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.
The Crystal Field Theory (CFT) of coordination compounds is based on the effect of different crystal fields (provided by the ligands taken as point charges) on the degeneracy of d-orbital energies of the central metal atom/ion. The splitting of the d-orbitals provides different electronic arrangements in strong and weak crystal fields. In tetrahedral coordination entity formation, the d-orbital splitting is smaller as compared to the octahedral entity.
What is crystal field splitting energy?
The Crystal Field Theory (CFT) of coordination compounds is based on the effect of different crystal fields (provided by the ligands taken as point charges) on the degeneracy of d-orbital energies of the central metal atom/ion. The splitting of the d-orbitals provides different electronic arrangements in strong and weak crystal fields. In tetrahedral coordination entity formation, the d-orbital splitting is smaller as compared to the octahedral entity.
On the basis of CFT, explain why [Ti(H$_2$O)$_6$]Cl$_3$ complex is coloured? What happens on heating the complex [Ti(H$_2$O)$_6$]Cl$_3$? Give reason.
If \[ A = \begin{bmatrix} 2 & -3 & 5 \\ 3 & 2 & -4 \\ 1 & 1 & -2 \end{bmatrix}, \] find \( A^{-1} \).
Using \( A^{-1} \), solve the following system of equations:
\[ \begin{aligned} 2x - 3y + 5z &= 11 \quad \text{(1)} \\ 3x + 2y - 4z &= -5 \quad \text{(2)} \\ x + y - 2z &= -3 \quad \text{(3)} \end{aligned} \]