For a reaction $3\mathrm{A}\to 2\mathrm{B}$, the average rate of appearance of B is given by $\frac{\Delta [\mathrm{B}]}{\Delta t}$. The correct relation between the average rate of appearance of B and the average rate of disappearance of A is:

Answer: (A) $-\frac{2}{3}\frac{\Delta [\mathrm{A}]}{\Delta t}$. \textbf{Answer:} (A) $-\frac{2}{3}\frac{\Delta [\mathrm{A}]}{\Delta t}$ \textbf{Solution:} For $3\mathrm{A}\to 2\mathrm{B}$, the rate of reaction is: $-\frac{1}{3}\frac{\Delta [\mathrm{A}]}{\Delta t}=+\frac{1}{2}\frac{\Delta [\mathrm{B}]}{\Delta t}$ Rearranging for the rate of appearance of B: $\frac{\Delta [\mathrm{B}]}{\Delta t}=2\times \left(-\frac{1}{3}\frac{\Delta [\mathrm{A}]}{\Delta t}\right)=-\frac{2}{3}\frac{\Delta [\mathrm{A}]}{\Delta t}$ This matches option (A).