KCET · Chemistry · Chemical Kinetics
The activation energy of a reaction at a given temperature is found to be \(2.303 R T \mathrm{~J} \mathrm{~mol}^{-1}\). The ratio of rate constant to the Arrhenius factor is
- A \(0.01\)
- B \(0.1\)
- C \(0.02\)
- D \(0.001\)
Answer & Solution
Correct Answer
(B) \(0.1\)
Step-by-step Solution
Detailed explanation
\(k=A e^{-E_{a} / R T}\)
\[
\begin{aligned}
\frac{k}{A} &=e^{-E_{a} / R T} \\
\ln \left(\frac{k}{A}\right) &=\frac{-E_{a}}{R T} \\
2.303 \log \left(\frac{k}{A}\right) &=\frac{-E_{a}}{R T} \\
\log \left(\frac{k}{A}\right) &=\frac{-E_{a}}{2.303 R T} \\
\log \left(\frac{k}{A}\right) &=\frac{-2.303 R T}{2.303 R T} \\
\log \left(\frac{k}{A}\right) &=-1 \\
\frac{k}{A} &=0.1
\end{aligned}
\]
\[
\begin{aligned}
\frac{k}{A} &=e^{-E_{a} / R T} \\
\ln \left(\frac{k}{A}\right) &=\frac{-E_{a}}{R T} \\
2.303 \log \left(\frac{k}{A}\right) &=\frac{-E_{a}}{R T} \\
\log \left(\frac{k}{A}\right) &=\frac{-E_{a}}{2.303 R T} \\
\log \left(\frac{k}{A}\right) &=\frac{-2.303 R T}{2.303 R T} \\
\log \left(\frac{k}{A}\right) &=-1 \\
\frac{k}{A} &=0.1
\end{aligned}
\]
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Chemistry
- Which is the most suitable reagent for the following conversion?
KCET 2019 Medium - In which one of the following, does the given amount of chlorine exert the least pressure in a vessel of capacity \(1 \mathrm{dm}^{3}\) at \(273 \mathrm{~K}\) ?KCET 2010 Easy
- Which of the following aqueous solutions should have the highest boiling point?KCET 2018 Medium
- Which is the most suitable reagent for the following conversion ?
KCET 2021 Easy - Pick the correct statement among the following :KCET 2017 Easy
- \( \mathrm{H}_{2} \mathrm{O}_{2} \) isKCET 2018 Medium
More PYQs from KCET
- The annual net primary productivity of the biosphere is approximatelyKCET 2024 Easy
- In apple, the chromosome number of gametes is 17. What is the chromosome number in its Primarily Endosperm Nucleus (PEN)?KCET 2020 Hard
- \(1 \mathrm{dm}^{3}\) solution containing \(10^{-5}\) moles each of \(\mathrm{Cl}^{-}\)ions and \(\mathrm{CrO}_{4}^{2-}\) ions is treated with \(10^{-4}\) moles of silver nitrate. Which one of the following observations is made?
\(\begin{aligned} {\left[\mathrm{K}_{\mathrm{sp}} \mathrm{Ag}_{2} \mathrm{CrO}_{4}\right.} &\left.=4 \times 10^{-12}\right] \\ {\left[\mathrm{K}_{\mathrm{sp}} \mathrm{AgCl}\right.} &\left.=1 \times 10^{-10}\right] \end{aligned}\)KCET 2010 Medium - The order and degree of the differential equation \( \left[1+\left(\frac{d y}{d x}\right)^{2}+\sin \left(\frac{d y}{d x}\right)\right]^{\frac{3}{4}}=\frac{d^{2} y}{d x^{2}} \)KCET 2016 Easy
- When an electron jumps from the orbit \(n=2\) to \(n=4\), then wavelength of the radiations absorbed will be ( \(R\) is Rydberg's constant)KCET 2011 Medium
- Excess of silver nitrate solution is added to \(100 \mathrm{~mL}\) of \(0.01 \mathrm{M}\) pentaaqua chloro chromium (III) chloride solution. The mass of silver chloride obtained in grams is [Atomic mass of silver is 108].KCET 2011 Medium