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Chapter 19: Problem 27

Write the Nernst equation and explain all the terms.

Short Answer

Expert verified
The Nernst equation, \( E = E^0 - \frac{RT}{nF}lnQ \), explains the correlation between the cell potential and the concentration of products and reactants. Each term stands for specific quantities involved, such as electrode potential (E), standard potential (\( E^0 \)), gas constant (R), temperature (T), number of electrons in the reaction (n), Faraday's constant (F), and the reaction quotient (Q).

Step by step solution

01

Write Nernst Equation

The Nernst equation is given by: \( E = E^0 - \frac{RT}{nF}lnQ \). Here E is the electrode potential, \( E^0 \) is standard potential, R is the gas constant, T is the temperature, n is number of electrons participating in the reaction, F is Faraday's constant, and Q is the reaction quotient.
02

Define Electrode Potential (E)

The Electrode Potential (E) is the voltage (electric potential) of a cell when it is not operating.
03

Define Standard Potential (\(E^0\))

\(E^0\), the standard potential, is the potential of the cell under standard conditions, which is its maximal possible voltage.
04

Define Gas constant (R)

R is the gas constant, which equals \(8.314 Joule / Mol \cdot K\).
05

Define Temperature (T)

T is the temperature, measured in Kelvins (K). It should be in absolute temperature (Kelvin) in the formula.
06

Define Number of electrons (n)

n is the number of electrons exchanged in the electrochemical reaction involved.
07

Define Faraday's Constant (F)

F is the Faraday constant, equal to the charge of one mole of electrons (\( 96485 C / mol \)).
08

Define Reaction Quotient (Q)

Q is the reaction quotient, a ratio that provides a measure of the relative amounts of the products and reactants present in a reaction at a specific moment.

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Most popular questions from this chapter

A piece of magnesium ribbon and a copper wire are partially immersed in a \(0.1 \mathrm{M} \mathrm{HCl}\) solution in a beaker. The metals are joined externally by another piece of metal wire. Bubbles are seen to evolve at both the \(\mathrm{Mg}\) and \(\mathrm{Cu}\) surfaces. (a) Write equations representing the reactions occurring at the metals. (b) What visual evidence would you seek to show that \(\mathrm{Cu}\) is not oxidized to \(\mathrm{Cu}^{2+} ?\) (c) At some stage, \(\mathrm{NaOH}\) solution is added to the beaker to neutralize the HCl acid. Upon further addition of \(\mathrm{NaOH},\) a white precipitate forms. What is it?

In the electrolysis of an aqueous \(\mathrm{AgNO}_{3}\) solution, \(0.67 \mathrm{~g}\) of \(\mathrm{Ag}\) is deposited after a certain period of time. (a) Write the half-reaction for the reduction of \(\mathrm{Ag}^{+}\). (b) What is the probable oxidation halfreaction? (c) Calculate the quantity of electricity used, in coulombs.

A spoon was silver-plated electrolytically in a \(\mathrm{AgNO}_{3}\) solution. (a) Sketch a diagram for the process. (b) If \(0.884 \mathrm{~g}\) of \(\mathrm{Ag}\) was deposited on the spoon at a constant current of \(18.5 \mathrm{~mA},\) how long (in minutes) did the electrolysis take?

Describe the basic features of a galvanic cell. Why are the two components of the cell separated from each other?

A galvanic cell is constructed as follows. One halfcell consists of a platinum wire immersed in a solution containing \(1.0 M \mathrm{Sn}^{2+}\) and \(1.0 M \mathrm{Sn}^{4+} ;\) the other half-cell has a thallium rod immersed in a solution of \(1.0 M \mathrm{TI}^{+}\). (a) Write the half-cell reactions and the overall reaction. (b) What is the equilibrium constant at \(25^{\circ} \mathrm{C} ?\) (c) What is the cell voltage if the \(\mathrm{TI}^{+}\) concentration is increased tenfold? \(\left(E_{\mathrm{T} 1^{+} / \mathrm{T} 1}^{\circ}=-0.34 \mathrm{~V} .\right)\)
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