Electrochemistry Class 12th Chemistry Part I CBSE Solution

Class 12^th Chemistry Part I CBSE Solution

Intext Questions Pg-68

1. How would you determine the standard electrode potential of the system Mg2+|Mg?…
2. Can you store copper sulphate solutions in a zinc pot?
3. Consult the table of standard electrode potentials and suggest three substances that can…

Intext Questions Pg-73

1. Calculate the potential of hydrogen electrode in contact with a solution whose pH is 10.…
2. Calculate the emf of the cell in which the following reaction takes place: Ni(S) + 2Ag+…
3. The Cell in which the following reaction occurs: 2Fe3+(aq) + 2I- (aq) → 2Fe2+(aq) + I2(s)…

Intext Questions Pg-83

1. Why does the conductivity of a solution decrease with dilution?
2. Suggest a way to determine the Λ°m value of water
3. The molar conductivity of 0.025 mol L-1 methanoic acid is 46.1 S cm^2 mol-1. Calculate its…

Intext Questions Pg-86

1. If a current of 0.5 ampere flows through a metallic wire for 2 hours, then how many…
2. Suggest a list of metals that are extracted electrolytically.
3. Consider the reaction: Cr2O72- + 14H+ + 6e-⇒ 2Cr3+ + 7H2O. What is the quantity of…

Intext Questions Pg-90

1. Write the chemistry of recharging the lead storage battery, highlighting all the materials…
2. Suggest two materials other than hydrogen that can be used as fuels in fuel cells.…
3. Explain how rusting of iron is envisaged as setting up of an electrochemical cell.…

Exercises

1. Arrange the following metals in the order in which they displace each other from the…
2. Given the standard electrode potentials, K+ /K = -2.93V, Ag+ /Ag = 0.80V, Hg2+ /Hg = 0.79V…
3. Depict the galvanic cell in which the reaction Zn(s) + 2Ag+ (aq) → Zn2+ (aq) + 2Ag(s)…
4. Calculate the standard cell potentials of galvanic cell in which the following reactions…
5. Write the Nernst equation and emf of the following cells at 298 K: (i) Mg(s)|Mg2+…
6. In the button cells widely used in watches and other devices the following reaction takes…
7. Define conductivity and molar conductivity of the solution of an electrolyte. Discuss…
8. The conductivity of 0.20 M solution of KCl at 298 K is 0.0248 S cm-1. Calculate its molar…
9. The resistance of a conductivity cell containing 0.001M KCl solution at 298 K is 1500 Ω.…
10. The conductivity of sodium chloride at 298 K has been determined at different…
11. Conductivity of 0.00241 M acetic acid is 7.896 × 10-5 S cm-1. Calculate its molar…
12. How much charge is required for the following reductions: (i) 1 mol of Al3 + to Al? (ii) 1…
13. How much electricity in terms of Faraday is required to produce (i) 20.0 g of Ca from…
14. How much electricity is required in coulomb for the oxidation of (i) 1 mol of H2O to O2?…
15. A solution of Ni(NO3)2 is electrolysed between platinum electrodes using a current of 5…
16. Three electrolytic cells A,B,C containing solutions of ZnSO4, AgNO3 and CuSO4,…
17. Using the standard electrode potentials given in Table 3.1, predict if the reaction…
18. Predict the products of electrolysis in each of the following: (i) An aqueous solution of…

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Intext Questions Pg-68

Question 1.

How would you determine the standard electrode potential of the system Mg²⁺|Mg?

Answer:

To determine the standard electrode potential of the system Mg²⁺|Mg, connect it to the standard hydrogen electrode (SHE). Keep the Mg²⁺|Mg system as cathode and SHE as anode. This is represented as shown below.

Pt(s) | H₂(g, 1 bar)| H⁺ (aq, 1 M) ||Mg²⁺ (aq, 1M)| Mg

The electrode potential of a cell is given by

E^⊖ = E^⊖_R – E^⊖_L

Where,

E^⊖_R- Potential of the half-cell in the right side of the above representation

E^⊖_L- Potential of the half-cell in the left side of the above representation

It is to be noted that the potential of the standard hydrogen electrode is zero.

Therefore, E^⊖_L = 0

E^⊖ = E^⊖_R – 0

⇒ E^⊖ = E^⊖_R

Question 2.

Can you store copper sulphate solutions in a zinc pot?

Answer:

NO, because Zn is very reactive with Cu. It reacts with copper sulphate to form zinc sulphate i.e., Zn displaces Cu and metallic Cu is also formed.

