Answer :
Using the concepts of Electrochemistry, we got that battery needs to be recharged when the sulfuric acid and sodium hydroxide is titrated.
A solution of the unknown concentration of sulfuric acid is titrated with sodium hydroxide. The neutralization reaction is given by:
2 NaOH + H₂SO₄ ⇒ Na₂SO₄ + 2 H₂O
31.26 mL of 0.621 M NaOH react. The reacting moles of NaOH are:
0.03126×0.621=0.0194mol
The molar ratio of NaOH to H₂SO₄ is 2:1. The reacting moles of H₂SO₄ are:
0.0194mol NaOH × (1 mol of H₂SO₄)/(2 mol of NaOH)
=0.00970mol of H₂SO₄
We know that molarity is define as
=Number of moles of solute /Total Volume of solution
0.00970 moles of H₂SO₄ are in 2.00 mL of solution. So, The molarity of H₂SO₄ is:
M=(0.00970)/0.00200
=>M=4.85M
Since the molarity of sulfuric acid in a fully charged car battery is 5.2 M and in a fully discharged battery is 4.8 M, the battery needs to be recharged.
Hence, when 31.26 mL of 0.621 M NaOH is used to titrate 2.00 mL of 4.85 M H₂SO₄. with this concentration, battery needs to be recharged.
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