Chemical Kinetics - Result Question 81

####80. Rate of reaction, $A+B \rightarrow$ products is given below as a function of different initial concentrations of $A$ and $B$

$[\boldsymbol{A}] mol / L$ $[\boldsymbol{B}](mol / L)$ Initial rate
$\left(mol L^{-1} min^{-1}\right)$
0.01 0.01 0.005
0.02 0.01 0.010
0.01 0.02 0.005

Determine the order of the reaction with respect to $A$ and $B$. What is the half-life of $A$ in the reaction?

$(1982,4 M)$

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Solution:

  1. Looking at the rate data of experiment number 1 and 2 indicates that rate is doubled on doubling concentration of $A$ while concentration of $B$ is constant. Therefore, order with respect to $A$ is 1. Similarly, comparing data of experiment number 1 and 3 , doubling concentration of $B$, while concentration of $A$ is constant, has no effect on rate.

Therefore, order with respect to $B$ is zero.

$$ \begin{aligned} \Rightarrow & \text { Rate } & =k[A] \ \Rightarrow & k & =\frac{0.005}{0.010}=0.5 min^{-1}=\frac{0.693}{t _{1 / 2}} \ \Rightarrow & t _{1 / 2} & =\frac{0.693}{0.5}=1.386 min \end{aligned} $$

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