The reaction is given as:

Zn + CuSO₄ ⇒ ZnSO₄ + Cu

Question 3.

Consult the table of standard electrode potentials and suggest three substances that can oxidise ferrous ions under suitable conditions

Answer:

For a substance to oxidise Fe²⁺to Fe³⁺ ion, it must have high reduction potential than Fe³⁺. The reduction potential of Fe³⁺ to Fe²⁺ reaction is 0.77V, the substances which have reduction potentials higher than this value will oxidise Fe²⁺ ions. Comparing the values, from the table:

F₂,Br₂,Cl₂,H₂O₂ can oxidise ferrous ions.

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Intext Questions Pg-73

Question 1.

Calculate the potential of hydrogen electrode in contact with a solution whose pH is 10.

Answer:

Given:

For hydrogen electrode, pH = 10

n = 1

(n = moles of e^- from balanced redox reaction)

pH= 10

⇒ [H⁺] = 10^-10 M

We know,

Here, E⁰ = 0 (because it is a concentration cell)

P[H₂] = 1

⇒ 

⇒ 

⇒ 

⇒ 

⇒ 

Question 2.

Calculate the emf of the cell in which the following reaction takes place:

Ni(S) + 2Ag⁺ (0.002M) → Ni²⁺ (0.160 M) + 2Ag(s)

Given that 

Answer:

Given:

[Ag⁺] = 0.002 M

[Ni²⁺] = 0.160 M

n = 2

(n = moles of e^- from balanced redox reaction)

E⁰_cell= 1.05 V

Now, using the Nernst equation we get,

⇒ 

⇒ 

⇒ 

Question 3.

The Cell in which the following reaction occurs:

2Fe³⁺(aq) + 2I^– (aq) → 2Fe²⁺(aq) + I₂(s) has E⁰_cell = 0.236V at 298 K.

Calculate the standard Gibbs energy and the equilibrium constant of the cell reaction.

Answer:

Given:

2Fe³⁺(aq) + 2I^– (aq) → 2Fe²⁺(aq) + I₂(s)

E⁰_cell = 0.236V

n = moles of e^- from balanced redox reaction = 2

F = Faraday's constant = 96,485 C/mol

T = 298 K.

Using the formula, we get,

∆_rG⁰ = – nFE⁰_cell

⇒ ∆_rG⁰ = – 2 × FE⁰_cell

⇒ ∆_rG⁰ = −2 × 96485 C mol^-1 × 0.236 V

⇒ ∆_rG⁰ = −45540 J mol⁻¹

⇒ ∆_rG⁰ = −45.54 kJ mol⁻¹

Now,

∆_rG⁰ = −2.303RT log K_c

Where, K is the equilibrium constant of the reaction.

R is the gas constant; R = 8.314 J-mol-C^-1

⇒ −45540 J mol⁻¹ = –2.303× (8.314 J-mol-C^-1)× (298 K) × (log Kc)

Solving for K_c we get,

⇒ log Kc = 7.98

Taking antilog both side, we get

⇒ Kc = Antilog (7.98)

⇒ K_c = 9.6 × 107

Trick to remember:

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Intext Questions Pg-83

Question 1.

Why does the conductivity of a solution decrease with dilution?

Answer:

The conductivity of a solution depends on the amount of ions present per volume of the solution. When diluted, the concentration of the ions decreases which implies that the number of ions per volume decreases thus, in turn, conductivity decreases.

Question 2.

Suggest a way to determine the Λ°_m value of water

Answer:

Λ°_{m (H2O)} = Λ°_m(H⁺) + Λ°_m(OH^-)

For calculation purpose, Λ°_m(Na⁺) and Λ°_m(Cl^-) are added and subtracted.

Λ°_{m (H2O)} = Λ°_m(H⁺) + Λ°_m(OH^-)+ Λ°_m(Na⁺) - Λ°_m(Na⁺) + Λ°_m(Cl^-) - Λ°_m(Cl^-)

Λ°_{m (H2O)} = Λ°_m(HCl) + Λ°_m(NaOH) - Λ°_m(NaCl)

If we know the other values, Λ°_{m (H2O)} can be calculated.

Question 3.

The molar conductivity of 0.025 mol L^–1 methanoic acid is 46.1 S cm² mol^–1. Calculate its degree of dissociation and dissociation constant. Given λ⁰_(H+) = 349.6 S cm² mol^–1 and λ⁰ (HCOO^–) = 54.6 S cm² mol^–1.

