Unit 4 Chemical Kinetics (Intext Questions-3)
Intext Questions
4.5 A first order reaction has a rate constant $1.15 \times 10^{-3} \mathrm{~s}^{-1}$. How long will $5 \mathrm{~g}$ of this reactant take to reduce to $3 \mathrm{~g}$ ?
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Answer
From the question, we can write down the following information:
Initial amount $=5 \mathrm{~g}$
Final concentration $=3 \mathrm{~g}$
Rate constant $=1.1510^{-3} \mathrm{~s}^{-1}$
We know that for a $1^{\text {storder }}$ reaction,
$ \begin{aligned} t & =\frac{2.303}{k} \log \frac{[\mathrm{R}]_{0}}{[\mathrm{R}]} \\ & =\frac{2.303}{1.15 \times 10^{-3}} \log \frac{5}{3} \\ & =\frac{2.303}{1.15 \times 10^{-3}} \times 0.2219 \\ & =444.38 \mathrm{~s} \\ & =444 \mathrm{~s} \text { (approx) } \end{aligned} $
4.6 Time required to decompose $\mathrm{SO_2} \mathrm{Cl_2}$ to half of its initial amount is 60 minutes. If the decomposition is a first order reaction, calculate the rate constant of the reaction.
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Answer
We know that for a $1^{\text {storder reaction, }}$
$t_{1 / 2}=\frac{0.693}{k}$
It is given that $t_{1 / 2}=60 \mathrm{~min}$
$ \begin{aligned} \therefore k & =\frac{0.693}{t_{1 / 2}} \\ & =\frac{0.693}{60} \\ & =0.01155 \mathrm{~min}^{-1} \\ & =1.155 \mathrm{~min}^{-1} \end{aligned} $
Or $k=1.925 \times 10^{-4} \mathrm{~s}^{-1}$
