Final answer:
To determine the molarity of Pb²⁺ in a galvanic cell, the provided cell potential and the standard reduction potentials of lead and nickel are used within the Nernst equation framework. Solving the equation with the given cell potential allows us to find the concentration of Pb²⁺.
Step-by-step explanation:
The question asks to determine the molarity of the lead ion (Pb²⁺) in a lead-nickel galvanic cell, based on the standard reduction potentials of lead and nickel and the given cell potential of -0.0200 V. To answer this question, we can use the Nernst equation, which relates the reduction potential of an electrochemical cell to the concentrations of the ions involved.
The Nernst equation is expressed as:
E = E° - (RT/nF) * ln(Q)
Where:
- E is the cell potential
- E° is the standard cell potential
- R is the ideal gas constant (8.314 J/(mol·K))
- T is the temperature in Kelvin (298 K)
- n is the number of moles of electrons exchanged
- F is the Faraday's constant (96485 C/mol)
- Q is the reaction quotient
For the lead-nickel cell, we are looking at the reaction:
Pb²⁺ (aq) + Ni (s) → Pb (s) + Ni²⁺ (aq)
The standard cell potential (E°) is obtained by subtracting the standard reduction potential of the anode (nickel) from that of the cathode (lead). However, since we are dealing with a galvanic cell under non-standard conditions, we must use the actual cell potential (E), which is provided as -0.0200 V.
By re-arranging the Nernst equation and substituting the given values, we can solve for the unknown concentration of Pb²⁺.