Concentration Cells - Practice Questions & MCQ

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18 Questions around this concept.

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EASY

Aqueous solution of which of the following compounds is the best conductor of electric current ?

Acetic acid, C₂H₄O₂

Hydrochloric acid, HCl

Ammonia, NH₃

Fructose, C₆H₁₂O₆

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The highest electrical conductivity of the following aqueous solutions is of

0.1 M acetic acid

0.1 M chloroacetic acid

0.1 M fluoroacetic acid

0.1 M difluoroacetic acid

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Concepts Covered - 3

Concentration Cells

The device in which a decrease in Gibbs energy during the transfer of matter from one concentration (higher) to other (lower) brings in an equivalent mass of electrical work. Oxidation and reduction occurs at respective electrodes but no net redox change is noticed. In other words, concentration cell is one in which emf arises as a result of different concentrations of the same electrolyte in the component half-cells.

The two solutions are connected by a salt bridge and the electrodes are joined by a piece of metallic wire.
The reduction occurs in the more concentrated compartment while oxidation occurs in the diluted compartment.

$\begin{array}{l}{\mathrm{E}=\mathrm{E}^{\circ}-\frac{2.303 \mathrm{RT}}{\mathrm{nF}} \log \frac{\left[\mathrm{C}_{2}\right]}{\left[\mathrm{C}_{1}\right]}} \\ {\text { or }} \\ {\mathrm{E}=\mathrm{E}^{\circ}+\frac{2.303 \mathrm{RT}}{\mathrm{nF}} \log \frac{\left[\mathrm{C}_{1}\right]}{\left[\mathrm{C}_{2}\right]}}\end{array}$

Concentration Cell With Respect to S.H.E

The cell representation of the concentration cell with respect to hydrogen is given as follows:

$\begin{matrix} Pt| & H_{2}(g) &| & H^{+}(aq) & || & H^{+}(aq) & | & H_{2}(g)& | Pt \\ &P_1 & & C_1 & &C_2 && P_2 & & \end{matrix}$

At anode:

$\mathrm{\frac{1}{2}H_{2} \rightarrow H^{+}+1 e^{-}}$

At cathode:

$\mathrm{H^{+}+1 e^{-} \longrightarrow \frac{1}{2}H_{2}}$

The complete cell reaction is the addition of both of these reactions and is given as follows:

$\mathrm{\frac{1}{2}H_{2}(g)\: +\: H^{+}(aq)\rightarrow H^{+}(aq)\: +\frac{1}{2}H_{2}(g)}$

Thus, the reaction quotient is given as follows:

$\mathrm{Q\: =\: \frac{[H^{+}][P_{H2}]^{1/2}}{[H^{+}][P_{H2}]^{1/2}}\: =\: \frac{c_{1}(P_{2})^{1/2}}{c_{2}(P_{1})^{1/2}}}$
where P₁and P₂ are the pressures of hydrogen gas at anode and cathode, respectively.

Now, we have:

$\\\mathrm{E^{o}_{cell}\: =\: 0}\\\mathrm{n\: =\: 1}$

Thus, at T = 298K, the cell equation can be given as follows:

$\\\mathrm{E_{cell}\: =\: -\frac{0.059}{n}log_{10}Q}\\\\\\\mathrm{E_{cell}\: =\: \frac{0.059}{1}log_{10}\frac{c_{1}}{c_{2}}\: x\: \left ( \frac{P_{2}}{P_{1}} \right )^{1/2}}\\\\\\\mathrm{E_{cell}\: =\: -\frac{0.059}{1}\left [ log_{10}[H^{+}]_{A}-log_{10}[H^{+}]_{c}\: +\: log_{10}\left ( \frac{P_{2}}{P_{1}} \right )^{1/2} \right ]}\\\\\\\mathrm{E_{cell}\: =\: 0.059\left [- log_{10}[H^{+}]_{A}-(-log_{10}[H^{+}]_{c})\: -\: log_{10}\left ( \frac{P_{2}}{P_{1}} \right )^{1/2} \right ]}$

$\\\mathrm{E_{cell}\: =\: 0.059\left [pH_{(anode)}- pH_{(cathode)} -\:\frac{1}{2} log_{10}\left ( \frac{P_{2}}{P_{1}} \right )\right ]}\\\\\\\mathrm{E_{cell}\: =\: 0.059\left [pH_{(anode)}- pH_{(cathode)} +\:\frac{1}{2} log_{10}\left ( \frac{P_{1}}{P_{2}} \right )\right ]}$

This is the final equation for the value of E_cell for concentration cell with respect to standard hydrogen electrode.

