Electrochemical cells Questions in English

(N/A) $1$. The standard potential of a Daniell cell is $1.1 \ V$.
$2$. In a Daniell cell,chemical energy is converted into electrical energy.
$3$. In a Daniell cell,$Zn$ (zinc) is the anode and $Cu$ (copper) is the cathode.

(A) Statement $(1)$ is true: In a Daniell cell,the anode reaction is $Zn(s) \rightarrow Zn^{2+}(aq) + 2e^-$,where $Zn$ dissolves,and the cathode reaction is $Cu^{2+}(aq) + 2e^- \rightarrow Cu(s)$,where $Cu$ is deposited.
Statement $(2)$ is true: The standard $EMF$ of a Daniell cell is $1.1 \ V$. When an external opposing potential of exactly $1.1 \ V$ is applied,the potential difference becomes zero,the cell reaction stops,and no current flows through the circuit.

(N/A) Galvanic cell: It is an electrochemical cell that converts the chemical energy of a spontaneous redox reaction into electrical energy.
$(b)$ Chemical reactions in a Daniell cell:
$(i)$ $Cu^{2+}_{(aq)} + 2e^{-} \longrightarrow Cu_{(s)}$ (reduction half-reaction)
$(ii)$ $Zn_{(s)} \longrightarrow Zn^{2+}_{(aq)} + 2e^{-}$ (oxidation half-reaction)
$(iii)$ $Zn_{(s)} + Cu^{2+}_{(aq)} \longrightarrow Zn^{2+}_{(aq)} + Cu_{(s)}$ (overall redox reaction)
These reactions occur in two different portions of the Daniell cell. The reduction half-reaction occurs on the copper electrode,while the oxidation half-reaction occurs on the zinc electrode. These two portions are called half-cells. $A$ redox couple is defined as having together the oxidized and reduced forms of a substance taking part in an oxidation or reduction half-reaction. For example,$Zn^{2+}/Zn$ and $Cu^{2+}/Cu$ are redox couples.

(N/A) Construction of a galvanic cell based on the Daniell cell: We can construct various galvanic cells following the pattern of the Daniell cell by using different combinations of half-cells.
$(i)$ Each half-cell consists of a metallic electrode dipped into an electrolyte solution.
$(ii)$ The two half-cells are connected externally by a metallic wire through a voltmeter and a switch.
$(iii)$ The electrolytes of the two half-cells are connected internally through a salt bridge. In some cases,both electrodes may dip into the same electrolyte solution,in which case a salt bridge is not required.
$(b)$ Positive and negative electrodes and reactions in the Daniell cell:
Positive electrode (Cathode): At the electrode-electrolyte interface,metal ions from the solution tend to deposit on the metal electrode,making it positively charged.
$M^{n+}_{(aq)} + ne^{-} \longrightarrow M_{(s)}$ (Reduction)
In the Daniell cell,the $Cu$ electrode acts as the cathode (positive electrode),where the reduction reaction occurs.
Negative electrode (Anode): Metal atoms of the electrode tend to enter the solution as ions,leaving behind electrons on the electrode,making it negatively charged.
$M_{(s)} \longrightarrow M^{n+}_{(aq)} + ne^{-}$ (Oxidation)
In the Daniell cell,the $Zn$ electrode acts as the anode (negative electrode),where the oxidation reaction occurs.

(N/A) The redox reaction for the copper-silver cell is:
$Cu_{(s)} + 2Ag_{(aq)}^{+} \rightarrow Cu_{(aq)}^{2+} + 2Ag_{(s)}$
Half-cell reactions are as follows:
Cathode (reduction): $2Ag_{(aq)}^{+} + 2e^{-} \rightarrow 2Ag_{(s)}$
Anode (oxidation): $Cu_{(s)} \rightarrow Cu_{(aq)}^{2+} + 2e^{-}$
The cell representation is:
$Cu_{(s)} | Cu_{(aq)}^{2+} \| Ag_{(aq)}^{+} | Ag_{(s)}$
The formula for the cell potential is:
$E_{cell} = E_{cathode} - E_{anode} = E_{Ag^{+}|Ag} - E_{Cu^{2+}|Cu}$