Answer:

C = 0.025 mol L^-1

A_m = 46.1 Scm² mol^-1

λ⁰ (H⁺) = 349.6 Scm² mol^-1

λ⁰ (HCOO^-) = 54.6 Scm² mol^-1

Λ⁰_m (HCOOH) = Λ ⁰(H⁺) + Λ⁰(HCOO^-)

= 349.6 + 54.6

= 404.2 S cm² mol^-1

Now, the degree of dissociation:

∴ α = 0.114(approximately)

Thus, dissociation constant:

⇒ K = 3.67 × 10^-4 mol L^-1

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Intext Questions Pg-86

Question 1.

If a current of 0.5 ampere flows through a metallic wire for 2 hours, then how many electrons would flow through the wire?

Answer:

Current I = 0.5A

Time t = 2hrs = 2×60×60 = 7200 seconds

Charge Q = I×t

Q = 0.5×7200 = 3600 C

Charge carried by 1 mole of electrons (6.023×10²³electrons) is equal to 96487C.

No of electrons = 6.023×10²³ × 3600/96487

No of electrons = 2.25×10²² electrons.

Question 2.

Suggest a list of metals that are extracted electrolytically.

Answer:

Metals with greater reactivity can be extracted electrolytically. Sodium, potassium, calcium, lithium, magnesium, aluminium which are present in the top of the reactivity series are extracted electrolytically.

Question 3.

Consider the reaction: Cr₂O₇^2– + 14H⁺ + 6e^–⇒ 2Cr³⁺ + 7H₂O. What is the quantity of electricity in coulombs needed to reduce 1 mol of Cr₂O₇^2–?

Answer:

Cr₂O₇^2– + 14H⁺ + 6e^–⇒ 2Cr³⁺ + 7H₂O

For reducing one mole of Cr₂O₇^2–, 6 mole of electrons are required. Hence, 6 faraday charge is needed. Hence, 6F = 6×96487 = 578922 C. Thus, the quantity of electricity is needed is 578922 C.

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Intext Questions Pg-90

Question 1.

Write the chemistry of recharging the lead storage battery, highlighting all the materials that are involved during recharging

Answer:

Anode: Lead (Pb)

Cathode: a grid of lead packed with lead oxide (PbO₂)

Electrolyte: 38% solution of sulphuric acid (H₂SO₄)

The cell reactions are as follows :

Pb (s) + SO₂^-4(aq) ⇒ PbSO₄(s) + 2e^- (anode)

PbO₂(s) + SO₂^-4(aq) + 4H⁺(aq) +2e^-⇒ PbSO₄(s) +2H₂O(l) (cathode)

Pb(s) + PbO₂(s) +2H₂SO₄(aq)⇒ 2PbSO₄(s) +2H₂O(l)

(overall cell reaction)

On charging, all these reactions will be reversed.

Question 2.

Suggest two materials other than hydrogen that can be used as fuels in fuel cells.

Answer:

Methane, oxygen & methanol can be used as fuels in fuel cells other than hydrogen.

Question 3.

Explain how rusting of iron is envisaged as setting up of an electrochemical cell.

Answer:

In the corrosion reaction, due to the presence of air and moisture, oxidation takes place at a particular point of an object made of iron. That spot behaves as the anode. The reaction at the anode is given by,

Fe(s) ⇒ Fe²⁺_(aq) + 2e^-

Electrons released at the anodic spot move through the metal and go to another spot of the object, wherein presence of H⁺ ions, the electrons reduce oxygen. This spot behaves as the cathode. These H⁺ ions come either from H₂CO₃, which are formed due to the dissolution of carbon dioxide from the air into water. The cathodic reaction is given by

O_2(air) + 4H_(aq)⁺+4e^-⇒ 2H₂O

The overall reaction is given by,

2Fe_(s) + O_2(air) + 4H_(aq)⁺⇒ 2Fe²⁺+2H₂O

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Exercises

Question 1.

Arrange the following metals in the order in which they displace each other from the solution of their salts.

Al, Cu, Fe, Mg, and Zn.

Answer:

The order in which the given metals displace each other from the solution of their salts is given by,

Mg>Al> Zn> Fe> Cu

Explanation -

A metal of stronger reducing power displaces another metal of weaker reducing power from its solution of salt. The order of increasing the reducing power of given metals is Cu< Fe< Zn< Al<Mg. Hence, we can interpret as Mg can displace Cu from its salt solution, but Cu cannot displace Mg. The order in which the given metals displace each other from the solution of their salts is given by, Mg>Al> Zn> Fe> Cu. This is hence arranged in decreasing order of its reactivity.

Question 2.

