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Chapter 18: Problem 23

The free energy change for a reaction, \(\Delta G\), is an extensive property. What is an extensive property? Surprisingly, one can calculate \(\Delta G\) from the cell potential, \(\mathscr{E}\), for the reaction. This is surprising because \(\mathscr{E}\) is an intensive property. How can the extensive property \(\Delta G\) be calculated from the intensive property \(\mathscr{E}\) ?

Short Answer

Expert verified
An extensive property depends on the amount of substance, while an intensive property does not. Free energy change (ΔG) is an extensive property, and cell potential (ℰ) is an intensive property. However, they can be related through the equation \( \Delta G = -nFE \), where n is the number of moles of electrons involved in the redox reaction, and F is Faraday's constant. This equation allows us to calculate an extensive property (ΔG) using an intensive property (ℰ) when considering the number of moles of electrons involved and Faraday's constant.

Step by step solution

01

Understand extensive properties

Extensive properties are properties that depend on the amount of a substance. They are additive, which means that if you have two separate systems with their own extensive properties and combine them, the extensive property of the entire system will be the sum of the individual extensive properties. Examples of extensive properties include mass, volume, and energy, such as free energy change (ΔG).
02

Understand intensive properties

Intensive properties are properties that do not depend on the amount of a substance. The value of an intensive property remains the same regardless of the amount or size of the sample in the system. Examples of intensive properties include temperature, pressure, and cell potential (ℰ).
03

Connect cell potential to free energy change

Although ΔG is an extensive property and ℰ is an intensive property, they can be related through the following equation: \[ \Delta G = -nFE \] where: - ΔG is the free energy change, - n is the number of moles of electrons involved in the redox reaction, - F is Faraday's constant (9.6485 x 10^4 C/mol), which is the charge of one mole of electrons, - ℰ is the cell potential. This equation shows that, although the cell potential (ℰ) is an intensive property, it can be used to calculate an extensive property (ΔG) when considering the number of moles of electrons involved and Faraday's constant.
04

Apply the equation to an example

Now, let's consider a simple example: Suppose we have a cell potential (ℰ) of 1.5 V and the redox reaction involves 2 moles of electrons (n = 2). We can calculate the free energy change (ΔG) as follows: \[ \Delta G = -nFE = -(2)(9.6485 \times 10^4 \text{ C/mol})(1.5 \text{V}) \] \[ \Delta G = -2.8986 \times 10^5 \text{ J/mol} \] Thus, using the cell potential (ℰ), we can calculate the free energy change (ΔG) of the reaction, even though one is an extensive property and the other is an intensive property.

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Most popular questions from this chapter

When magnesium metal is added to a beaker of \(\mathrm{HCl}(a q)\), a gas is produced. Knowing that magnesium is oxidized and that hydrogen is reduced, write the balanced equation for the reaction. How many electrons are transferred in the balanced equation? What quantity of useful work can be obtained when \(\mathrm{Mg}\) is added directly to the beaker of \(\mathrm{HCl}\) ? How can you harness this reaction to do useful work?

An electrochemical cell consists of a nickel metal electrode immersed in a solution with \(\left[\mathrm{Ni}^{2+}\right]=1.0 M\) separated by a porous disk from an aluminum metal electrode. a. What is the potential of this cell at \(25^{\circ} \mathrm{C}\) if the aluminum electrode is placed in a solution in which \(\left[\mathrm{Al}^{3+}\right]=7.2 \times\) \(10^{-3} M ?\) b. When the aluminum electrode is placed in a certain solution in which \(\left[\mathrm{Al}^{3+}\right]\) is unknown, the measured cell potential at \(25^{\circ} \mathrm{C}\) is \(1.62 \mathrm{~V}\). Calculate \(\left[\mathrm{Al}^{3+}\right]\) in the unknown solution. (Assume \(\mathrm{Al}\) is oxidized.)

The compound with the formula \(\mathrm{TII}_{3}\) is a black solid. Given the following standard reduction potentials, $$ \begin{aligned} \mathrm{Tl}^{3+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{Tl}^{+} & \mathscr{E}^{\circ}=1.25 \mathrm{~V} \\ \mathrm{I}_{3}^{-}+2 \mathrm{e}^{-} \longrightarrow 3 \mathrm{I}^{-} & \mathscr{E}^{\circ}=0.55 \mathrm{~V} \end{aligned} $$ would you formulate this compound as thallium(III) iodide or thallium(I) triiodide?

What volumes of \(\mathrm{H}_{2}(g)\) and \(\mathrm{O}_{2}(g)\) at STP are produced from the electrolysis of water by a current of \(2.50 \mathrm{~A}\) in \(15.0 \mathrm{~min} ?\)

When aluminum foil is placed in hydrochloric acid, nothing happens for the first 30 seconds or so. This is followed by vigorous bubbling and the eventual disappearance of the foil. Explain these observations.
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