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Reaction \( \mathrm{A}+\mathrm{B} \rightarrow \mathrm{D}+\mathrm{E} \) take place as
\[
\begin{array}{l}
\mathrm{A}+\mathrm{B} \stackrel{\mathrm{k}_{1}}{\longrightarrow} 2 \mathrm{C} \\
\mathrm{C}+\mathrm{B} \stackrel{\mathrm{k}_{2}}{\longrightarrow} 2 \mathrm{D} \\
\mathrm{C}+\mathrm{A} \stackrel{\mathrm{k}_{3}}{\longrightarrow} 2 \mathrm{E}
\end{array}
\]
The rate of disapperance of \( \mathrm{C} \) is given by
(a) \( -\frac{\mathrm{d}[\mathrm{C}]}{\mathrm{dt}}=\mathrm{k}_{2}[\mathrm{~B}][\mathrm{C}]+\mathrm{k}_{3}[\mathrm{~A}][\mathrm{C}]-2 \mathrm{k}_{1}[\mathrm{~A}][\mathrm{B}] \)
(b) \( -\frac{\mathrm{d}[\mathrm{C}]}{\mathrm{dt}}=\mathrm{k}_{2}[\mathrm{~B}][\mathrm{C}]+\mathrm{k}_{3}[\mathrm{E}]-\mathrm{k}_{1}[\mathrm{C}] \)
(c) \( -\frac{\mathrm{d}[\mathrm{C}]}{\mathrm{dt}}=\mathrm{k}_{2}[\mathrm{D}] \mathrm{O}+\mathrm{k}_{3}[\mathrm{E}]-\mathrm{k}_{1}[\mathrm{C}] \)
(d) \( -\frac{\mathrm{d}}{\mathrm{dt}}[\mathrm{C}]=2 \mathrm{k}_{1}[\mathrm{~A}][\mathrm{B}]+\mathrm{k}_{2}[\mathrm{~B}][\mathrm{C}]-\mathrm{k}_{3}[\mathrm{~A}][\mathrm{C}] \)
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