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:
- 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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