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Q2.4 (i):
Calculate the standard cell potentials of galvanic cell in which the following reaction takes place:
(i) (2Cr(s) + 3Cd^{2+}(aq) \rightarrow 2Cr^{3+}(aq) + 3Cd)
Calculate the (\Delta_{r}G^{o}) and equilibrium constant of the reaction.
Solution :
Step 1: Identification of Half-Cell Reactions and Standard Potentials
To calculate the standard cell potential ($E^o_{cell}$), we identify the oxidation and reduction half-reactions from the given global equation:
- Oxidation (Anode): $2Cr(s) \rightarrow 2Cr^{3+}(aq) + 6e^-$
- Reduction (Cathode): $3Cd^{2+}(aq) + 6e^- \rightarrow 3Cd(s)$
Referring to standard electrode potential tables [$E^o_{Cr^{3+}/Cr} = -0.74\text{ V}$ and $E^o_{Cd^{2+}/Cd} = -0.40\text{ V}$]:
Step 2: Calculation of Standard Cell Potential ($E^o_{cell}$)
The standard cell potential is defined as the difference between the reduction potential of the cathode and the anode [Per Nernst Equation principles at standard conditions]:
$E^o_{cell} = E^o_{cathode} - E^o_{anode}$
$E^o_{cell} = E^o_{Cd^{2+}/Cd} - E^o_{Cr^{3+}/Cr}$
$E^o_{cell} = -0.40\text{ V} - (-0.74\text{ V}) = +0.34\text{ V}$
Step 3: Calculation of Standard Gibbs Free Energy Change ($\Delta_r G^o$)
The relationship between the standard Gibbs free energy and the cell potential is given by the formula [Per Faraday’s Laws of Electrolysis and Thermodynamic Relations]:
$\Delta_r G^o = -nFE^o_{cell}$
Where:
- $n = 6$ (moles of electrons transferred)
- $F = 96487\text{ C mol}^{-1}$ (Faraday's Constant)
- $E^o_{cell} = 0.34\text{ V}$
$\Delta_r G^o = -(6) \times (96487\text{ C mol}^{-1}) \times (0.34\text{ J C}^{-1})$
$\Delta_r G^o = -196833.48\text{ J mol}^{-1} \approx -196.83\text{ kJ mol}^{-1}$
Step 4: Calculation of Equilibrium Constant ($K_c$)
The equilibrium constant is related to the standard cell potential by the expression [Derived from the Nernst Equation at equilibrium, where $E_{cell} = 0$]:
$\ln K_c = \frac{nFE^o_{cell}}{RT}$ or $\log K_c = \frac{nE^o_{cell}}{0.0591}$
Using the value $0.0591$ for $2.303RT/F$ at $298\text{ K}$:
$\log K_c = \frac{6 \times 0.34}{0.0591} = \frac{2.04}{0.0591} \approx 34.5177$
$K_c = \text{antilog}(34.5177) = 3.29 \times 10^{34}$
Final Solution: The standard cell potential $E^o_{cell} = 0.34\text{ V}$, the standard Gibbs free energy $\Delta_r G^o = -196.83\text{ kJ mol}^{-1}$, and the equilibrium constant $K_c = 3.29 \times 10^{34}$.
More Questions from Class 12 Chemistry Electrochemistry Exercises
- Q2.1: 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.
- Q2.1: 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.
- Q2.10: The conductivity of sodium chloride at 298 K has been determined at different concentrations and the results are given below: Calculate (\Lambda_{m}) for all concentrations and draw a plot between (\Lambda_{m}) and (c^{1/2}). Find the value of (\Lambda^{0}_{m}).
- Q2.10: The conductivity of sodium chloride at 298 K has been determined at different concentrations and the results are given below: Calculate \(\Lambda_{m}\) for all concentrations and draw a plot between \(\Lambda_{m}\) and \(c^{1/2}\). Find the value of \(\Lambda_{m}^{\circ}\).
- Q2.11: Conductivity of 0.00241 M acetic acid is 7.896 (\times) (10^{-5}) S (cm^{-1}). Calculate its molar conductivity. If (\Lambda^{0}_{m}) for acetic acid is 390.5 S (cm^{2} mol^{-1}), what is its dissociation constant?
