Question

Two important characteristics of voltaic cells are their cell potential and the total charge that they can deliver. Which of these characteristics depends on theamount of reactants in the cell, and which one depends on their concentration?

Short answer

In summary, the cell potential of a voltaic cell depends on the concentration of reactants, as shown by the Nernst equation (\(E_{cell} = E^0_{cell} - \dfrac{RT}{nF} \ln(Q)\)). On the other hand, the total charge a voltaic cell can deliver depends on the amount of reactants present in the cell, as indicated by Faraday's law of electrolysis (\(q = n \times F \times moles \; of \; limiting \; reactant\)).

Step-by-step solution

Understanding Cell Potential

Cell potential, also known as electromotive force (EMF) or cell voltage, is the force that drives the flow of electrons through a voltaic cell, pushing the electrons from one electrode (anode) to another electrode (cathode). Cell potential depends on the concentration of reactants because it is directly related to the Gibbs free energy change of the reaction, which is affected by the concentration of the reactants involved. According to the Nernst equation, cell potential can be expressed as: \(E_{cell} = E^0_{cell} - \dfrac{RT}{nF} \ln(Q)\) where: - \(E^0_{cell}\) is the standard cell potential - R is the gas constant - T is the temperature in Kelvin - n is the number of electrons transferred in the cell (integer) - F is the Faraday constant (the charge of one mole of electrons) - Q is the reaction quotient, which depends on the concentrations of reactant and product ions in the cell As we can see from the equation, cell potential (\(E_{cell}\)) is dependent on the concentrations of reactants (involved in the value of Q), but NOT their initial amounts.

Understanding Total Charge

The total charge a voltaic cell can deliver is determined by the maximum amount of redox reaction that can occur inside the cell. The total charge of a voltaic cell depends on the number of electrons that can be transferred during the redox reaction and the number of moles of reactants. Mathematically, the total charge, q, can be calculated from Faraday's law of electrolysis: \(q = n \times F \times moles \; of \; limiting \; reactant\) In this equation, n is the number of electrons transferred per mole of reactant, F is the Faraday constant, and the moles of limiting reactant are directly related to the amount of reactants present in the cell. From the equation, it is evident that the total charge a voltaic cell can deliver depends on the amount of reactants present in the cell, NOT their concentrations.

Conclusion

Based on our analysis, the cell potential of a voltaic cell depends on the concentration of reactants, while the total charge that the cell can deliver depends on the amount of reactants in the cell.