A thallium amalgam of 4.93 % Tl in mercury and another...

A thallium amalgam of $4.93 \%$ Tl in mercury and another amalgam of $10.02 \%$ Tl are placed in separate legs of a glass cell and covered with a solution of thallous sulfate to form a concentration cell. The voltage of the cell is $0.029480 \mathrm{V}$ at $20^{\circ} \mathrm{C}$ and $0.029071 \mathrm{V}$ at $30^{\circ} \mathrm{C} .(a)$ Which is the negative electrode? (b) What is the heat of dilution per mole of Tl when Hg is added at $30^{\circ} \mathrm{C}$ to change the concentration from $10.02 \%$ to $4.93 \% ?(c)$ What is the voltage of the cell at $40^{\circ} \mathrm{C} ?$.

A thallium amalgam of $4.93 \%$ Tl in mercury and another amalgam of $10.02 \%$ Tl are placed in separate legs of a glass cell and covered with a solution of thallous sulfate to form a concentration cell. The voltage of the cell is $0.029480 \mathrm{V}$ at $20^{\circ} \mathrm{C}$ and $0.029071 \mathrm{V}$ at $30^{\circ} \mathrm{C} .(a)$ Which is the negative electrode?
(b) What is the heat of dilution per mole of Tl when Hg is added at $30^{\circ} \mathrm{C}$ to change the concentration from $10.02 \%$ to $4.93 \% ?(c)$ What is the voltage of the cell at $40^{\circ} \mathrm{C} ?$.

Key Concepts

Concentration Cell

A concentration cell is an electrochemical cell where both electrodes are made of the same material (or involve the same redox couple), but they are immersed in solutions or systems of different concentrations. The cell generates an electromotive force due to this concentration difference, and its voltage can be calculated using the Nernst equation. This concept underpins the principle that a gradient in chemical potential drives a redox reaction, making it fundamental in understanding variable cell potentials without changing electrode materials.

Electrode Reactions and Sign Conventions

In an electrochemical cell, the electrode where oxidation occurs is known as the anode (negative electrode in a concentration cell), and the electrode where reduction occurs is the cathode (positive electrode). Determining which electrode is negative or positive in a concentration cell involves understanding how the concentration gradient affects the direction of the electron flow. This concept is essential for setting up and correctly analyzing the redox reactions and interpreting the cell's behavior.

Nernst Equation

The Nernst equation describes how the cell potential is related to the standard electrode potential, temperature, and activities (or concentrations) of the chemical species involved in the reaction. In concentration cells, it simplifies to relate the potential difference solely to concentration differences. This equation is crucial for predicting how changes in concentration and temperature affect the voltage of the cell, allowing for quantitative analysis of systems like the one described.

Temperature Dependence of Electrode Potentials

Temperature has a direct impact on the cell potential as seen through the Nernst equation, where the potential is proportional to temperature when concentration terms are involved. Understanding how temperature variations influence cell voltage is vital because it affects both the reaction kinetics and the thermodynamic properties (like Gibbs free energy) of the process. This concept helps in analyzing and recalculating cell potentials at different temperatures.

Heat of Dilution

The heat of dilution concerns the enthalpy change when a solution is diluted or, more broadly, when a component's concentration is changed. In the context of electrochemical cells, this concept can be applied when a more concentrated solution is altered to a less concentrated one. The process has implications on the energy profile of the system, and calculating the heat of dilution per mole of a species helps in understanding the thermal effects accompanying such concentration changes.

Transcript

00:06 For a cell in which hgo react with water molecule in the and gain two electrons to form mercury and hydroxyl ions.

00:31 On the other hand, the e .e .0 of this reaction is 0 .0 of this reaction is 0 .098 watt.

00:44 On the other hand, the zinc oxide and the presence of water molecule to gain two electrons from zinc and two hardfaxyl ion.

01:01 So e0 of the cell is equal to minus 1 .260 volt.

01:11 So in this reaction, zinc is oxidized while the mercury is oxidized.

01:15 Is reduced so when zinc react with the two hydroxyl ions forming zinc oxide and water molecule here two electrons are released so the e oxidation of the zinc is equal to 1 .260 volt on the other hand the mercury oxide react with the water molecule and gain the electron lost by the zinc form mercury and two hydroxyl ion.

02:04 E -reduction is equal to 0 .098 watt.

02:12 Adding the value of e -oxidation and e -reduction to get e -0 of the cell, we get it is equal to 1 .358 world.

02:25 Adding the two equations we can cross the hydroxyl ions and the electrons as well as the water molecule so the simple equation our overall equation is that zinc react with mercury oxide forming zinc oxide and mercury is formed.

02:50 Now to calculate delta g -not for this cell we know delta g -not is equal to minus n f e -not so delta g -not is equal to minus where n is the number of electron last end gain which is equal to two moles of electron if a spirada constant 96 ,500 coulum per mole of electrons multiply by e knot of the cell 1 .358 volt...

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