Given the standard electrode potentials,

K⁺ /K = –2.93V, Ag⁺ /Ag = 0.80V,

Hg²⁺ /Hg = 0.79V

Mg²⁺ /Mg = –2.37 V, Cr³⁺ /Cr = – 0.74V

Arrange these metals in their increasing order of reducing power.

Answer:

Reducing power of metals increase with the decrease of reduction potential. Hence, the increasing order of reducing power will be as,

Ag < Hg < Cr < Mg < K

Explanation -

When the reduction potential is lower, the element has more tendency to get oxidized and thus more will be reducing power. The metal that has more negative electrode potential will be the one with more reducing power. Thus, here potassium(K) has the highest reducing power among the given elements.

Question 3.

Depict the galvanic cell in which the reaction

Zn(s) + 2Ag⁺ (aq) → Zn²⁺ (aq) + 2Ag(s) takes place. Further show:

1) Which of the electrode is negatively charged?

2) The carriers of the current in the cell.

3) Individual reaction at each electrode.

Answer:

The galvanic cell corresponding to the given redox reaction can be represented as:

Zn|Zn^{2 +}_(aq)||Ag ⁺_(aq)|Ag

1) Zn electrode (anode) is negatively charged because, at this electrode, Zn is oxidized to Zn²⁺, causing electron accumulation at the anode.

2) Electrons (ions) are the carriers of the current in the cell and in the external circuit, current flows from Ag (cathode) to Zn(anode) which is normally opposite to the electron flow which is from anode to cathode.

3) At anode:

Zn_(s)⇒ Zn^{2 +}_(aq) + 2e^–

At cathode:

Ag ⁺_(aq) + e ^–⇒ Ag_(s)

Question 4.

Calculate the standard cell potentials of galvanic cell in which the following reactions take place:

(i) 2Cr(s) + 3Cd²⁺ (aq) → 2Cr³⁺ (aq) + 3Cd

(ii) Fe² + (aq) + Ag⁺ (aq) → Fe³⁺ (aq) + Ag(s)

Calculate the Δ_rG⁰ and equilibrium constant(K) of the reactions.

Answer:

(i) Known - E⁰_Cr^{3 +}_/Cr = - 0.74 V

E⁰_Cd^{2 +}_/Cd = - 0.40 V

∆_rG⁰ = ?

K = ?

The galvanic cell of the given reaction is written as -

Cr_(s)|Cr^{3 +}_(aq)|| Cd^{2 +}_(aq)|Cd_(s)→ Reaction 1

Hence, the standard cell potential is given as,

E⁰ = E⁰_R - E⁰_L

= - 0.40 - (- 0.74)

∴ E⁰ = + 0.34 V

To calculate the standard Gibb’s free energy, ∆_rG⁰, we use,

∆_rG⁰ = - nE⁰F → Equation 1

where nF is the amount of charge passed and E⁰ is the standard reduction electrode potential.

Substituting n = 6 (no. of e ^- involved in the reaction 1), F = 96487 C mol^-1,

E⁰ = + 0.34 V in Equation 1, we get,

∆_rG⁰ = - 6×0.34V×96487 C mol^-1

= - 196833.48 CV mol^-1

= - 196833.48 J mol^-1

∴ ∆_rG⁰ = - 196.83348 kJ mol^-1

To find out the equilibrium constant, K, we use the formula,

log K = 34.5177

K = antilog 34.5177

∴ K = 3.294 × 10³⁴

Thestandard Gibb’s free energy, ∆_rG⁰ is - 196.83348 kJ mol ^{– 1} and equilibrium constant, K is3.294 × 10³⁴

(ii) Known -

E⁰_Fe^{3 +}_/Fe^{2 +} = 0.77V

E⁰_Ag⁺_/Ag = 0.80 V

∆_rG⁰ = ?

K = ?

The galvanic cell of the given reaction is written as -

Fe^{2 +}_(aq)|Fe^{3 +}_(aq)|| Ag ⁺_(aq)|Ag_(s)→ Reaction 1

Hence, the standard cell potential is given as,

E⁰ = E⁰_R - E⁰_L

= 0.80 - (0.77)

∴ E⁰ = + 0.03 V

To calculate the standard Gibb’s free energy, ∆_rG⁰, we use,

∆_rG⁰ = - nE⁰F → Equation 1

where nF is the amount of charge passed and E⁰ is the standard reduction electrode potential.

