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.
A current-carrying coil is placed in an external uniform magnetic field. The coil is free to turn in the magnetic field. What is the net force acting on the coil? Obtain the orientation of the coil in stable equilibrium. Show that in this orientation the flux of the total field (field produced by the loop + external field) through the coil is maximum.
Three students, Neha, Rani, and Sam go to a market to purchase stationery items. Neha buys 4 pens, 3 notepads, and 2 erasers and pays ₹ 60. Rani buys 2 pens, 4 notepads, and 6 erasers for ₹ 90. Sam pays ₹ 70 for 6 pens, 2 notepads, and 3 erasers.
Based upon the above information, answer the following questions:
(i) Form the equations required to solve the problem of finding the price of each item, and express it in the matrix form \( A \mathbf{X} = B \).