Equal 10.0 mL aliquots of decomposing H2O2 are titrated with 0.0200 M KMnO4 in acid, using 2MnO4^- + 5H2O2 + 6H+ -> 2Mn^2+ + 5O2 + 8H2O. The titre is 25.0 mL at t = 0 and 16.0 mL at t = 20 min; decomposition is first order. Find the mass of H2O2 (molar mass 34 g/mol) per litre at t = 50 min, in g (two decimals).

JEE Advanced levelNumerical answerDifficulty 3 of 3ck151

Equal 10.0 mL aliquots of decomposing $H X_{2} O X_{2}$ are titrated with 0.0200 M $KMnO X_{4}$ in acid, using $2 MnO X_{4} X^{-} + 5 H X_{2} O X_{2} + 6 H X^{+} 2 Mn X^{2 +} + 5 O X_{2} + 8 H X_{2} O$ . The titre is 25.0 mL at t = 0 and 16.0 mL at t = 20 min; decomposition is first order. Find the mass of $H X_{2} O X_{2}$ (molar mass 34 g/mol) per litre at t = 50 min, in g (two decimals).

Numerical answer type, answer in g/L, tolerance 0.04.

Titre is proportional to concentration, so

k = \frac{1}{20} ln \frac{25.0}{16.0} = 0.02231 mi n^{- 1}

and

V_{50} = 25.0 e^{- k \cdot 50} = 8.19

mL. Moles of

MnO X_{4} X^{-}

in one aliquot give

[H X_{2} O X_{2}] = \frac{8.19 \times 0.0200 \times 2.5}{10.0} = 0.0410

M. Mass

= 0.0410 \times 34 = 1.39

g/L.