(N/A) Electrode: In a galvanic or electrolytic cell,the system formed by placing a metal rod or plate into its own salt solution is known as an electrode,where the flow of current or electrons occurs.
Half-cell: $A$ system consisting of an electrode and the solution in which it is immersed,where either an oxidation or a reduction reaction takes place,is called a half-cell.
Symbolic representation of a half-cell: $A$ vertical line is used to separate the metal and its ion. By convention,for a reduction reaction,the representation is written as $\text{metal ion} \mid \text{metal}$.
For reduction: The symbolic representation of $Zn^{2+} + 2e^{-} \rightarrow Zn$ is $Zn_{(aq)}^{2+} \mid Zn_{(s)}$.
For oxidation: The symbolic representation of $Zn_{(s)} \rightarrow Zn^{2+} + 2e^{-}$ is $Zn_{(s)} \mid Zn_{(aq)}^{2+}$.
If the reactant or product is a gas or liquid,platinum $(Pt)$ is typically used as an inert electrode. Examples:
$(i)$ Hydrogen electrode:
Anode (Oxidation): $Pt_{(s)} \mid H_{2(g)} \ (1 \ \text{bar}) \mid H_{(aq)}^{+}$
Cathode (Reduction): $H_{(aq)}^{+} \mid H_{2(g)} \ (1 \ \text{bar}) \mid Pt_{(s)}$
$(ii)$ Bromine electrode:
Cathode (Reduction): $Pt_{(s)} \mid Br_{2(aq)} \mid Br_{(aq)}^{-}$
Anode (Oxidation): $Br_{(aq)}^{-} \mid Br_{2(aq)} \mid Pt_{(s)}$

(N/A) In the symbolic representation of an electrochemical cell,the reactions of the anode (left side) and cathode (right side) half-cells are denoted by placing a single vertical line between the metal and the metal ion,or the ion and the metal,respectively.
Anode and cathode are represented on the left and right sides,respectively.
Negative $(-)$ and positive $(+)$ signs are denoted on the anode and cathode,respectively.
Two parallel vertical lines $(||)$ are placed to denote the salt bridge between these two half-cells.
If an inert electrode is used,it is denoted by symbols like $Pt$ or $C$,depending on the metal used.
Example-$1$: Symbolic representation of the Daniell cell: $Zn_{(s)} | Zn^{2+}_{(aq)} || Cu^{2+}_{(aq)} | Cu_{(s)}$
Example-$2$: Symbolic representation of a galvanic cell constructed with an inert electrode: $Pt_{(s)} | H_{2(g)} | H^{+}_{(aq)} || Cu^{2+}_{(aq)} | Cu_{(s)}$

(N/A) On the basis of the reaction occurring on the surface of the electrode:
In a galvanic cell,the half-cell in which oxidation takes place is called the anode,and the other half-cell in which reduction takes place is called the cathode.
$(b)$ On the basis of electric charge on the electrode:
Positive and negative electrode: More electrons are present in the negative electrode with respect to the positive electrode. $E$.g.,in a galvanic cell,the anode is negative and the cathode is positive.
$(c)$ Classification based on the nature of electrodes:
$(i)$ Active electrode: In a cell,an electrode that shows either an increase or a decrease in its weight is called an active electrode. If an active metal dissolves in the solution during the reaction,its weight is reduced. If,during the reaction,ions from the solution undergo reduction and convert into metal particles that deposit on the electrode,the weight of the metal increases. For example,$Zn$ and $Cu$ metals are active electrodes in a Daniell cell.
$Zn(s) \rightarrow Zn^{2+}(aq) + 2e^{-}$ (Oxidation)
$Cu^{2+}(aq) + 2e^{-} \rightarrow Cu(s)$ (Reduction)
Here,the weight of $Zn$ decreases and the weight of $Cu$ increases.
$(ii)$ Inert electrode: An electrode that provides only its surface for the cell reaction but does not take part in the reaction is termed an inert electrode. $E$.g.,metals like platinum,graphite,etc.,are used in half-cells having either gas or liquid reactants or products. Platinum-$H_2$ gas is an example of an inert electrode.

(N/A) In a galvanic cell,the electrode with the lower reduction potential acts as the anode (oxidation) and the electrode with the higher reduction potential acts as the cathode (reduction).
Here,$E^o_{Zn^{2+}|Zn} = -0.76 \ V$ (lower) and $E^o_{Ag^{+}|Ag} = 0.80 \ V$ (higher).
Therefore,$Zn$ acts as the anode and $Ag$ acts as the cathode.
The symbolic representation of the cell is: $Zn(s) | Zn^{2+}(aq) || Ag^{+}(aq) | Ag(s)$.
The standard cell potential is calculated as:
$E^o_{cell} = E^o_{cathode} - E^o_{anode}$
$E^o_{cell} = E^o_{Ag^{+}|Ag} - E^o_{Zn^{2+}|Zn}$
$E^o_{cell} = 0.80 \ V - (-0.76 \ V)$
$E^o_{cell} = 0.80 \ V + 0.76 \ V = 1.56 \ V$.

