MHT CET · Chemistry · Chemical Kinetics
Consider the reaction \(3 \mathrm{I}^{-}+\mathrm{S}_2 \mathrm{O}_8^{2-} \longrightarrow \mathrm{I}_3^{-}+2 \mathrm{SO}_4^{2-}\), at a particular time t , \(\frac{\mathrm{d}\left[\mathrm{SO}_4^{2-}\right]}{\mathrm{dt}}\) is \(2.2 \times 10^{-2} \mathrm{~mol} \mathrm{dm}^{-3} \mathrm{~s}^{-1}\). What is the value of \(\frac{\mathrm{d}\left[\mathrm{S}_2 \mathrm{O}_8^{2-}\right]}{\mathrm{dt}}\) ?
- A \(1.1 \times 10^{-2} \mathrm{~mol} \mathrm{dm}^{-3} \mathrm{~s}^{-1}\).
- B \(2.2 \times 10^{-2} \mathrm{~mol} \mathrm{dm}^{-3} \mathrm{~s}^{-1}\)
- C \(3.3 \times 10^{-2} \mathrm{~mol} \mathrm{dm}^{-3} \mathrm{~s}^{-1}\)
- D \(6.6 \times 10^{-2} \mathrm{~mol} \mathrm{dm}^{-3} \mathrm{~s}^{-1}\)
Answer & Solution
Correct Answer
(A) \(1.1 \times 10^{-2} \mathrm{~mol} \mathrm{dm}^{-3} \mathrm{~s}^{-1}\).
Step-by-step Solution
Detailed explanation
\(3 \mathrm{I}^{-}+\mathrm{S}_2 \mathrm{O}_8^{2-} \longrightarrow \mathrm{I}_3^{-}+2 \mathrm{SO}_4^{2-}\)
Rate of reaction
\(=-\frac{1}{3} \frac{\mathrm{~d}\left[\mathrm{I}^{-}\right]}{\mathrm{dt}}=-\frac{\mathrm{d}\left[\mathrm{~S}_2 \mathrm{O}_8^{2-}\right]}{\mathrm{dt}}=\frac{\mathrm{d}\left[\mathrm{I}_3^{-}\right]}{\mathrm{dt}}=\frac{1}{2} \frac{\mathrm{~d}\left[\mathrm{SO}_4^{2-}\right]}{\mathrm{dt}}\)
Hence, \(\frac{\mathrm{d}\left[\mathrm{S}_2 \mathrm{O}_8^{2-}\right]}{\mathrm{dt}}=\frac{1}{2} \frac{\mathrm{~d}\left[\mathrm{SO}_4^{2-}\right]}{\mathrm{dt}}\)
\(=\frac{1}{2} \times 2.2 \times 10^{-2}=1.1 \times 10^{-2} \mathrm{~mol} \mathrm{dm}^{-3} \mathrm{~s}^{-1}\)
Rate of reaction
\(=-\frac{1}{3} \frac{\mathrm{~d}\left[\mathrm{I}^{-}\right]}{\mathrm{dt}}=-\frac{\mathrm{d}\left[\mathrm{~S}_2 \mathrm{O}_8^{2-}\right]}{\mathrm{dt}}=\frac{\mathrm{d}\left[\mathrm{I}_3^{-}\right]}{\mathrm{dt}}=\frac{1}{2} \frac{\mathrm{~d}\left[\mathrm{SO}_4^{2-}\right]}{\mathrm{dt}}\)
Hence, \(\frac{\mathrm{d}\left[\mathrm{S}_2 \mathrm{O}_8^{2-}\right]}{\mathrm{dt}}=\frac{1}{2} \frac{\mathrm{~d}\left[\mathrm{SO}_4^{2-}\right]}{\mathrm{dt}}\)
\(=\frac{1}{2} \times 2.2 \times 10^{-2}=1.1 \times 10^{-2} \mathrm{~mol} \mathrm{dm}^{-3} \mathrm{~s}^{-1}\)
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