Substituting n = 1 (no. of e ^- involved in the reaction 1), F = 96487 C mol^-1, E⁰ = + 0.03V in Equation 1, we get,

∆_rG⁰ = - 1×0.03V×96487 C mol^-1

= - 2894.61 CV mol ^{- 1}

= - 2894.61 J mol^-1

∴ ∆_rG⁰ = - 2.89461 kJ mol^-1

To find out the equilibrium constant, K, we use the formula,

log K = 0.5076

K = Antilog 0.5076

∴ K = 3.218

Thestandard Gibb’s free energy, ∆_rG⁰ is - 2.89461 kJ mol ^{– 1} and equilibrium constant, K is3.218

Question 5.

Write the Nernst equation and emf of the following cells at 298 K:

(i) Mg(s)|Mg²⁺ (0.001M)||Cu²⁺ (0.0001 M)|Cu(s)

(ii) Fe(s)|Fe²⁺ (0.001M)||H⁺ (1M)|H₂(g)(1bar)| Pt(s)

(iii) Sn(s)|Sn²⁺ (0.050 M)||H⁺ (0.020 M)|H₂(g) (1 bar)|Pt(s)

(iv) Pt(s)|Br₂(l)|Br^–(0.010 M)||H⁺ (0.030 M)| H₂(g) (1 bar)|Pt(s).

Answer:

E_cell = ?

(i) Mg + Cu^{2 +} → Mg^{2 +} + Cu (n = 2)

E⁰_Cu^{2 +}_/Cu⁺ = 0.34V

E⁰_Mg^{2 +}_/Mg = - 2.37 V

E⁰_cell = E⁰_R - E⁰_L

E⁰_cell = 0.34 - ( - 2.37) → Equation 1

Using Nernst equation, we get,

 → Equation 2

Substituting Equation 1 in equation 2, we get,

∴ E_cell = 0.34 - ( - 2.37) - 

= 2.71 - 

= 2.71 - 0.02955

∴ E_cell = 2.68 V

The e.m.f of the cell, E_cell is 2.68 V

ii) Fe + 2H ⁺ → Fe^{2 +} + H₂ (n = 2)

E⁰_H⁺_/H2 = 0 V

E⁰_Fe^{2 +}_/Fe = - 0.44 V

E⁰_cell = E⁰_R - E⁰_L

E⁰_cell = 0 - ( - 0.44) → Equation 1

Using Nernst equation, we get,

 →Equation 2

Substituting Equation 1 in equation 2, we get,

∴ E_cell = 0 - ( - 0.44) - 

= 0.44 - 

= 0.44 - 0.0887

∴ E_cell = 0.5287 V

The e.m.f of the cell, E_cell is 0.5287 V

iii) Sn + 2H ⁺ → Sn^{2 +} + H₂ (n = 2)

E⁰_H⁺_/H2 = 0 V

E⁰_Sn^{2 +}_/Sn = - 0.14V

E⁰_cell = E⁰_R - E⁰_L

E⁰_cell = 0 - ( - 0.14) → Equation 1

Using Nernst equation, we get,

 →Equation 2

Substituting Equation 1 in equation 2, we get,

∴ E_cell = 0 - ( - 0.14) - 

= 0.14 - 

= 0.14 - 0.0295×2.0969

∴ E_cell = 0.08 V

The e.m.f of the cell, E_cell is 0.08 V

iv) 2Br ^- + 2H ⁺ → Br₂ + H₂ (n = 2)

E⁰_H⁺_/H2 = 0 V

E⁰_Br2/Br^- = 1.08V

E⁰_cell = E⁰_R - E⁰_L

E⁰_cell = 0 - (1.08) → Equation 1

Using Nernst equation, we get,

 →Equation 2

Substituting Equation 1 in equation 2, we get,

∴ E_cell = 0 - (1.08) - 

= - 1.08 - 

= - 1.08 - 0.208

∴ E_cell = 1.288 V

The e.m.f of the cell, E_cell is 1.288 V

Question 6.

In the button cells widely used in watches and other devices the following reaction takes place:

Zn_(s) + Ag₂O_(s) + H₂O_(l)→ Zn²⁺_(aq) + 2Ag_(s) + 2OH^–(aq). Determine Δ_rG⁰ and E⁰ for the reaction.

Answer:

Given - Zn → Zn^{2 +} + 2e ^- , E⁰ = 0.76V (anode)

Ag₂O + H₂O + 2e ^- →2Ag + 2OH ^- , E⁰ = 0.344V (cathode), n = 2

Δ_rG⁰ = ?

E⁰_cell = ?

Zn is oxidized and Ag₂O is reduced.