Conductance of Electrolytic Solutions

It is necessary to define a few terms before we consider the subject of conductance of electricity through electrolytic solutions. The electrical resistance is represented by the symbol ‘R’ and it is measured in ohm (Ω) which in terms of SI base units is equal to (kg m²)/(S³A²). It can be measured with the help of a Wheatstone bridge with which you are familiar with your study of physics. The electrical resistance of any object is directly proportional to its length, l, and inversely proportional to its area of cross-section, A. That is,
$\mathrm{R \propto \frac{l}{A} \text { or } R=\rho \frac{l}{A}}$
The constant of proportionality, ρ (Greek, rho), is called resistivity (specific resistance). Its SI units are ohm metre (Ω m) and quite often its submultiple, ohm centimetre (Ω cm) is also used. IUPAC recommends the use of the term resistivity over specific resistance and hence in the rest of the book we shall use the term resistivity. Physically, the resistivity for a substance is its resistance when it is one metre long and its area of cross-section is one m². It can be seen that:
1 Ω m = 100 Ω cm or 1 Ω cm = 0.01 Ω m
The inverse of resistance, R, is called conductance, G, and we have the relation:
$\mathrm{G=\frac{1}{R}=\frac{A}{\rho l}=\kappa \frac{A}{l}}$
The SI unit of conductance is siemens, represented by the symbol ‘S’ and is equal to ohm^–1 (also known as mho) or Ω^–1. The inverse of resistivity, called conductivity (specific conductance) is represented by the symbol, κ (Greek, kappa). IUPAC has recommended the use of term conductivity over specific conductance and hence we shall use the term conductivity in the rest of the book. The SI units of conductivity are S m^–1 but quite often, κ is expressed in S cm^–1. Conductivity of a material in S m^–1 is its conductance when it is 1 m long and its area of cross-section is 1 m². It may be noted that 1 S cm^–1 = 100 S m^–1.

It has been observed that the magnitude of conductivity varies a great deal and depends on the nature of the material. It also depends on the temperature and pressure at which the measurements are made. Materials are classified into conductors, insulators and semiconductors depending on the magnitude of their conductivity. Metals and their alloys have very large conductivity and are known as conductors. Certain non-metals like carbon-black, graphite and some organic polymers* are also electronically conducting. Substances like glass, ceramics, etc., having very low conductivity are known as insulators. Substances like silicon, doped silicon and gallium arsenide having conductivity between conductors and insulators are called semiconductors and are important electronic materials. Certain materials called superconductors by definition have zero resistivity or infinite conductivity. Earlier, only metals and their alloys at very low temperatures (0 to 15 K) were known to behave as superconductors, but nowadays a number of ceramic materials and mixed oxides are also known to show superconductivity at temperatures as high as 150 K.
Electrical conductance through metals is called metallic or electronic conductance and is due to the movement of electrons. The electronic conductance depends on:
(i) the nature and structure of the metal
(ii) the number of valence electrons per atom
(iii) temperature (it decreases with increase of temperature).

As the electrons enter at one end and go out through the other end, the composition of the metallic conductor remains unchanged. The mechanism of conductance through semiconductors is more complex.
We already know that even very pure water has small amounts of hydrogen and hydroxyl ions (~10^–7M) which lend it very low conductivity (3.5 × 10–5 S m^–1). When electrolytes are dissolved in water, they furnish their own ions in the solution hence its conductivity also increases. The conductance of electricity by ions present in the solutions is called electrolytic or ionic conductance. The conductivity of electrolytic (ionic) solutions depends on:
(i) the nature of the electrolyte added
(ii) size of the ions produced and their solvation
(iii) the nature of the solvent and its viscosity
(iv) concentration of the electrolyte
(v) temperature (it increases with the increase of temperature).
Passage of direct current through ionic solution over a prolonged period can lead to change in its composition due to electrochemical reactions.