To solve the problem, we need to write the anode and cathode reactions and the overall cell reaction occurring in a lead storage battery during its use.
1. Understanding the Lead Storage Battery:
A lead storage battery, commonly known as a lead-acid battery, consists of two lead (Pb) electrodes: a lead dioxide (PbO₂) cathode and a sponge lead (Pb) anode, immersed in a sulfuric acid (H₂SO₄) solution as the electrolyte.
2. Anode Reaction:
The anode in a lead storage battery consists of spongy lead (Pb). During discharge (when the battery is providing power), lead at the anode reacts with the sulfate ions (SO₄²⁻) from the sulfuric acid electrolyte to form lead sulfate (PbSO₄) and release two electrons. The anode reaction is:
\[ \text{Pb}(s) + \text{SO₄}^{2-} (aq) \rightarrow \text{PbSO₄}(s) + 2e^- \]
3. Cathode Reaction:
The cathode in a lead storage battery consists of lead dioxide (PbO₂). During discharge, lead dioxide reacts with hydrogen ions (H⁺) from the sulfuric acid to form lead sulfate (PbSO₄) and water (H₂O), while accepting electrons. The cathode reaction is:
\[ \text{PbO₂}(s) + 4H^+ (aq) + 2e^- \rightarrow \text{PbSO₄}(s) + 2H₂O (l) \]
4. Overall Cell Reaction:
The overall cell reaction is the sum of the anode and cathode reactions. Adding the two reactions together, the lead (Pb) and lead dioxide (PbO₂) react with sulfuric acid to form lead sulfate (PbSO₄) and water. The overall reaction is:
\[ \text{Pb}(s) + \text{PbO₂}(s) + 2\text{H₂SO₄}(aq) \rightarrow 2\text{PbSO₄}(s) + 2\text{H₂O}(l) \]
5. Final Answer:
The anode reaction is:
\[ \text{Pb}(s) + \text{SO₄}^{2-} (aq) \rightarrow \text{PbSO₄}(s) + 2e^- \]
The cathode reaction is:
\[ \text{PbO₂}(s) + 4H^+ (aq) + 2e^- \rightarrow \text{PbSO₄}(s) + 2H₂O (l) \]
The overall cell reaction is:
\[ \text{Pb}(s) + \text{PbO₂}(s) + 2\text{H₂SO₄}(aq) \rightarrow 2\text{PbSO₄}(s) + 2\text{H₂O}(l) \]
During discharge, the battery releases energy as the lead plates are converted into lead sulfate.
(i) Draw the diagram which indicates the splitting of d-orbitals in tetrahedral field.
(ii) Write any one limitation of valence bond theory.
(i)[Ni(CN)₄]²⁻ and [Ni(CO)(_4)] have different structures, but do not differ in their magnetic behaviour. Explain.
(ii) Write the formula of Tetraamineaquachloridocobalt(III)chloride.
(i) Write two postulates of Werner's coordination theory.
(ii) Draw the geometrical isomers of [(NH_3)_3(NO_2)_3] and give their structures.
A racing track is built around an elliptical ground whose equation is given by \[ 9x^2 + 16y^2 = 144 \] The width of the track is \(3\) m as shown. Based on the given information answer the following: 
(i) Express \(y\) as a function of \(x\) from the given equation of ellipse.
(ii) Integrate the function obtained in (i) with respect to \(x\).
(iii)(a) Find the area of the region enclosed within the elliptical ground excluding the track using integration.
OR
(iii)(b) Write the coordinates of the points \(P\) and \(Q\) where the outer edge of the track cuts \(x\)-axis and \(y\)-axis in first quadrant and find the area of triangle formed by points \(P,O,Q\).