(N/A) To construct a galvanic cell,we identify the anode and cathode based on standard reduction potentials.
$E^o_{Mg^{2+}|Mg} = -2.37 \ V$ (Anode,as it is more negative)
$E^o_{Co^{2+}|Co} = -0.28 \ V$ (Cathode,as it is more positive)
In a galvanic cell,oxidation occurs at the anode and reduction occurs at the cathode.
Anode reaction: $Mg(s) \rightarrow Mg^{2+}(aq) + 2e^-$
Cathode reaction: $Co^{2+}(aq) + 2e^- \rightarrow Co(s)$
The symbolic representation of a galvanic cell is written as: $\text{Anode} | \text{Anode electrolyte} || \text{Cathode electrolyte} | \text{Cathode}$
Therefore,the representation is: $Mg(s) | Mg^{2+}(aq) || Co^{2+}(aq) | Co(s)$

(N/A) $1$. Identify the anode and cathode based on standard reduction potentials: Since $E^o_{Ag^{+}|Ag} (0.80 \ V) > E^o_{Ni^{2+}|Ni} (-0.23 \ V)$,$Ag$ acts as the cathode and $Ni$ acts as the anode.
$2$. Symbolic representation: The cell is represented as $Ni(s) | Ni^{2+}(aq) || Ag^{+}(aq) | Ag(s)$.
$3$. Cell reactions:
At anode (oxidation): $Ni(s) \rightarrow Ni^{2+}(aq) + 2e^-$
At cathode (reduction): $2Ag^{+}(aq) + 2e^- \rightarrow 2Ag(s)$
Overall cell reaction: $Ni(s) + 2Ag^{+}(aq) \rightarrow Ni^{2+}(aq) + 2Ag(s)$.

(N/A) $1$. Identify the anode and cathode based on standard reduction potentials: $E^o_{Al^{3+}|Al} = -1.66 \ V$ (Anode) and $E^o_{Ag^{+}|Ag} = 0.80 \ V$ (Cathode).
$2$. The cell reaction is: $Al(s) + 3Ag^+(aq) \rightarrow Al^{3+}(aq) + 3Ag(s)$.
$3$. In a galvanic cell,electrons flow from the anode ($Al$ electrode) to the cathode ($Ag$ electrode) through the external circuit.
$4$. The conventional current flows in the opposite direction,i.e.,from the cathode ($Ag$ electrode) to the anode ($Al$ electrode).
$5$. Diagram description: An $Al$ electrode is placed in an $Al(NO_3)_3$ solution and an $Ag$ electrode is placed in an $AgNO_3$ solution,connected by a salt bridge and an external wire with a voltmeter.

(N/A) An $inert \ electrode$ is an electrode that does not participate in the chemical reaction of the cell but provides a surface for the transfer of electrons. Example: $Platinum \ (Pt)$ or $Graphite$.
An $active \ electrode$ is an electrode that participates in the chemical reaction by either losing ions to the solution or gaining ions from the solution. Examples: $Zinc \ (Zn)$ electrode,$Copper \ (Cu)$ electrode,or $Silver \ (Ag)$ electrode.

(N/A) In an electrochemical cell,the electrode where oxidation occurs is called the $Anode$. It is the site where electrons are released into the external circuit.
In an electrochemical cell,the electrode where reduction occurs is called the $Cathode$. It is the site where electrons are consumed from the external circuit.

(A) In an electrochemical cell,the electrode where oxidation occurs is called the $Anode$,and the electrode where reduction occurs is called the $Cathode$.
In a $Galvanic$ cell,the $Anode$ is the negative electrode and the $Cathode$ is the positive electrode.
In an $Electrolytic$ cell,the $Anode$ is the positive electrode and the $Cathode$ is the negative electrode.
However,by standard convention in general electrochemistry,the $Anode$ is defined as the site of oxidation and the $Cathode$ as the site of reduction.
Given the options,$A$ describes the standard $Electrolytic$ cell configuration.

(D) salt bridge serves multiple critical functions in an electrochemical cell:
$1$. It completes the electrical circuit by allowing the flow of ions between the two half-cells.
$2$. It maintains electrical neutrality in both half-cells by providing ions to balance the charge accumulation.
$3$. It minimizes or prevents the liquid junction potential that arises due to the unequal migration of ions at the interface of the two solutions.

(N/A) In a galvanic cell,the flow of electrons is completed through two paths:
$1$. External Circuit: Electrons flow from the anode to the cathode through an external metallic wire. This flow is driven by the potential difference between the two electrodes.
$2$. Internal Circuit: The internal circuit is completed by a salt bridge or a porous membrane containing an electrolyte. This allows the movement of ions ($cations$ and $anions$) to maintain electrical neutrality in the half-cells and prevents the buildup of charge,thereby allowing the continuous flow of electrons.

