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Chapter 3: Problem 87

To deposit exactly one mole of \(\mathrm{Ag}\) from an aqueous solution containing \(\mathrm{Ag}^{+}\) requires a quantity of electricity known as one faraday (F). The electrodeposition requires that each \(\mathrm{Ag}^{+}\) ion gain one electron to become an Ag atom. Use appropriate physical constants listed on the inside back cover to obtain a precise value of the Avogadro constant, \(N_{A}\).

Short Answer

Expert verified
The Avogadro constant \(N_{A}\), the number of entities per mole, calculated from the Faraday's laws of electrolysis, is approximately \(6.022 × 10^{23} mol^{-1}\).

Step by step solution

01

Understand Faraday's laws of electrolysis

Faraday's first law of electrolysis states that the amount of material transformed at an electrode during electrolysis is directly proportional to the quantity of electricity that passes through the solution. One mole of electrons, known as one faraday (F), is equivalent to \(96485.3 C/mol\). This is the Faraday constant.
02

Write the electrodeposition reaction for Ag

Silver is deposited from its aqueous solution according to the following reaction: \(Ag^{+} + e^{-} -> Ag\). In this reaction, each silver ion \(\mathrm{Ag}^{+}\) gains one electron to become a silver atom, Ag. Therefore, if we have 1 mol of silver ions, they will require 1 faraday of charge to be fully reduced to silver atoms.
03

Calculate the Avogadro constant

We know that 1 faraday corresponds to 1 mol of electrons, and the charge of a faraday is given by the Faraday constant \(96485.3 C/mol\). Therefore, the number of electrons in one mole (also the Avogadro's number, \(N_{A}\)) would be given by \(N_{A} = F/e\), where e is the elementary charge, \(1.602176634 × 10^{-19} C\). Using these values, we find that \(N_{A} = 96485.3 C/mol / 1.602176634 × 10^{-19} C = 6.02214076 × 10^{23} mol^{-1}\).
04

Summarize the results

So, the Avogadro constant, the number of entities per mole, is approximately \(6.022 × 10^{23} mol^{-1}\). One mole of silver ions requires one faraday (1 mole of electrons) to be deposited as silver atoms.

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