Question

(a) A voltaic cell is constructed with all reactants and products in their standard states. Will this condition hold as the cell operates? Explain. (b) Can the Nernst equation be used at temperatures other than room temperature? Explain. (c) What happens to the emf of a cell if the concentrations of the products are increased?

Short answer

(a) No, the standard state conditions will not hold as the cell operates because the concentrations of reactants and products change during operation. (b) Yes, the Nernst equation can be used at temperatures other than room temperature, as it includes temperature (T) as a variable. (c) When the concentrations of the products are increased, the emf of the cell will decrease, according to the Nernst equation.

Step-by-step solution

(a) Standard states condition for reactants and products

The question asks if the standard state conditions (all reactants and products being in their standard states) will hold while the cell operates. The standard states for reactants and products help in calculating the emf of the cell. However, as the cell operates, the concentrations of reactants and products change. Since the concentrations are no longer in their standard states, this condition will not hold as the cell operates.

(b) Nernst equation at different temperatures

The Nernst equation is given by: \[E = E° - \frac{RT}{nF} \ln Q\] where E is the cell potential, E° is the standard cell potential, R is the gas constant, T is the temperature in Kelvin, n is the number of moles of electrons transferred in the redox reaction, F is the Faraday constant, and Q is the reaction quotient. The Nernst equation can be used at temperatures other than room temperature, as it includes the temperature (T) as a variable. The equation helps in determining the cell potential at different temperatures and reaction conditions by adjusting the value of T.

(c) Effect of increasing product concentrations on emf

According to the Nernst equation, the cell potential (E) is related to the reaction quotient (Q) where Q depends on the concentrations of reactants and products. With increasing concentrations of the products, the value of Q will increase. As a result, the natural logarithm term \(\ln Q\) in the Nernst equation will also increase. Keeping the other terms constant, we get the relation: \[E = E° - \frac{RT}{nF} \ln Q\] As \(\ln Q\) increases, the overall subtractive term also increases, resulting in a decrease in the cell potential (E). Therefore, when the concentrations of the products are increased, the emf of the cell will decrease.

Key concepts

Voltaic Cell

A voltaic cell, sometimes known as a galvanic cell, is an electrochemical device that converts chemical energy into electrical energy through a spontaneous redox reaction. It consists of two half-cells, each containing an electrode and an electrolyte. These half-cells are connected by a salt bridge or a porous membrane to maintain charge balance.

In a typical setup, oxidation occurs at the anode, and reduction takes place at the cathode, creating a flow of electrons through an external circuit from anode to cathode. As a voltaic cell operates, the reactants are consumed, and the products are formed, inevitably causing the cell to deviate from its initial standard state conditions.

Cell Potential

The cell potential, represented as E, signifies the electrical potential difference between two electrodes of a voltaic cell. It's the driving force behind the flow of electrons from one electrode to another, and it's a measure of how much voltage the cell can produce. This potential difference is determined under standard conditions, giving us the standard cell potential (E°).

The cell potential varies with changes in concentration of reactants and products, temperature, and pressure. If you can manipulate these factors, you can influence the amount of voltage a cell can produce. Understanding how to calculate and predict the cell potential is crucial for all applications of electrochemical cells, from batteries to corrosion protection.

Reaction Quotient

The reaction quotient, Q, plays a pivotal role in electrochemistry as it represents the ratio of the concentration of the products to the concentration of the reactants at a given moment, each raised to the power of their stoichiometric coefficient.

When a cell operates, the reaction quotient dynamically changes, and it is these changes that are documented in the Nernst equation. The equation adjusts the standard cell potential according to the current state of the cell, which may not be at equilibrium. As the cell reaches equilibrium, the reaction quotient becomes equal to the equilibrium constant (K), and the cell potential drops to zero, at which point the cell can no longer do electrical work.

Standard States

Standard states refer to the default conditions set for the reference environment of a chemical reaction: a pressure of 1 bar and a concentration of 1 M for aqueous solutions, unless dealing with gases, which have a standard state at 1 bar. Pure solids and liquids are considered to have a standard state at these conditions as well. Moreover, standard temperature is often taken as 25°C (298 K) but isn't a strict requirement for defining standard states.

It's important to point out that actual cell conditions often deviate from these standard states, which is why the Nernst equation is so useful. This deviation is normal since as a cell operates, reactants will be consumed, and products will be generated, resulting in a shifting ratio which no longer matches the 1 M concentrations or other standards set at the start.