$(i)$ For a Daniell cell $(Zn|Zn^{2+}||Cu^{2+}|Cu)$:
Anode reaction: $Zn(s) \rightarrow Zn^{2+}(aq) + 2e^-$
Cathode reaction: $Cu^{2+}(aq) + 2e^- \rightarrow Cu(s)$
Overall redox reaction: $Zn(s) + Cu^{2+}(aq) \rightarrow Zn^{2+}(aq) + Cu(s)$
$(ii)$ For a $Cu-Ag$ galvanic cell $(Cu|Cu^{2+}||Ag^+|Ag)$:
Anode reaction: $Cu(s) \rightarrow Cu^{2+}(aq) + 2e^-$
Cathode reaction: $2Ag^+(aq) + 2e^- \rightarrow 2Ag(s)$
Overall redox reaction: $Cu(s) + 2Ag^+(aq) \rightarrow Cu^{2+}(aq) + 2Ag(s)$

(N/A) $(i)$ For the Daniell cell,the reaction is $Zn(s) + Cu^{2+}(aq) \rightarrow Zn^{2+}(aq) + Cu(s)$. The symbolic representation is $Zn(s) | Zn^{2+}(aq) || Cu^{2+}(aq) | Cu(s)$.
$(ii)$ For the Copper-Silver cell,the reaction is $Cu(s) + 2Ag^+(aq) \rightarrow Cu^{2+}(aq) + 2Ag(s)$. The symbolic representation is $Cu(s) | Cu^{2+}(aq) || Ag^+(aq) | Ag(s)$.

(A) In an electrochemical cell,the anode is the electrode where oxidation occurs,and the cathode is where reduction occurs.
For the $Daniell$ cell $(Zn|Zn^{2+}||Cu^{2+}|Cu)$:
$Zn$ acts as the anode (negative electrode) and $Cu$ acts as the cathode (positive electrode).
For the $Copper-Silver$ cell $(Cu|Cu^{2+}||Ag^+|Ag)$:
$Cu$ acts as the anode (negative electrode) and $Ag$ acts as the cathode (positive electrode).
Therefore,the correct configuration is:
$Daniell$ cell: Anode $(Zn)$,Cathode $(Cu)$,Positive $(Cu)$,Negative $(Zn)$;
$Cu-Ag$ cell: Anode $(Cu)$,Cathode $(Ag)$,Positive $(Ag)$,Negative $(Cu)$.

(N/A) $(1)$ In a galvanic cell,the anode is the negative electrode (site of oxidation) and the cathode is the positive electrode (site of reduction). Thus,the charges are negative and positive respectively.
$(2)$ By convention,in a standard cell diagram (cell notation),the anode is written on the left side and the cathode is written on the right side.

(A) The overall cell reaction is the sum of the two half-reactions:
$Zn + Ag_{2}O + H_{2}O \rightarrow Zn^{2+} + 2Ag + 2OH^{-}$
The standard cell potential $E^{o}_{cell}$ is given by:
$E^{o}_{cell} = E^{o}_{cathode} - E^{o}_{anode}$
$E^{o}_{cell} = 0.34 \ V - (-0.76 \ V) = 1.10 \ V$
The number of electrons transferred in the balanced equation is $n = 2$.
The standard Gibbs free energy change is calculated using the formula:
$\Delta G^{o} = -nFE^{o}_{cell}$
where $F \approx 96500 \ C \ mol^{-1}$.
$\Delta G^{o} = -2 \times 96500 \ C \ mol^{-1} \times 1.10 \ V$
$\Delta G^{o} = -212300 \ J \ mol^{-1} = -2.123 \times 10^{5} \ J \ mol^{-1}$.

(N/A) The following reaction takes place during the extraction of $Cl_2$ from brine:
$2Cl^{-} + 2H_2O \rightarrow Cl_2 + 2OH^{-} + H_2$
The standard Gibbs free energy change for this reaction is $\Delta G^{\circ} = +422 \ kJ \ mol^{-1}$.
Using the relation $\Delta G^{\circ} = -nFE^{\circ}$,where $n = 2$ and $F = 96500 \ C \ mol^{-1}$,we calculate the standard cell potential:
$E^{\circ} = -\frac{\Delta G^{\circ}}{nF} = -\frac{422000 \ J \ mol^{-1}}{2 \times 96500 \ C \ mol^{-1}} \approx -2.2 \ V$.
Since the standard cell potential is negative,the reaction is non-spontaneous. Therefore,an external $emf$ greater than $2.2 \ V$ is required to drive the reaction.