- Q2.11: Conductivity of 0.00241 M acetic acid is \(7.896 \times 10^{-5} S cm^{-1}\). Calculate its molar conductivity. If \(\Lambda_{m}^{\circ}\) for acetic acid is \(390.5 S cm^{2} mol^{-1}\), what is its dissociation constant?
- Q2.12 (i): How much charge is required for the following reduction: (i) 1 mol of (Al^{3+}) to Al?
- Q2.12 (ii): How much charge is required for the following reduction: (ii) 1 mol of (Cu^{2+}) to Cu?
- Q2.12 (iii): How much charge is required for the following reduction: (iii) 1 mol of (MnO_{4}^{-}) to (Mn^{2+})?
- Q2.12(i): How much charge is required for the following reduction: 1 mol of \(Al^{3+}\) to Al?
- Q2.12(ii): How much charge is required for the following reduction: 1 mol of \(Cu^{2+}\) to Cu?
- Q2.12(iii): How much charge is required for the following reduction: 1 mol of \(MnO_{4}^{-}\) to \(Mn^{2+}\)?
- Q2.13 (i): How much electricity in terms of Faraday is required to produce (i) 20.0 g of Ca from molten (CaCl_{2})?
- Q2.13 (ii): How much electricity in terms of Faraday is required to produce (ii) 40.0 g of Al from molten (Al_{2}O_{3})?
- Q2.13(i): How much electricity in terms of Faraday is required to produce 20.0 g of Ca from molten \(CaCl_{2}\)?
- Q2.13(ii): How much electricity in terms of Faraday is required to produce 40.0 g of Al from molten \(Al_{2}O_{3}\)?
- Q2.14 (i): How much electricity is required in coulomb for the oxidation of (i) 1 mol of (H_{2}O) to (O_{2})?
- Q2.14 (ii): How much electricity is required in coulomb for the oxidation of (ii) 1 mol of (FeO) to (Fe_{2}O_{3})?
- Q2.14(i): How much electricity is required in coulomb for the oxidation of 1 mol of \(H_{2}O\) to \(O_{2}\)?
- Q2.14(ii): How much electricity is required in coulomb for the oxidation of 1 mol of FeO to \(Fe_{2}O_{3}\)?
- Q2.15: A solution of (Ni(NO_{3})_{2}) is electrolysed between platinum electrodes using a current of 5 amperes for 20 minutes. What mass of Ni is deposited at the cathode?
- Q2.15: A solution of \(Ni(NO_{3})_{2}\) is electrolysed between platinum electrodes using a current of 5 amperes for 20 minutes. What mass of Ni is deposited at the cathode?
- Q2.16: Three electrolytic cells A,B,C containing solutions of (ZnSO_{4}), (AgNO_{3}) and (CuSO_{4}), 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?
- Q2.16: Three electrolytic cells A,B,C containing solutions of \(ZnSO_{4}\), \(AgNO_{3}\) and \(CuSO_{4}\), 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?
- Q2.17 (i): Using the standard electrode potentials, predict if the reaction between the following is feasible: (i) (Fe^{3+}(aq)) and (I^{-}(aq))
- Q2.17 (ii): Using the standard electrode potentials, predict if the reaction between the following is feasible: (ii) (Ag^{+} (aq)) and Cu(s)
- Q2.17 (iii): Using the standard electrode potentials, predict if the reaction between the following is feasible: (iii) (Fe^{3+} (aq)) and (Br^{-} (aq))
- Q2.17 (iv): Using the standard electrode potentials, predict if the reaction between the following is feasible: (iv) Ag(s) and (Fe^{3+} (aq))
- Q2.17 (v): Using the standard electrode potentials, predict if the reaction between the following is feasible: (v) (Br_{2} (aq)) and (Fe^{2+} (aq)).
- Q2.17(i): Using the standard electrode potentials given in Table 3.1, predict if the reaction between the following is feasible: \(Fe^{3+}(aq)\) and \(I^{-}(aq)\)
- Q2.17(ii): Using the standard electrode potentials given in Table 3.1, predict if the reaction between the following is feasible: \(Ag^{+} (aq)\) and \(Cu(s)\)
- Q2.17(iii): Using the standard electrode potentials given in Table 3.1, predict if the reaction between the following is feasible: \(Fe^{3+} (aq)\) and \(Br^{-} (aq)\)
- Q2.17(iv): Using the standard electrode potentials given in Table 3.1, predict if the reaction between the following is feasible: \(Ag(s)\) and \(Fe^{3+} (aq)\)
- Q2.17(v): Using the standard electrode potentials given in Table 3.1, predict if the reaction between the following is feasible: \(Br_{2} (aq)\) and \(Fe^{2+} (aq)\).
