Chemistry - Chemical Kinetics Question with Solution | TestHub

A $\stackrel{K_1=0.02{\min }^{-1}}{\to }$ B $\stackrel{K_2=0.02{\min }^{-1}}{\to }$ C

At $t=0$, $0.2M$ 0

Formula for Maximum [B] (for $k_1=k_2=k$)

$[B]=k[A{]}_{0}t{e}^{-kt}$

Time at Maximum [B]

$\frac{d[B]}{dt}=0⟹1-kt=0⟹t_{max}=\frac{1}{k}$

$t_{max}=\frac{1}{0.02mi{n}^{-1}}=50min$

Maximum [B]

$[B{]}_{max}=k[A{]}_0{t}_{max}{e}^{-k{t}_{max}}$

$[B{]}_{max}=(0.02mi{n}^{-1})(0.2M)(50min)e^{-(0.02mi{n}^{-1})(50min)}$

$[B{]}_{max}=0.2M\cdot e^{-1}=\frac{0.2}{e}M$

$[B{]}_{max}\approx 0.0736M$

$t_{max}=50min$, $[B{]}_{max}=\frac{0.2}{e}M$