Question

During the discharge of a lead storage battery, the density of sulphuric acid fell from 1.5 to 1.1 g/ml. Sulphuric acid of density 1.5 g/ml is 40% $H_2SO_4$, by weight, and that of density 1.1 g/ml is 10% $H_2SO_4$, by weight. The battery holds 3.6 L of the acid and the volume remained practically constant during the discharge. Calculate the number of ampere-hours which the battery should have been used. The electrode reactions are:

$Pb + SO_4^{2-} \rightarrow PbSO_4 + 2e$

$PbO_2 + 4H^+ + SO_4^{2-} + 2e \rightarrow PbSO_4 + 2H_2O$

• A. 482.5 Ah
• B. 241.25 Ah
• C. 965 Ah
• D. 1764 Ah

Answer 1

Answer: (A)

482.5 Ah

Answer 2

1. Calculate the initial and final mass of sulfuric acid ($H_2SO_4$) in the battery.
   • Initial mass of solution = Initial density × Volume = 1.5 g/mL × 3600 mL = 5400 g.
   • Initial mass of $H_2SO_4$ = 40% of 5400 g = 0.40 × 5400 g = 2160 g.
   • Final mass of solution = Final density × Volume = 1.1 g/mL × 3600 mL = 3960 g.
   • Final mass of $H_2SO_4$ = 10% of 3960 g = 0.10 × 3960 g = 396 g.
2. Calculate the mass of $H_2SO_4$ consumed during discharge.
   • Mass consumed = Initial mass - Final mass = 2160 g - 396 g = 1764 g.
3. Calculate the moles of $H_2SO_4$ consumed.
   • Molar mass of $H_2SO_4$ = 98 g/mol.
   • Moles of $H_2SO_4$ consumed = Mass consumed / Molar mass = 1764 g / 98 g/mol = 18 mol.
4. Determine the number of moles of electrons transferred.
   • The overall discharge reaction is $Pb + PbO_2 + 2H_2SO_4 \rightarrow 2PbSO_4 + 2H_2O$.
   • This reaction shows that 2 moles of $H_2SO_4$ are consumed for every 2 moles of electrons transferred. Therefore, 1 mole of $H_2SO_4$ consumed corresponds to 1 mole of electrons transferred.
   • Moles of electrons transferred = Moles of $H_2SO_4$ consumed = 18 mol.
5. Calculate the total charge passed in Ampere-hours (Ah).
   • Total charge (Q) = Moles of electrons × Faraday's constant (F).
   • Using F = 96500 C/mol.
   • Q = 18 mol × 96500 C/mol = 1,737,000 C.
   • To convert Coulombs to Ampere-hours, divide by 3600 (since 1 Ah = 3600 C).
   • Charge in Ah = 1,737,000 C / 3600 C/Ah = 482.5 Ah.