(N/A) In the Daniell cell,the overall cell reaction is: $Zn(s) + Cu^{2+}(aq) \rightarrow Zn^{2+}(aq) + Cu(s)$.
Here,$Zn$ is oxidized to $Zn^{2+}$ by losing $2$ electrons,and $Cu^{2+}$ is reduced to $Cu$ by gaining $2$ electrons.
Since the number of electrons transferred in the balanced redox reaction is $2$,the value of $n$ is $2$.

(A) The electrical work done by a galvanic cell is equal to the decrease in Gibbs energy $(-\Delta G)$.
Since $\Delta G = -nFE_{cell}$,the electrical work $(W)$ is given by $W = -\Delta G = nFE_{cell}$.
Therefore,the electrical work done by the system is $nFE_{cell}$.

(A) $1.$ The standard cell potential $(E_{cell}^o)$ of a Daniell cell is $1.1 \ V$.
$2.$ In a Daniell cell,the reaction is $Zn(s) + Cu^{2+}(aq) \rightarrow Zn^{2+}(aq) + Cu(s)$. Here,the number of electrons transferred $(n)$ is $2$.
$3.$ For the reaction $Al + 3Ag^{+} \rightarrow Al^{3+} + 3Ag$,the oxidation half-reaction is $Al \rightarrow Al^{3+} + 3e^-$ and the reduction half-reaction is $Ag^{+} + e^- \rightarrow Ag$. Multiplying the reduction by $3$ gives $3Ag^{+} + 3e^- \rightarrow 3Ag$. Thus,the total number of electrons transferred $(n)$ is $3$.

(N/A) For a weak electrolyte,the degree of dissociation $\alpha$ is related to molar conductivity $\Lambda_m$ and limiting molar conductivity $\Lambda_m^o$ by the equation: $\alpha = \frac{\Lambda_m}{\Lambda_m^o}$.
For a weak electrolyte $AB$ dissociating as $AB \rightleftharpoons A^+ + B^-$,the dissociation constant $K_a$ is given by: $K_a = \frac{c \alpha^2}{1 - \alpha}$.
Substituting $\alpha = \frac{\Lambda_m}{\Lambda_m^o}$ into the expression for $K_a$:
$K_a = \frac{c (\frac{\Lambda_m}{\Lambda_m^o})^2}{1 - \frac{\Lambda_m}{\Lambda_m^o}}$.
Simplifying the expression:
$K_a = \frac{c \Lambda_m^2}{(\Lambda_m^o)^2 (\frac{\Lambda_m^o - \Lambda_m}{\Lambda_m^o})}$.
Thus,the final relation is: $K_a = \frac{c \Lambda_m^2}{\Lambda_m^o (\Lambda_m^o - \Lambda_m)}$.

(A) According to Kohlrausch's law of independent migration of ions:
$Al_{2}(SO_{4})_{3} \rightarrow 2 Al^{3+}_{(aq)} + 3 S{O_{4}}^{2-}_{(aq)}$
$\Lambda_{m}^{o}[Al_{2}(SO_{4})_{3}] = 2 \lambda_{m}^{o}(Al^{3+}) + 3 \lambda_{m}^{o}(SO_{4}^{2-})$
Given: $\Lambda_{m}^{o}[Al_{2}(SO_{4})_{3}] = 758 \ S \ cm^{2} \ mol^{-1}$ and $\lambda_{m}^{o}(SO_{4}^{2-}) = 160 \ S \ cm^{2} \ mol^{-1}$
Let $\lambda_{m}^{o}(Al^{3+}) = x$
$758 = 2(x) + 3(160)$
$758 = 2x + 480$
$2x = 758 - 480 = 278$
$x = \frac{278}{2} = 139 \ S \ cm^{2} \ mol^{-1}$

