Question

Can the displacement of \(\mathrm{Pb}(\mathrm{s})\) from \(1.0 \mathrm{M} \mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}\) be carried to completion by tin metal? Explain.

Short answer

No, the displacement of Lead from Lead(II) nitrate cannot be carried to completion by tin metal because the standard reduction potential for Lead is less than for Tin.

Step-by-step solution

Determining the standard reduction potentials

Consult a table of standard reduction potentials. We find that \(Pb^{2+}(aq) + 2e^- \rightarrow Pb(s)\) has a standard reduction potential (\(E^0\)) of -0.13 V, while \(Sn^{2+}(aq) + 2e^- \rightarrow Sn(s)\) has a standard reduction potential of -0.14 V.

Comparing the reduction potentials

Compare the standard reduction potentials. The reaction will proceed to the right (displacement will occur) if the oxidizing agent (in this case Lead) has a higher standard reduction potential than the reducing agent (Tin). However, the standard reduction potential for Lead is smaller than that for Tin.

Concluding

Since the standard reduction potential for Lead is less than for Tin, the reaction will not go to completion, meaning that the displacement of Lead by Tin will not be completed.

Key concepts

Electrochemistry

Electrochemistry is the branch of chemistry that deals with the relationship between electricity and chemical reactions. It encompasses the study of chemical changes caused by the movement of electrons from one molecule or ion to another—an essential process in batteries, electrolysis, and various types of sensors and electrodes. At its core, electrochemistry looks at how electric current can drive a chemical reaction which might not occur spontaneously as well as how chemical reactions can generate electric current.

Redox Reactions

Redox reactions, short for 'reduction-oxidation reactions', are a family of chemical reactions involving the transfer of electrons. One substance gets reduced by gaining electrons, while another gets oxidized by losing electrons. This electron dance is crucial in electrochemical processes, including the operation of batteries and corrosion. The understanding of redox reactions is crucial when we analyze displacement reactions and their feasibilities, such as in the given exercise involving lead and tin.

Chemical Displacement

Chemical displacement, or single replacement, occurs when an element displaces another in a compound, typically as a result of differences in reactivity. Metals can replace less reactive metals from their compounds. For instance, in the exercise question, tin (Sn) metal is considered for the displacement of lead (Pb) from lead nitrate solution. Whether such a displacement reaction will successfully occur can be predicted by looking at the reactivity of metals, which is generally informed by standard reduction potential values.

Standard Electrode Potentials

Standard Electrode Potentials, represented by the symbol \(E^0\), measure the tendency of a chemical species to be reduced, and by extension, the strength of its oxidizing ability. It's tabulated under standard conditions: a 1 M concentration, 25°C temperature, and a pressure of 1 atm. When comparing two standard reduction potentials, the substance with the higher (more positive) potential will act as the oxidizing agent and tends to gain electrons, being reduced in the process. During a displacement reaction, a metal with a less negative \(E^0\) can be displaced by a metal with a more negative \(E^0\). However, in the exercise, since Pb has a less negative standard reduction potential than Sn, the displacement will not be completed as one might initially think.