IIT-JEE 2008 · Paper 1 · Chemistry Q52

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ChemistrySingle correct+3 / -1Question 52 of 69

2.5 mL of $\frac25$ M weak monoacidic base ( $K_b=1\times10^{-12}$ at 25 °C) is titrated with $\frac2{15}$ M HCl in water at 25 °C. The concentration of H⁺ at equivalence point is ( $K_w=1\times10^{-14}$ at 25 °C)

3.7\times10^{-13}

3.2\times10^{-7}

3.2\times10^{-2}

2.7\times10^{-2}

Answer and worked solution

Official answer: D

Equivalence point. Base: $2.5\times\frac25=1$ mmol, needing $7.5$ mL of $\frac2{15}$ M HCl. Total volume 10 mL, so the salt $\ce{BH+}$ is 0.1 M.

Hydrolysis. $K_a=\dfrac{K_w}{K_b}=10^{-2}$ , which is large, so the approximation $x\ll c$ fails:
$\frac{x^2}{0.1-x}=0.01\implies x^2+0.01x-0.001=0\implies x=\frac{-0.01+\sqrt{0.0041}}2\approx0.027\text{ M}.$

(D) $[\ce{H+}]=2.7\times10^{-2}$ M

Topics:Hydrolysis of salts Indicators and titrations

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IIT-JEE 2008 · Paper 1, Chemistry question 52