(B) According to Kohlrausch's law,the molar conductivity of an electrolyte at infinite dilution is the sum of the ionic conductivities of its constituent ions.
$1$. For $NaBr$: $\Lambda_{m}^{o}(NaBr) = \lambda_{m}^{o}(Na^{+}) + \lambda_{m}^{o}(Br^{-}) = 128.2 \, S \, cm^{2} \, mol^{-1}$.
Given $\lambda_{m}^{o}(Br^{-}) = 78.1 \, S \, cm^{2} \, mol^{-1}$,we find $\lambda_{m}^{o}(Na^{+}) = 128.2 - 78.1 = 50.1 \, S \, cm^{2} \, mol^{-1}$.
$2$. For $NaCl$: $\Lambda_{m}^{o}(NaCl) = \lambda_{m}^{o}(Na^{+}) + \lambda_{m}^{o}(Cl^{-}) = 126.5 \, S \, cm^{2} \, mol^{-1}$.
Substituting $\lambda_{m}^{o}(Na^{+}) = 50.1$,we get $\lambda_{m}^{o}(Cl^{-}) = 126.5 - 50.1 = 76.4 \, S \, cm^{2} \, mol^{-1}$.
$3$. For $KCl$: $\Lambda_{m}^{o}(KCl) = \lambda_{m}^{o}(K^{+}) + \lambda_{m}^{o}(Cl^{-}) = 149.5 \, S \, cm^{2} \, mol^{-1}$.
Substituting $\lambda_{m}^{o}(Cl^{-}) = 76.4$,we get $\lambda_{m}^{o}(K^{+}) = 149.5 - 76.4 = 73.1 \, S \, cm^{2} \, mol^{-1}$.
Alternatively,$\lambda_{m}^{o}(K^{+}) = \Lambda_{m}^{o}(KCl) - \Lambda_{m}^{o}(NaCl) + \Lambda_{m}^{o}(NaBr) - \lambda_{m}^{o}(Br^{-}) = 149.5 - 126.5 + 128.2 - 78.1 = 73.1 \, S \, cm^{2} \, mol^{-1}$.
Rounding to the nearest option,the answer is $73.5 \, S \, cm^{2} \, mol^{-1}$.

(N/A) An electrolytic cell is a device in which an external source of voltage is used to drive a non-spontaneous chemical reaction. In this cell,external electrical energy is converted into chemical energy.
Uses: Electrochemical processes are widely used in laboratories and chemical industries. Some key uses are:
$(i)$ Purification of metals: For example,impure copper is refined to high-purity copper. The impure metal acts as the anode,which dissolves upon passing $DC$ current,while $Cu^{2+}$ ions from the solution are reduced and deposited on the cathode.
$(ii)$ Production of metals: Metals such as $Na, Mg,$ and $Al$ are produced by the reduction of their respective metal ions. Sodium and magnesium are obtained by the electrolysis of their molten chlorides,while $Al$ is produced by the electrolysis of aluminium oxide in the presence of cryolite.

(N/A) $1$. Reactive Electrode: These electrodes participate in the electrochemical reaction during electrolysis or in a galvanic cell. They either get oxidized or reduced during the process. Example: $Cu$ electrode in a copper sulfate solution.
$2$. Inert Electrode: These electrodes do not participate in the chemical reaction (neither oxidized nor reduced) but only provide a surface for the transfer of electrons. Example: $Pt$ (Platinum) or Graphite electrodes.

(N/A) What is a battery?: Any battery or cell used as a source of electrical energy is essentially a galvanic cell where the chemical energy of a redox reaction is converted into electrical energy.
$(b)$ Characteristics of a battery: It should be reasonably light,compact,and its voltage should not vary appreciably during its use.
$(c)$ Types of batteries: There are mainly two types of batteries: $(i)$ primary batteries and $(ii)$ secondary batteries.
$(d)$ Examples: Dry cell,lead storage cell,$Ni-Cd$ storage cell,hydrogen fuel cell,etc.,are well-known batteries.

(N/A) primary battery is a type of electrochemical cell in which the chemical reaction occurs only once. After use over a period of time,the reactants are consumed,the battery becomes dead,and it cannot be recharged or reused.
Dry Cell (Leclanché Cell):
It is the most common example of a primary battery.
Uses: It is commonly used in transistors,toys,and clocks.
Construction:
Anode: The cell consists of a zinc container that acts as the anode.
Cathode: The cathode is a carbon (graphite) rod,which is placed vertically in the center of the zinc cylinder.
Electrolyte: The space between the electrodes is filled with a moist paste of ammonium chloride $(NH_{4}Cl)$ and zinc chloride $(ZnCl_{2})$. The carbon rod is surrounded by a mixture of powdered manganese dioxide $(MnO_{2})$ and carbon.
Reactions:
Oxidation at the anode:
$Zn_{(s)} \rightarrow Zn^{2+} + 2e^{-}$
Reduction at the cathode:
$MnO_{2} + NH_{4}^{+} + e^{-} \rightarrow MnO(OH) + NH_{3}$
The $Zn^{2+}$ ions produced react with $NH_{3}$ to form a complex,$[Zn(NH_{3})_{4}]^{2+}$.
Overall cell reaction:
$Zn_{(s)} + 2MnO_{2} + 2NH_{4}^{+} \rightarrow Zn^{2+} + 2MnO(OH) + 2NH_{3}$
Cell potential: The potential of this cell is approximately $1.5 \ V$.

