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JEE Advanced levelSingle correct optionDifficulty 3 of 3ck145

In a first-order ester hydrolysis followed by NaOH titration, the titre at infinite time is 40.0 mL. The titre is 24.0 mL at t = 10 min and 36.0 mL at t = 30 min. The titre at t = 0 and the half-life are respectively

A $16.0$ mL and $10$ min
B $8.0$ mL and $20$ min
C $8.0$ mL and $10$ min
D $12.0$ mL and $20$ min

Answer: C

V_{\infty} - V_{t}

is 16 mL at 10 min and 4 mL at 30 min, a fall by a factor of 4 (two half-lives) in 20 min, so

t_{1/2} = 10

min. Going back 10 min (one half-life) doubles the difference to 32 mL, so

V_{0} = 40 - 32 = 8.0

mL.

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