(a) In the Nernst equation, what is the numerical value of the reaction quotient, \(Q,\) under standard conditions? (b) Can the Nernst equation be used at temperatures other than room temperature?

The Nernst equation is a fundamental equation in electrochemistry that relates the potential (voltage) of an electrochemical cell to the concentration of its components. Mathematically, the Nernst equation is given by: \[E = E^0 - \frac{RT}{nF} lnQ\] where - \(E\) is the potential of the cell, - \(E^0\) is the standard potential (also known as the standard reduction potential) of the cell, - \(R\) is the universal gas constant, \(8.314 J \cdot mol^{-1} \cdot K^{-1}\), - \(T\) is the temperature in Kelvin, - \(n\) is the number of electrons transferred in the redox reaction, and - \(F\) is Faraday's constant, \(96500 C \cdot mol^{-1}\), - \(Q\) is the reaction quotient. Now let us address each part of the problem. Part (a): We are asked to find the numerical value of the reaction quotient (Q) under standard conditions.

Under standard conditions, the concentrations of all aqueous species are set to 1 M, and the pressure of all gaseous species is set to 1 atm. In this case, the reaction quotient (Q) equals the equilibrium constant (K). However, at standard conditions, the cell potential, \(E\), equals the standard potential, \(E^0\). Now we will use the Nernst equation to find the numerical value of Q under standard conditions.

Since \(E = E^0\) under standard conditions, we can rewrite the Nernst equation as: \[E^0 = E^0 - \frac{RT}{nF} lnQ\] Now, we need to solve for Q. Rearrange the equation to isolate Q: \[0 = - \frac{RT}{nF} lnQ\] \[lnQ = 0\] To find the numerical value of Q, take the exponent on both sides: \[Q = e^0\] \[Q = 1\] Under standard conditions, the numerical value of the reaction quotient (Q) is 1. Part (b): We are asked if the Nernst equation can be used at temperatures other than room temperature.

Since the Nernst equation contains the temperature term \(T\) in Kelvin, there is no restriction on using the Nernst equation only at room temperature. The Nernst equation is valid at all temperatures as long as other variables such as the concentration of the species and standard electrode potentials are known. So, yes, the Nernst equation can be used at temperatures other than room temperature.