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The cell potential of a particular voltaic cell with the cell reaction $$2 \mathrm{Cr}(s)+3 \mathrm{Cu}^{2+}(a q) \longrightarrow 2 \mathrm{Cr}^{3+}(a q)+3 \mathrm{Cu}(s)$$ is \(1.14 \mathrm{~V}\). What is the maximum electrical work, per mole, that can be obtained from \(6.61 \mathrm{~g}\) of chromium metal?

Short Answer

Expert verified
The maximum electrical work is approximately \(-3.30 \times 10^5 \) J/mol of Cr.

Step by step solution

01

Determine the Molar Mass of Chromium

Find the molar mass of chromium (Cr) from the periodic table, which is approximately 51.9961 g/mol.
02

Calculate Moles of Chromium

Using the given mass of chromium, \(6.61 \text{ g}\), calculate the number of moles as follows:\[ \text{moles of Cr} = \frac{6.61 \text{ g}}{51.9961 \text{ g/mol}} \]
03

Relate Moles to Reaction

According to the reaction stoichiometry, 2 moles of Cr react to carry out one complete cell reaction. Therefore, calculate how many moles of reaction occur with the moles of Cr calculated.
04

Calculate Maximum Work per Mole of Reaction

The electrical work done by the cell is related to the free energy change (\(\Delta G\)) and is given by:\[ W_{max} = -nFE \]Where \(n\) is the number of moles of electrons transferred per mole of reaction, \(F\) is Faraday's constant \((96485 \text{ C/mol})\), and \(E\) is the cell potential \((1.14 \text{ V})\). Here, 6 electrons are transferred per reaction (\(n = 6\)).
05

Calculate the Work Per Mole of Chromium

The total work for the moles of chromium can now be calculated using the calculated moles from Step 2 and the fact that they are related to Step 3. Compute the maximum electrical work per mole of Cr used:\[ W_{max} = - \left( 3 \times 96485 \times 1.14 \right) \text{ J/mol} \]Calculate for the maximum work per mole of Cr using the moles value from Step 2.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Voltaic cells
Voltaic cells are a fascinating part of electrochemistry that helps us understand the conversion of chemical energy into electrical energy. Let's break it down to make it simple. When two different metals are connected by a salt bridge and immersed in solutions containing their respective ions, they form a voltaic cell. This setup causes a spontaneous redox reaction that generates electricity.

In our specific exercise, chromium (Cr) and copper (Cu) are the metal pairs forming the cell. As the reaction proceeds, electrons move from one metal to the other, creating an electric current. Here, the electrons travel from chromium to copper because of different tendencies to lose or gain electrons, which leads to the flow of current. This entire mechanism is what defines the functionality of voltaic cells.
  • Two different metals involved.
  • Submersion in their unique ionic solutions.
  • Electron flow generates electricity.
Understanding how voltaic cells operate is crucial in exploring electrochemical reactions that power numerous devices and systems in our daily lives.
Cell potential
Cell potential is a key concept when it comes to voltaic cells. It's the measure of the electrical potential difference between the electrodes of a voltaic cell. Imagine it as the driving force of the cell's electricity production.

Our exercise states that the cell potential is 1.14 V. This means that every movement of electrons from chromium to copper within the cell generates 1.14 volts of electric force. The potential arises from the differences in tendency between the two metals (electrodes) to lose or gain electrons, also known as their electrode potentials.
  • Represents electric force or voltage.
  • Determines the direction and magnitude of electron flow.
  • Depends on the nature of the involved metals.
A higher cell potential usually means more energy can be obtained from a cell, making understanding cell potential essential for maximizing the efficiency of electrochemical reactions.
Molar mass
In chemistry, molar mass is a crucial concept, especially when dealing with conversion between grams of a substance and moles. It represents the mass of one mole of a chemical element or compound and is typically given in grams per mole (g/mol).

In the context of our exercise, the molar mass of chromium is provided as approximately 51.9961 g/mol. This number allows us to convert the mass of chromium used in the reaction (6.61 g) into moles. By using the formula:\[\text{moles of Cr} = \frac{\text{mass of Cr in g}}{\text{molar mass of Cr}} = \frac{6.61 \text{ g}}{51.9961 \text{ g/mol}}\]
  • Molar mass links mass to the mole concept.
  • Facilitates stoichiometric calculations in chemical reactions.
Understanding molar mass is fundamental as it bridges the gap between the laboratory quantities you measure and the atomic-scale quantities chemistry deals with.
Stoichiometry
Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It helps us determine how much of each substance is needed or produced in a reaction, vital for achieving balance in chemical equations.

In our example reaction, stoichiometry tells us that 2 moles of chromium react with 3 moles of copper ions to produce 2 moles of Cr鲁鈦 and 3 moles of solid copper. This relationship guides us on how many moles of the cell reaction occur with the available moles of chromium.
  • Helps in balancing chemical reactions.
  • Determines proportions of reactants and products.
Knowing stoichiometry is like understanding a recipe for chemical reactions: it ensures the right proportions are used, minimizing waste and optimizing reaction results.

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Most popular questions from this chapter

Potassium was discovered by the British chemist Humphry Davy when he electrolyzed molten potassium hydroxide. What would be the anode reaction?

What would you expect to happen when chlorine gas, \(\mathrm{Cl}_{2}\), at 1 atm pressure is bubbled into a solution containing \(1.0 \mathrm{M} \mathrm{F}^{-}\) and \(1.0 \mathrm{M} \mathrm{Br}^{-}\) at \(25^{\circ} \mathrm{C} ?\) Write a balanced equation for the reaction that occurs.

Give the notation for a voltaic cell constructed from a hydrogen electrode (cathode) in \(1.0 \mathrm{M} \mathrm{HCl}\) and a nickel electrode (anode) in \(1.0 \mathrm{M} \mathrm{NiSO}_{4}\) solution. The electrodes are connected by a salt bridge.

The amount of lactic acid, \(\mathrm{HC}_{3} \mathrm{H}_{5} \mathrm{O}_{3}\), produced in a sample of muscle tissue was analyzed by reaction with hydroxide ion. Hydroxide ion was produced in the sample mixture by electrolysis. The cathode reaction was $$2 \mathrm{H}_{2} \mathrm{O}(l)+2 \mathrm{e}^{-} \longrightarrow \mathrm{H}_{2}(g)+2 \mathrm{OH}^{-}(a q)$$ Hydroxide ion reacts with lactic acid as soon as it is produced. The endpoint of the reaction is detected with an acid-base indicator. It required \(105 \mathrm{~s}\) for a current of \(15.6 \mathrm{~mA}\) to reach the endpoint. How many grams of lactic acid (a monoprotic acid) were present in the sample?

A silver oxide-zinc cell maintains a fairly constant voltage during discharge \((1.60 \mathrm{~V})\). The button form of this cell is used in watches, hearing aids, and other electronic devices. The half-reactions are $$\mathrm{Zn}(s)+2 \mathrm{OH}^{-}(a q) \longrightarrow \mathrm{Zn}(\mathrm{OH})_{2}(s)+2 \mathrm{e}^{-}$$ \(\mathrm{Ag}_{2} \mathrm{O}(s)+\mathrm{H}_{2} \mathrm{O}(l)+2 \mathrm{e}^{-} \longrightarrow 2 \mathrm{Ag}(s)+2 \mathrm{OH}^{-}(a q)\) Identify the anode and the cathode reactions. What is the overall reaction in the voltaic cell?

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