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Chemistry · 2022 · 5 marks
CBSE 2022 · Region 3 · Set 1 · Q12
Read the following passage and answer the questions that follow: The rate of reaction is concerned with decrease in concentration of reactants or…
Read the following passage and answer the questions that follow : The rate of reaction is concerned with decrease in concentration of reactants or increase in the concentration of products per unit time. It can be expressed as instantaneous rate at a particular instant of time and average rate over a large interval of time. A number of factors such as temperature, concentration of reactants, catalyst affect the rate of reaction. Mathematical representation of rate of a reaction is given by rate law : \[\text { Rate }=\mathrm{k}[\mathrm{~A}]^{x}[\mathrm{~B}]^{\mathrm{y}} \] $\displaystyle x$ and $\displaystyle \mathrm{y}$ indicate how sensitive the rate is to the change in concentration of A and B . Sum of $\displaystyle x+\mathrm{y}$ gives the overall order of a reaction. When a sequence of elementary reactions gives us the products, the reactions are called complex reactions. Molecularity and order of an elementary reaction are same. Zero order reactions are relatively uncommon but they occur under special conditions. All natural and artificial radioactive decay of unstable nuclei take place by first order kinetics.
(a)
What is the effect of temperature on the rate constant of a reaction ?
(b)
For a reaction $\displaystyle \mathrm{A}+\mathrm{B} \rightarrow$ Product, the rate law is given by, Rate = $\displaystyle \mathrm{k}[\mathrm{A}]^{2}[\mathrm{~B}]^{1 / 2}$. What is the order of the reaction?
(c)
How order and molecularity are different for complex reactions ?
(d)
A first order reaction has a rate constant $\displaystyle 2 \times 10^{-3} \mathrm{~s}^{-1}$. How long will 6g of this reactant take to reduce to 2g ?
The half life for radioactive decay of $\displaystyle { }^{14} \mathrm{C}$ is $\displaystyle 6930$ years. An archaeological artifact containing wood had only $\displaystyle 75$% of the $\displaystyle { }^{14} \mathrm{C}$ found in a living tree. Find the age of the sample. \[[\log 4=0.6021 \quad \log 3=0.4771 \quad \log 2=0.3010 \quad \log 10=1] \] \[1+1+1+2 \]
Marking-scheme solution
(a) The rate constant increases.
(b) \(\displaystyle 2+\frac{1}{2}=\frac{5}{2}\)
(c) Order is applicable for complex reaction whereas molecularity has no meaning for complex reaction.
(d)
\(\displaystyle k=\frac{2 \cdot 303}{t} \log \frac{[R]_{0}}{[R]}\)
\[\begin{aligned}
& t=\frac{2 \cdot 303}{2 \times 10^{-3}} \log \frac{6}{2} \\
& t=\frac{2 \cdot 303}{2 \times 10^{-3}} \times 0 \cdot 4771 \\
& t=549 \cdot 38 \mathrm{~s}
\end{aligned}
\]
\[\begin{aligned}
k & =\frac{2 \cdot 303}{t} \log \frac{[R]_{0}}{[R]} \\
t_{1 / 2} & =\frac{0 \cdot 693}{k} \\
k & =\frac{0 \cdot 693}{6930} \text { year }^{-1}=10^{-4} \text { year }^{-1} \\
t & =\frac{2 \cdot 303}{10^{-4}} \log \frac{100}{75} \\
& =\frac{2 \cdot 303}{10^{-4}}[0 \cdot 6021-0 \cdot 4771] \\
t & =2878 \cdot 75 \text { years }
\end{aligned}
\]
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CBSE Class 12 Chemistry past-paper question from the 2022 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.