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AIEEE 2010 Solved Paper

Section: Chemistry

Question : 20 of 89

Marks: +1, -0

\mathrm{Cl}_2(\mathrm{aq})+\mathrm{H}_2\mathrm{S}(\mathrm{aq})\rightarrow\mathrm{S}(\mathrm{s})+2\mathrm{H}^+(\mathrm{aq})+2\mathrm{Cl}^-(\mathrm{aq})

=k[\mathrm{Cl}_2][\mathrm{H}_2\mathrm{S}]

\mathrm{Cl}_2+\mathrm{H}_2\mathrm{S}\rightarrow\mathrm{H}^++\mathrm{Cl}^-+\mathrm{Cl}^++\mathrm{HS}^-

\mathrm{Cl}^++\mathrm{HS}^-\rightarrow\mathrm{H}^++\mathrm{Cl}^-+\mathrm{S}\;\text{(fast)}\;

\mathrm{H}_2\mathrm{S}\Leftrightarrow \mathrm{H}^++\mathrm{HS}^-

\mathrm{Cl}_2+\mathrm{HS}^-\rightarrow2\mathrm{Cl}^-+\mathrm{H}^++\mathrm{S}\;\text{(slow)}\;

Solution:

Since the slow step is the rate determining step hence-

if we consider option (1) we find

Rate

=k[\mathrm{Cl}_2][\mathrm{H}_2\mathrm{S}]

Now if we consider option (2) we find

Rate

=k[\mathrm{Cl}_2][\mathrm{HS}^-]\dots(1)

From equation

\text{(i)}

k=\frac{[\mathrm{H}^+][\mathrm{HS}^-]}{[\mathrm{H}_2\mathrm{S}]}

[\mathrm{HS}^-]=\frac{k[\mathrm{H}_2\mathrm{S}]}{[\mathrm{H}^+]}

Substituting this value in equation (1) we find

Rate

=k[\mathrm{Cl}_2]K\frac{[\mathrm{H}_2\mathrm{S}]}{[\mathrm{H}^+]}

=k'\frac{[\mathrm{Cl}_2][\mathrm{H}_2\mathrm{S}]}{[\mathrm{H}^+]}

hence only, mechanism (1) is consistent with the given rate equation.

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