During the discharge of a lead storage battery, density of `H_(2)SO_(4)` fall from 1.3 to `1.14g//mL` Sulphuric acid of density `1.3g//ml` is 40W % and that of `1.14g//mL` is 20W% The battery holds two litre of the acid and volume remains practically constant during dicharging. The number of ampere- sec used from the battery is.

Options

A. `3xx96,500`
B. `6xx96,500`
C. `9xx96,500`
D. `12xx96,500`

Explanation

To solve the problem, we need to determine the number of ampere-seconds (coulombs) used from the lead storage battery during its discharge. Here’s the step-by-step solution:

### Step 1: Understand the given data
- Initial density of `H2SO4` = 1.3 g/mL (40% w/w)
- Final density of `H2SO4` = 1.14 g/mL (20% w/w)
- Volume of acid in the battery = 2 L

### Step 2: Calculate the mass of `H2SO4` for both densities
1. **For density 1.3 g/mL (40% w/w)**:
- Volume = 2 L = 2000 mL
- Mass = Density × Volume = 1.3 g/mL × 2000 mL = 2600 g
- Mass of `H2SO4` = 40% of 2600 g = 0.40 × 2600 g = 1040 g

2. **For density 1.14 g/mL (20% w/w)**:
- Mass = Density × Volume = 1.14 g/mL × 2000 mL = 2280 g
- Mass of `H2SO4` = 20% of 2280 g = 0.20 × 2280 g = 456 g

### Step 3: Calculate the change in mass of `H2SO4`
- Change in mass = Initial mass - Final mass
- Change in mass = 1040 g - 456 g = 584 g

### Step 4: Calculate the number of moles of `H2SO4` consumed
- Molar mass of `H2SO4` = 98 g/mol
- Moles of `H2SO4` = Change in mass / Molar mass
- Moles = 584 g / 98 g/mol ≈ 5.96 moles

### Step 5: Calculate the total charge transferred
- Each mole of `H2SO4` can transfer 2 moles of electrons (since `H2SO4` dissociates to give 2 H+ ions).
- Total moles of electrons = 5.96 moles × 2 = 11.92 moles of electrons
- Total charge (Q) = moles of electrons × Faraday's constant
- Q = 11.92 moles × 96500 C/mol ≈ 1,149,380 C

### Step 6: Convert charge to ampere-seconds
- Since 1 ampere-second = 1 coulomb, the total charge in ampere-seconds is approximately 1,149,380 A·s.

### Final Answer
The number of ampere-seconds used from the battery is approximately **1,149,380 A·s**.

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