The reaction described by the equation
Zn + Hg2Cl2 <--> 2Hg +Zn+2 + 2Cl is run on electrochemical cell. The E^0 of the cell at 25 degrees C is 1.03V. In the same cell, [Cl-]=.10 M and [Zn+2] is unknown, and the measured cell voltage is 1.21V. Compute the value of [Zn+2] in the cell solution.
Ecell = Eocell - (0.0592/2)log(Q)
Ecell you know.
Eocell you know.
Q = (products)/(reactants) and each coefficent becomes an exponent.
Solve for the one unknown.
To compute the value of [Zn+2] in the cell solution, we can use the Nernst equation. The Nernst equation relates the measured cell voltage (E) to the standard cell voltage (E^0) and the concentration of the ions involved in the electrochemical reaction.
The Nernst equation is given as:
E = E^0 - (RT/nF) * ln(Q)
Where:
- E is the measured cell voltage
- E^0 is the standard cell voltage
- R is the gas constant (8.314 J/(mol*K))
- T is the temperature in Kelvin (25 degrees C = 298K)
- n is the number of electrons transferred in the balanced chemical equation (in this case, it is 2, because 2 electrons are transferred)
- F is the Faraday constant (96,485 C/mol)
- ln(Q) is the natural logarithm of the reaction quotient
The reaction quotient (Q) is given by:
Q = ([Zn+2]/[Hg2+2]) * [Cl-]^2
Given in the problem that [Cl-] = 0.10 M, we can substitute this value into the expression for Q.
Now, let's plug in the known values into the Nernst equation:
1.21V = 1.03V - [(8.314 J/(mol*K))/ (2 * 96,485 C/mol) * ln(([Zn+2]/[Hg2+2]) * (0.10 M)^2)
To solve for [Zn+2], we need to rearrange the equation and isolate the term that includes [Zn+2].
1.21V - 1.03V = - (8.314 J/(mol*K))/ (2 * 96,485 C/mol) * ln(([Zn+2]/[Hg2+2]) * (0.10 M)^2
0.18V = - (8.314 J/(mol*K))/ (2 * 96,485 C/mol) * ln(([Zn+2]/[Hg2+2]) * (0.10 M)^2
Now, we can rearrange the equation to solve for [Zn+2].
(ln(([Zn+2]/[Hg2+2]) * (0.10 M)^2) = - (0.18V * 2 * 96485 C/mol) / (8.314 J/(mol*K))
Take the natural logarithm of both sides:
(([Zn+2]/[Hg2+2]) * (0.10 M)^2) = e^(- (0.18V * 2 * 96485 C/mol) / (8.314 J/(mol*K)))
Now, isolate [Zn+2]. Divide both sides by ((0.10 M)^2), and multiply both sides by [Hg2+2]:
[Zn+2] = [Hg2+2] * e^(- (0.18V * 2 * 96485 C/mol) / (8.314 J/(mol*K))) / (0.10 M)^2
Substitute the remaining known value of [Cl-] and solve for [Zn+2].
Note: Make sure to check the units in the equation and convert them to consistent units if necessary.