alculate the cell voltage for a Daniell cell Zn(s) + Cu2+(aq) 🡪 Zn2+(aq) + Cu(s) at 50 °C, Zn2+ concentration: 10-3 M & Cu2+ concentration: 10-1 M
Question
alculate the cell voltage for a Daniell cell Zn(s) + Cu2+(aq) 🡪 Zn2+(aq) + Cu(s) at 50 °C, Zn2+ concentration: 10-3 M & Cu2+ concentration: 10-1 M
Solution
To calculate the cell voltage for a Daniell cell, we need to use the Nernst equation. The Nernst equation is used to calculate the potential of an electrochemical cell or to find out the concentration of one of the components of the cell. The Nernst equation is as follows:
E = E° - (RT/nF) * ln(Q)
Where:
- E is the cell potential
- E° is the standard cell potential
- R is the gas constant (8.314 J/(mol*K))
- T is the temperature in Kelvin
- n is the number of moles of electrons transferred in the redox reaction
- F is the Faraday constant (96485 C/mol)
- Q is the reaction quotient
For a Daniell cell, the standard cell potential E° is 1.10 V. The reaction is Zn(s) + Cu2+(aq) → Zn2+(aq) + Cu(s), so n = 2. The temperature is 50 °C, which is 273 + 50 = 323 K. The reaction quotient Q is [Zn2+]/[Cu2+] = 10^-3 M / 10^-1 M = 0.01.
Substituting these values into the Nernst equation gives:
E = 1.10 V - (8.314 J/(mol*K) * 323 K / (2 * 96485 C/mol)) * ln(0.01)
Solving this equation will give you the cell voltage at 50 °C with the given concentrations.
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