(N/A) This cell is an example of a primary cell. Its construction is as follows:
Construction: As shown in the diagram,
Anode: It consists of zinc-mercury amalgam.
Cathode: $A$ paste of $HgO$ and carbon.
Electrolyte: $A$ moist paste of $KOH$ and $ZnO$.
Reaction: The electrode reactions are given below:
Oxidation of $Zn$ in the zinc-mercury amalgam occurs at the anode:
$(i) \ Zn(Hg) + 2 OH^{-} \rightarrow ZnO_{(s)} + H_{2}O + 2 e^{-}$
Reduction of $HgO$ occurs at the cathode:
$(ii) \ HgO_{(s)} + H_{2}O + 2 e^{-} \rightarrow Hg_{(l)} + 2 OH^{-}$
The overall cell reaction is:
$(iii) \ Zn(Hg) + HgO_{(s)} \rightarrow ZnO_{(s)} + Hg_{(l)}$
In this cell,$Zn$ is oxidized and acts as a reducing agent,while $HgO$ is reduced and acts as an oxidizing agent.
Cell potential and characterization: The cell potential is approximately $1.35 \ V$ and remains constant throughout its life because the overall reaction does not involve any ions in the solution whose concentration changes during its operation.
Uses: Mercury cells are suitable for low-current devices like hearing aids,watches,etc.

(N/A) secondary cell is a type of electrochemical cell that can be recharged after use by passing an electric current through it in the opposite direction,allowing it to be used again.
$(i)$ $A$ good secondary cell can undergo a large number of discharging and charging cycles.
$(ii)$ The most important examples of secondary cells are the lead storage battery and the $Ni-Cd$ cell.

(N/A) The most important secondary cell is the lead storage battery. It can be recharged after its discharge.
Construction:
Anode: It consists of a grid of lead packed with spongy lead $(Pb)$.
Cathode: $A$ grid of lead packed with lead dioxide $(PbO_2)$.
Electrolyte: $A$ $38\%$ solution of sulphuric acid $(H_2SO_4)$ is used as an electrolyte.
(Density: initial $1.25$ to $1.30 \ g \ mL^{-1}$)
Discharging reaction of the cell:
When the cell is in working condition,the following reactions are carried out:
Anode: Oxidation of $Pb$ into $PbSO_4$.
$(i) \ Pb_{(s)} + SO_{4(aq)}^{2-} \rightarrow PbSO_{4(s)} + 2e^{-}$
Cathode: Reduction of $PbO_2$ into $PbSO_4$.
$(ii) \ PbO_{2(s)} + SO_{4(aq)}^{2-} + 4H^+_{(aq)} + 2e^- \rightarrow PbSO_{4(s)} + 2H_2O_{(l)}$
Overall reaction: Adding $(i)$ and $(ii)$ gives the overall reaction of the lead storage cell:
$(iii) \ Pb_{(s)} + PbO_{2(s)} + 2H_2SO_{4(aq)} \rightarrow 2PbSO_{4(s)} + 2H_2O_{(l)}$

(N/A) The $Ni-Cd$ cell is a secondary cell,meaning it is rechargeable.
Construction:
It consists of a cadmium anode and a metal grid containing nickel$(IV)$ oxide $(NiO_2)$ as the cathode. The electrolyte is an aqueous solution of potassium hydroxide $(KOH)$.
Cell Reactions:
The overall discharging reaction is:
$Cd_{(s)} + 2NiO(OH)_{(s)} + 2H_2O_{(l)} \rightarrow Cd(OH)_{2_{(s)}} + 2Ni(OH)_{2_{(s)}}$
During discharge,cadmium is oxidized to $Cd(OH)_2$ at the anode,and nickel$(IV)$ oxide is reduced to nickel$(II)$ hydroxide at the cathode.
Characteristics:
It has a longer life than the lead storage cell but is more expensive to manufacture.

(A) battery is essentially an electrochemical cell or a combination of electrochemical cells connected in series that can be used as a source of direct electric current at a constant voltage.
It converts stored chemical energy into electrical energy through redox reactions.

