^d / [A]^a*[B]^b
pure solids and pure liquids are not included. Also note that if we use partial pressure (for gases)
Q = P-A^a / (P-B)^b
substitute in Nernst Equation:
Ecell = E° - (RT/nF) x lnQ
0.22 = 0 - (8.314*298)/(2*96500) * ln(Q)
Q = [Cu+2]ox / [Cu+2]red
0.22 = 0 - (8.314*298)/(2*96500) * ln([Cu+2]ox / [Cu+2]red)
0.22 = -0.01283 * ln([Cu+2]ox / (1.6*10^-3))
0.22 /-0.01283 = ln([Cu+2]ox / (1.6*10^-3))
exp(-17.147) = [Cu+2]ox / (1.6*10^-3))
[Cu+2]ox = (1.6*10^-3)*exp(-17.147) = 5.79*10^-11 --> 5.8 *10^-11 M
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