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  3. Chemistry
  4. PCl 5(g) arrow PCl 3(g)+ Cl 2(g) In the above first order reaction the concentration of PCl 5 reduces from initial concentration 50 mol L-1 to 10 mol L-1 in 120 minutes at 300 ∼ K. The rate constant for the reaction at 300 K is x × 10-2 min -1. The value of x is [Given log 5=0.6989]

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Q. $PCl _{5}(g) \rightarrow PCl _{3}(g)+ Cl _{2}(g)$
In the above first order reaction the concentration of $PCl _{5}$ reduces from initial concentration $50\, mol L^{-1}$ to $10 \,mol$ $L^{-1}$ in $120$ minutes at $300 \sim K$. The rate constant for the reaction at $300\, K$ is $x \times 10^{-2} min ^{-1}$. The value of $x$ is _______
[Given $ \log 5=0.6989]$

JEE MainJEE Main 2021Chemical Kinetics

Solution:

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$\Rightarrow K=\frac{2.303}{t} \log \frac{\left[A_{0}\right]}{\left[A_{t}\right]}$
$\Rightarrow K=\frac{2.303}{120} \log \frac{50}{10}$
$\Rightarrow K=\frac{2.303}{120} \times 0.6989$
$=0.013413\, min ^{-1}$
$=1.3413 \times 10^{-2} min ^{-1}$