(N/A) In a dry cell (Leclanché cell),the reactions are as follows:
$1.$ Anode reaction (Oxidation of zinc):
$Zn(s) \rightarrow Zn^{2+}(aq) + 2e^-$
$2.$ Cathode reaction (Reduction of manganese dioxide):
$2MnO_2(s) + 2NH_4^+(aq) + 2e^- \rightarrow Mn_2O_3(s) + 2NH_3(g) + H_2O(l)$

$1.$ Lead storage cell:
Anode (Oxidation): $Pb(s) + SO_4^{2-}(aq) \rightarrow PbSO_4(s) + 2e^-$
Cathode (Reduction): $PbO_2(s) + SO_4^{2-}(aq) + 4H^+(aq) + 2e^- \rightarrow PbSO_4(s) + 2H_2O(l)$
$2.$ $Ni-Cd$ cell:
Cell reaction: $Cd(s) + 2Ni(OH)_3(s) \rightarrow CdO(s) + 2Ni(OH)_2(s) + H_2O(l)$
$3.$ Mercury cell:
Anode (Oxidation): $Zn(Hg) + 2OH^-(aq) \rightarrow ZnO(s) + H_2O(l) + 2e^-$
Cathode (Reduction): $HgO(s) + H_2O(l) + 2e^- \rightarrow Hg(l) + 2OH^-(aq)$
Overall reaction: $Zn(Hg) + HgO(s) \rightarrow ZnO(s) + Hg(l)$

(C) The $Ni-Cd$ (Nickel-Cadmium) cell is a type of rechargeable battery.
It has a longer life than the lead storage cell.
It is commonly used in cordless appliances,cameras,and various portable electronic devices.

(N/A) Mercury cells are primarily used in low-current devices such as hearing aids,watches,and cameras.

(N/A) fuel cell is a device that converts chemical energy directly into electrical energy and possesses a construction similar to a galvanic cell.
Construction: In fuel cells,reactants are fed continuously to the electrodes,and products are removed continuously from the electrolyte compartment. These cells are designed to convert the energy of combustion of fuels like $H_2$,$CH_4$,or $CH_3OH$ directly into electrical energy.
Advantages of fuel cells:
$(i)$ There is no air or noise pollution.
$(ii)$ Fuel cells have high efficiency of $70 \%$ or more,whereas thermal power stations have low efficiency of $40 \%$ or less.
$(iii)$ Various types of fuels can be used in fuel cells.

(B) In a car,lead-acid batteries are typically connected in series to achieve the required voltage.
Each lead-acid cell provides approximately $2 \ V$.
$A$ standard car battery consists of $6$ such cells connected in series.
Total voltage = $6 \times 2 \ V = 12 \ V$.

(A) During the discharging of a lead storage cell,the lead anode $(Pb)$ and the lead dioxide cathode $(PbO_2)$ react with sulfuric acid $(H_2SO_4)$ to form lead sulfate $(PbSO_4)$ and water $(H_2O)$.
The overall cell reaction is:
$Pb_{(s)} + PbO_{2(s)} + 2H_2SO_{4(aq)} \rightarrow 2PbSO_{4(s)} + 2H_2O_{(l)}$

(D) dry cell (Leclanché cell) is a primary cell that is portable and provides a steady voltage.
It is commonly used in low-drain electronic devices such as:
$1$. Wall clocks and wristwatches.
$2$. Toys and remote controls.
$3$. Flashlights and portable radios.
Therefore,all the given options are correct applications of a dry cell.

(A) The lead storage cell is a secondary battery. Its primary uses are:
$1$. It is widely used in automobiles (cars,trucks) to start the engine and power electrical systems.
$2$. It is used in inverters to provide backup power during electricity outages.

(B) $1.$ False: $A$ battery (galvanic or voltaic cell) converts chemical energy into electrical energy,not vice versa. The conversion of electrical energy into chemical energy occurs in an electrolytic cell.
$2.$ True: Batteries act as a source of electrical energy by converting stored chemical energy into current.

(A) $1.$ False: The life of a Nickel-Cadmium cell is longer than that of a lead storage cell because it can be recharged many times.
$2.$ False: $A$ dry cell is a primary cell (non-rechargeable),while a Nickel-Cadmium cell is a secondary cell (rechargeable).
$3.$ False: $A$ dry cell is a primary cell,but a Nickel-Cadmium cell is a secondary cell.

(N/A) fuel cell is a galvanic cell that converts the chemical energy of fuels directly into electrical energy.
Construction: In fuel cells,reactants are fed continuously to the electrodes,and products are removed continuously from the electrolyte compartment. These cells are designed to convert the energy of combustion of fuels like $H_2$,$CH_4$,$CH_3OH$,etc.,directly into electrical energy.
Advantages of fuel cell:
$(i)$ There is no air or noise pollution.
(ii) Fuel cells have a high efficiency of $70 \%$ or more,whereas thermal power stations have a low efficiency of $40 \%$ or less.
(iii) Various fuels can be used in fuel cells.