Hence, the standard cell potential, E⁰_cell is given as,

E⁰_cell = E⁰_R - E⁰_L

E⁰_cell = 0.344 + 0.76

∴ E⁰_cell = 1.104 V

To calculate the standard Gibb’s free energy, ∆_rG⁰, we use,

∆_rG⁰ = - nE⁰F → Equation 1

= - 2×96487×1.104 J

= - 213043.296 J

∴ ∆_rG⁰ = - 2.13×10⁵ J

The standard cell potential,E⁰_cell is 1.104 V and thestandard Gibb’s free energy, ∆_rG⁰ is- 2.13×10⁵ J

Question 7.

Define conductivity and molar conductivity of the solution of an electrolyte. Discuss their variation with concentration.

Answer:

The conductivityof a solution is defined as the conductance of one unit volume of solution kept between two platinum electrodes with a unit area of cross-section and at a distance of unit length.

The molar conductivityof the solution is defined as the conducting power of all the ions produced by one gram mole of an electrolyte in a solution. It is denoted by ∧_m.

The conductivityof a solution (both for strong and weak electrolytes) always decreases with the decrease in concentration of the electrolyte i.e., on dilution. This pattern is seen because the number of ions per unit volume that carry the current in the solution decreases on dilution. The molar conductivity of the solution increases with the decrease in concentration of the electrolyte. This is because both the number of ions as well as mobility of ions increase with dilution.

Question 8.

The conductivity of 0.20 M solution of KCl at 298 K is 0.0248 S cm^–1. Calculate its molar conductivity.

Answer:

Given -

Molarity, C = 0.20 M

Electrolytic conductivity of a solution, κ = 0.0248 S cm^–1

Molar conductivity = ?

Molar conductivity, ∧_m =  S cm² mol^-1

∴ ∧_m = 124 S cm² mol^-1

Molar conductivity(∧_m) of 0.20 M solution of KCl at 298 K is 124 Scm² mol^-1

Question 9.

The resistance of a conductivity cell containing 0.001M KCl solution at 298 K is 1500 Ω. What is the cell constant if the conductivity of 0.001M KCl solution at 298 K is 0.146 × 10^–3 S cm^–1.

Answer:

Given -

Resistance of a conductivity cell, R = 1500 

Electrolytic conductivity of a solution, κ = 0.146 × 10^–3 S cm^–1

Cell constant = ?

Conductivity, κ = 

Cell constant = κ × R

= 0.146 × 10^–3 S cm^–1×1500 

Cell constant = 0.219 cm^-1

The cell constant of the cell containing 0.001M KCl solution at 298 K is 0.219 cm^-1

Question 10.

The conductivity of sodium chloride at 298 K has been determined at different concentrations and the results are given below:


Calculate Λ_m for all concentrations and draw a plot between Λ_m and c^1/2. Find the value of Λ⁰_m.

Answer:

(unit conversion factor)

∧⁰_m= Intercept on the∧_maxis = 124.0 S cm² mol^-1, which is obtained by extrapolation to zero concentration.

Question 11.

Conductivity of 0.00241 M acetic acid is 7.896 × 10^–5 S cm^–1. Calculate its molar conductivity. If ∧⁰_m for acetic acid is 390.5 S cm²mol^–1, what is its dissociation constant?

Answer:

Given -

Molarity, C = 0.00241 M

Conductivity, κ = 7.896 × 10^–5 S cm^–1

Molar conductivity, ∧_m = ?

 for acetic acid = 390.5 S cm²mol^–1

Molar conductivity, ∧_m =  S cm² mol^-1

∴ ∧_m = 32.76 S cm² mol^-1

To calculate the dissociation constant, K_a, we use

K_a =  → Equation 1

Here, we need to find the value of α (degree of dissociation), by the formula,

∴ α = 8.4×10^-2 ⇒ Equation 2

→ Thus, substituting Equation 2 in Equation 1, we get,

K_a = 

= 

∴ K_a = 1.86×10 ^{- 5}

Themolar conductivity,∧_mis32.76S cm² mol^-1 and thedissociation constant, K_a is1.86×10^-5

Question 12.

How much charge is required for the following reductions:

(i) 1 mol of Al^{3 +} to Al?

(ii) 1 mol of Cu^{2 +} to Cu?

(iii) 1 mol of MnO^–₄ to Mn²⁺ ?

