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))

Solution :

Step 1: Identification of Half-Cell Reactions

Based on the cell notation $Mg(s)|Mg^{2+}(0.001 M)||Cu^{2+}(0.0001 M)|Cu(s)$, the anodic (oxidation) and cathodic (reduction) processes are defined as follows:

Anode (Oxidation): $Mg(s) \rightarrow Mg^{2+}(aq) + 2e^-$
Cathode (Reduction): $Cu^{2+}(aq) + 2e^- \rightarrow Cu(s)$
Overall Cell Reaction: $Mg(s) + Cu^{2+}(aq) \rightarrow Mg^{2+}(aq) + Cu(s)$

[Per the IUPAC convention for electrochemical cell representation, the oxidation half-cell is on the left and reduction half-cell is on the right.]

Step 2: Determination of Standard Cell Potential ($E^{\circ}_{cell}$)**

Using standard electrode potential values ($E^{\circ}_{Mg^{2+}/Mg} = -2.37 V$ and $E^{\circ}_{Cu^{2+}/Cu} = +0.34 V$):

$E^{\circ}_{cell} = E^{\circ}_{cathode} - E^{\circ}_{anode}$

$E^{\circ}_{cell} = 0.34 V - (-2.37 V) = 2.71 V$

Step 3: Formulation of the Nernst Equation

The Nernst equation at $T = 298 K$ is given by:

$E_{cell} = E^{\circ}_{cell} - \frac{0.0591}{n} \log Q$

Where:

$n = 2$ (number of electrons transferred)

$Q = \frac{[Mg^{2+}]}{[Cu^{2+}]} = \frac{10^{-3}}{10^{-4}} = 10^1 = 10$

[Justification: The reaction quotient $Q$ includes only aqueous ionic species; solids have unit activity.]

Step 4: Calculation of emf ($E_{cell}$)**

Substitute the identified values into the Nernst equation:

$E_{cell} = 2.71 - \frac{0.0591}{2} \log(10)$

Since $\log(10) = 1$:

$E_{cell} = 2.71 - 0.02955 \times 1$

$E_{cell} = 2.68045 V$

Step 5: Final Summary**

The Nernst equation for the given reaction is: $E_{cell} = 2.71 - 0.02955 \log \frac{[Mg^{2+}]}{[Cu^{2+}]}$

Final Solution: The emf of the cell is 2.68 V

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 (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.

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 (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 $0.146 \times 10^{-3} S cm^{-1}$.

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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))

Step 1: Identification of Half-Cell Reactions

Step 2: Determination of Standard Cell Potential ($E^{\circ}_{cell}$)**

Step 3: Formulation of the Nernst Equation

Step 4: Calculation of emf ($E_{cell}$)**

Step 5: Final Summary**

More Questions from Class 12 Chemistry Electrochemistry Exercises

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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))