- Q2.18 (i): Predict the products of electrolysis in each of the following: (i) An aqueous solution of (AgNO_{3}) with silver electrodes.
- Q2.18 (ii): Predict the products of electrolysis in each of the following: (ii) An aqueous solution of (AgNO_{3}) with platinum electrodes.
- Q2.18 (iii): Predict the products of electrolysis in each of the following: (iii) A dilute solution of (H_{2}SO_{4}) with platinum electrodes.
- Q2.18 (iv): Predict the products of electrolysis in each of the following: (iv) An aqueous solution of (CuCl_{2}) with platinum electrodes.
- Q2.18(i): Predict the products of electrolysis in each of the following: An aqueous solution of \(AgNO_{3}\) with silver electrodes.
- Q2.18(ii): Predict the products of electrolysis in each of the following: An aqueous solution of \(AgNO_{3}\) with platinum electrodes.
- Q2.18(iii): Predict the products of electrolysis in each of the following: A dilute solution of \(H_{2}SO_{4}\) with platinum electrodes.
- Q2.18(iv): Predict the products of electrolysis in each of the following: An aqueous solution of \(CuCl_{2}\) with platinum electrodes.
- Q2.2: Given the standard electrode potentials, (K^{+}/K) = –2.93V, (Ag^{+}/Ag) = 0.80V, (Hg^{2+}/Hg) = 0.79V (Mg^{2+}/Mg) = –2.37 V, (Cr^{3+}/Cr) = – 0.74V Arrange these metals in their increasing order of reducing power.
- Q2.2: Given the standard electrode potentials, \(K^{+}/K = –2.93V\), \(Ag^{+}/Ag = 0.80V\), \(Hg^{2+}/Hg = 0.79V\) \(Mg^{2+}/Mg = –2.37 V\), \(Cr^{3+}/Cr = – 0.74V\) Arrange these metals in their increasing order of reducing power.
- Q2.3 (i): Depict the galvanic cell in which the reaction (Zn(s)+2Ag^{+}(aq) \rightarrow Zn^{2+}(aq)+2Ag(s)) takes place. Further show: (i) Which of the electrode is negatively charged?
- Q2.3 (ii): Depict the galvanic cell in which the reaction (Zn(s)+2Ag^{+}(aq) \rightarrow Zn^{2+}(aq)+2Ag(s)) takes place. Further show: (ii) The carriers of the current in the cell.
- Q2.3 (iii): Depict the galvanic cell in which the reaction (Zn(s)+2Ag^{+}(aq) \rightarrow Zn^{2+}(aq)+2Ag(s)) takes place. Further show: (iii) Individual reaction at each electrode.
- Q2.3(i): Depict the galvanic cell in which the reaction \(Zn(s)+2Ag^{+}(aq) \rightarrow Zn^{2+}(aq)+2Ag(s)\) takes place. Further show: Which of the electrode is negatively charged?
- Q2.3(ii): Depict the galvanic cell in which the reaction \(Zn(s)+2Ag^{+}(aq) \rightarrow Zn^{2+}(aq)+2Ag(s)\) takes place. Further show: The carriers of the current in the cell.
- Q2.3(iii): Depict the galvanic cell in which the reaction \(Zn(s)+2Ag^{+}(aq) \rightarrow Zn^{2+}(aq)+2Ag(s)\) takes place. Further show: Individual reaction at each electrode.
- Q2.4 (ii): Calculate the standard cell potentials of galvanic cell in which the following reaction takes place: (ii) (Fe^{2+}(aq) + Ag^{+}(aq) \rightarrow Fe^{3+}(aq) + Ag(s)) Calculate the (\Delta_{r}G^{o}) and equilibrium constant of the reaction.