Answer:

(i) The electrode reaction is given as,

Al^{3 +}_(aq) + 3e ^- → Al_(s)

∴ The quantity of charge required for the reduction of 1 mol of Al³⁺ = 3F

= 3×96487 C

= 289461 C

(ii) The electrode reaction is given as,

Cu^{2 +}_(aq) + 2e ^- → Cu_(s)

∴ The quantity of charge required for the reduction of 1 mol of Cu²⁺ = 2F

= 2×96487 C

= 192974 C

(iii) The electrode reaction is given as,

MnO₄→ Mn^{2 +}

i.e., Mn^{7 +} + 5e ^- → Mn^{2 +}

∴ The quantity of charge required for the reduction of 1 mol of Mn⁷⁺ = 5F

= 5×96487 C

= 482435 C

Question 13.

How much electricity in terms of Faraday is required to produce

(i) 20.0 g of Ca from molten CaCl₂?

(ii) 40.0 g of Al from molten Al₂O₃?

Answer:

(i) Ca²⁺ + 2e^- → Ca

⇒ Here, 1 mole of Ca, i.e., 40g of Ca requires = 2 F electricity (F if Faraday)

∴ 20g of Ca requires = 

= 1 F of electricity

Electricity in terms of Faraday required to produce 20.0 g of Ca from molten CaCl₂ is1 F of electricity.

(ii) Al^{3 +} + 3e ^- → Al

⇒ 1 mole of Al, i.e., 27g of Al requires = 3 F electricity (F if Faraday)

∴ 40.0 g of Al will require = 

= 4.44 F of electricity

Electricity in terms of Faraday required to produce 40.0 g of Al from molten Al₂O₃ is 4.44 F of electricity

Question 14.

How much electricity is required in coulomb for the oxidation of

(i) 1 mol of H₂O to O₂?

(ii) 1 mol of FeO to Fe₂O₃?

Answer:

(i)The electrode reaction for 1 mole of H₂O is given as,

H₂O → H₂ + O₂

i.e., O^{2 -} →O₂ + 2e ^-

∴ The quantity of electricity required = 2F

= 2×96487 C

= 192974 C

The quantity of electricity required in coulomb for the oxidation of 1 mol of H₂O to O₂ is 192974 C

(ii) The electrode reaction for 1 mole of FeO is

FeO + O₂ → Fe₂O₃

i.e., Fe^{2 +} → Fe^{3 +} + e ^-

∴ The quantity of electricity required = 1F

= 1×96487 C

= 96487 C

The quantity of electricity required in coulomb for the oxidation of 1 mol of FeO to Fe₂O₃ is 96487 C

Question 15.

A solution of Ni(NO₃)₂ is electrolysed between platinum electrodes using a current of 5 amperes for 20 minutes. What is mass of Ni deposited at the cathode?

Given -

Current = 5A

Time - 20 minutes

Mass of Ni deposited = ?

Answer:

Quantity of electricity passed = 5 A × (20 × 60 sec)

= 6000 C ⇒ Equation 1

The electrode reaction is written as,

Ni^{2 +} + 2e → Ni

Thus, the quantity of electricity required = 2F

= 2×96487 C

= 192974 C

∵ 192974 C of electricity deposits 1 mole of Ni, which is 58.7 g ⇒ Equation 2

Thus, equating equations 1 and 2, we get,

192974 C of electricity deposits = 58.7 g

6000 C of electricity will deposit = 

= 1.825g of Ni

The mass of Ni deposited at the cathode is 1.825g of Ni

Question 16.

Three electrolytic cells A,B,C containing solutions of ZnSO₄, AgNO₃ and CuSO₄, respectively are connected in series. A steady current of 1.5 amperes was passed through them until 1.45 g of silver deposited at the cathode of cell B. How long did the current flow? What mass of copper and zinc were deposited?

Given -

I = 1.5 A

W = 1.45 g of Ag

t = ?

n = 1

Answer:

Equivalent weight is Ag, E_Ag =  = 180

Equivalent weight is Cu, E_Cu =  = 31.75

Equivalent weight is Zn, E_Zn=  = 32.5

Using Faraday’s second law of electrolysis, to find the mass of Cu and Zn, we use Equation 1,

 → Equation 1

⇒ 

∴ W_Cu = 0.426 g

⇒ 

∴ W_Zn = 0.436 g

To find the time of current flow, using Faraday’s first law of electrolysis we get,

M = Z ×I ×t ⇒ Equation 2

∵ Z = , Equation 2 becomes,

M = 

t = 

t = 864 seconds.

The time of current flow, t = 864 seconds, the mass of Cu is 0.426 g and mass of Zn is 0.436 g

Question 17.