- Q2.4(i): Calculate the standard cell potentials of galvanic cell in which the following reaction takes place: \(2Cr(s) + 3Cd^{2+}(aq) \rightarrow 2Cr^{3+}(aq) + 3Cd(s)\) Calculate the \(\Delta_{r}G^{\circ}\) and equilibrium constant of the reaction.
- Q2.4(ii): Calculate the standard cell potentials of galvanic cell in which the following reaction takes place: \(Fe^{2+}(aq) + Ag^{+}(aq) \rightarrow Fe^{3+}(aq) + Ag(s)\) Calculate the \(\Delta_{r}G^{\circ}\) and equilibrium constant of the reaction.
- Q2.5 (i): Write the Nernst equation and emf of the following cell at 298 K: (i) (Mg(s)|Mg^{2+}(0.001M)||Cu^{2+}(0.0001 M)|Cu(s))
- Q2.5 (ii): Write the Nernst equation and emf of the following cell at 298 K: (ii) (Fe(s)|Fe^{2+}(0.001M)||H^{+}(1M)|H_{2}(g)(1bar)| Pt(s))
- Q2.5 (iii): Write the Nernst equation and emf of the following cell at 298 K: (iii) (Sn(s)|Sn^{2+}(0.050 M)||H^{+}(0.020 M)|H_{2}(g) (1 bar)|Pt(s))
- Q2.5 (iv): Write the Nernst equation and emf of the following cell at 298 K: (iv) (Pt(s)|Br^{-}(0.010 M)|Br_{2}(l )||H^{+}(0.030 M)| H_{2}(g) (1 bar)|Pt(s)).
- Q2.5(i): Write the Nernst equation and emf of the following cell at 298 K: \(Mg(s)|Mg^{2+}(0.001M)||Cu^{2+}(0.0001 M)|Cu(s)\)
- Q2.5(ii): Write the Nernst equation and emf of the following cell at 298 K: \(Fe(s)|Fe^{2+}(0.001M)||H^{+}(1M)|H_{2}(g)(1bar)| Pt(s)\)
- Q2.5(iii): Write the Nernst equation and emf of the following cell at 298 K: \(Sn(s)|Sn^{2+}(0.050 M)||H^{+}(0.020 M)|H_{2}(g) (1 bar)|Pt(s)\)
- Q2.5(iv): Write the Nernst equation and emf of the following cell at 298 K: \(Pt(s)|Br^{-}(0.010 M)|Br_{2}(l )||H^{+}(0.030 M)| H_{2}(g) (1 bar)|Pt(s)\).
- Q2.6: In the button cells widely used in watches and other devices the following reaction takes place: (Zn(s) + Ag_{2}O(s) + H_{2}O(l ) \rightarrow Zn^{2+}(aq) + 2Ag(s) + 2OH^{-}(aq)) Determine (\Delta_{r}G^{o}) and (E^{o}) for the reaction.
- Q2.6: In the button cells widely used in watches and other devices the following reaction takes place: \(Zn(s) + Ag_{2}O(s) + H_{2}O(l ) \rightarrow Zn^{2+}(aq) + 2Ag(s) + 2OH^{-}(aq)\) Determine \(\Delta_{r}G^{\circ}\) and \(E^{\circ}\) for the reaction.
- Q2.7: Define conductivity and molar conductivity for the solution of an electrolyte. Discuss their variation with concentration.
- Q2.7: Define conductivity and molar conductivity for the solution of an electrolyte. Discuss their variation with concentration.
- Q2.8: The conductivity of 0.20 M solution of KCl at 298 K is 0.0248 S (cm^{-1}). Calculate its molar conductivity.
- Q2.8: The conductivity of 0.20 M solution of KCl at 298 K is \(0.0248 S cm^{-1}\). Calculate its molar conductivity.
- Q2.9: The resistance of a conductivity cell containing 0.001M KCl solution at 298 K is 1500 (\Omega). What is the cell constant if conductivity of 0.001M KCl solution at 298 K is 0.146 (\times) (10^{-3}) S (cm^{-1}).
- Q2.9: The resistance of a conductivity cell containing 0.001M KCl solution at 298 K is \(1500 \Omega\). What is the cell constant if conductivity of 0.001M KCl solution at 298 K is \(0.146 \times 10^{-3} S cm^{-1}\).
CBSE Solutions for Class 12 Chemistry Electrochemistry
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