Using the standard electrode potentials given in Table 3.1, predict if the reaction between the following is feasible:

(i) Fe^{3 +} (aq) and I^–(aq)

(ii) Ag ⁺ (aq) and Cu(s)

(iii) Fe^{3 +} (aq) and Br^– (aq)

(iv) Ag(s) and Fe^{3 +} (aq)

(v) Br₂ (aq) and Fe^{2 +} (aq).

Answer:

(i) The electrode reaction is written as,

2Fe^{3 +} + 2I ^- → 2Fe^{2 +} + I₂

E⁰_cell = 

= 0.54V - 0.77V

∴ E⁰_cell = - 0.23 V

It is not feasible, as E⁰_cell is negative, ∴ ∆G⁰ is positive.

(ii) The electrode reaction is written as,

2Ag ⁺_(aq) + Cu_(s)→ Cu^{2 +}_(aq) + Ag_(s)

E⁰_cell = 

= + 0.80V - 0.34V

∴ E⁰_cell = 0.46V

It is feasible, as E⁰_cell is positive, ∴ ∆G⁰ is negative.

(iii) The electrode reaction is written as,

2Fe^{3 +}_(aq) + 2Br ^-_(aq)→ 2Fe^{2 +}_(aq) + Br₂

E⁰_cell = 

= 0.77V - 1.09V

∴ E⁰_cell = - 0.32 V

It is not feasible, as E⁰_cell is negative, ∴ ∆G⁰ is positive.

(iv) The electrode reaction is written as,

Ag_(s) + Fe^{3 +}_(aq) → Fe^{2 +}_(aq) + Ag ⁺_(aq)

E⁰_cell = 

= 0.77V - 0.80V

∴ E⁰_cell = - 0.03

It is not feasible, as E⁰_cell is negative, ∴ ∆G⁰ is positive.

(v) The electrode reaction is written as,

Br₂ + 2Fe^{2 +}_(aq) → 2Br ^-_(aq) + 2Fe^{3 +}_(aq)

E⁰_cell = 

= 1.09V - 0.77V

∴ E⁰_cell = 0.32 V

It is feasible, as E⁰_cell is positive, ∴ ∆G⁰ is negative.

Question 18.

Predict the products of electrolysis in each of the following:

(i) An aqueous solution of AgNO₃ with silver electrodes.

(ii) An aqueous solution of AgNO₃ with platinum electrodes.

(iii) A dilute solution of H₂SO₄ with platinum electrodes.

(iv) An aqueous solution of CuCl₂ with platinum electrodes.

Answer:

Given -

All the ions are in aqueous state.

(i) Reaction in solution:

AgNO_3(s) + aq → Ag ⁺ + NO^{3 -}

H₂O ó H ⁺ + OH ^-

At cathode:

Ag ⁺_(aq) + e ^- →Ag_(s)

Ag ⁺ ions have lower discharge potential than H ⁺ ions. Hence, Ag ⁺ ions get deposited as Ag in preference to H ⁺ ions.

At anode:

Ag_(s)→ Ag ⁺_(aq) + e ^-

As Ag anode is attacked by NO^{3 -} ions, Ag of the anode will dissolve to form Ag ⁺ ions in the aqueous solution.

(ii) Reaction in solution:

AgNO_3(s) + aq → Ag ⁺ + NO^{3 -}

H₂O óH ⁺ + OH ^-

At cathode:

2Ag ⁺_(aq) + 2e ^- →2Ag_(s)

Ag ⁺ ions have lower discharge potential than H ⁺ ions. Hence, Ag ⁺ ions get deposited as Ag in preference to H ⁺ ions.

At anode:

2OH ^-_(aq) → O_2(g) + 2H ⁺_(aq) + 4e ^-

As anode is not attackable, out of OH ^- and NO^{3 -} ions, OH ^- having lower discharge potential, will be discharged in preference to NO^{3 -} ions. These then decompose to give out O₂.

(iii) Reaction in solution:

H₂SO_4(aq) → 2H ⁺_(aq) + SO₄^{2 -}_(aq)

At cathode:

2H ⁺_(aq) + 2e ^- →H_2(g)

At anode:

2OH ^-_(aq) → O_2(g) + 2H ⁺_(aq) + 4e ^-

∴H₂ gas is evolved at cathode and O_2(g) is evolved at anode.

(iv) Reaction in solution:

CuCl_2(s) + aq → Cu^{2 +}_(aq) + Cl ^-_(aq)

H₂O óH ⁺ + OH ^-

At cathode:

Cu^{2 +}_(aq) + 2e ^- →Cu_(g)

At anode:

2Cl ^-_(aq) - 2e ^- → Cl_2(g)

∴Cu will be deposited at cathode and Cl₂ gas will be liberated at anode.