KCET · Chemistry · Chemical Kinetics
A first order reaction is half completed in \(45 \mathrm{~min}\). How long does it need \(99.9 \%\) of the reaction to be completed ?
- A 7.5 Hours
- B 10 Hours
- C 20 Hours
- D 5 Hours
Answer & Solution
Correct Answer
(A) 7.5 Hours
Step-by-step Solution
Detailed explanation
\(t_{1 / 2}\) for first order reaction is \(45^{\circ} \mathrm{min}\)
\[
t_{1 / 2}=\frac{0.693}{k} \Rightarrow k=\frac{0.693}{I_{1 / 2}}=\frac{0.693}{45}
\]
\[
\begin{aligned}
t & =\frac{2.303}{k} \log \frac{a}{a-x}=\frac{2.303}{0.693} \times 45 \log \frac{100}{0.1} \\
& =448 \text { min } \approx 7.5 \mathrm{hrs} .
\end{aligned}
\]
\[
t_{1 / 2}=\frac{0.693}{k} \Rightarrow k=\frac{0.693}{I_{1 / 2}}=\frac{0.693}{45}
\]
\[
\begin{aligned}
t & =\frac{2.303}{k} \log \frac{a}{a-x}=\frac{2.303}{0.693} \times 45 \log \frac{100}{0.1} \\
& =448 \text { min } \approx 7.5 \mathrm{hrs} .
\end{aligned}
\]
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
- Cryolite isKCET 2015 Hard
- Which of the following is the correct electron dot structure of \( \mathrm{N}_{2} \mathrm{O} \) molecule ?KCET 2017 Easy
- The "spin only" magnetic moment of \(\mathrm{Ni}^{2+}\) in aqueous solution would be [At. no. of \(\mathrm{Ni}=28\) ]KCET 2012 Easy
- Which of the following will not act as an oxidising agent?KCET 2026 Medium
- The vapour pressures of two liquids \(A\) and \(B\) in their pure states are in the ratio of \(1: 2\). A binary solution of \(A\) and \(B\) contains \(A\) and \(B\) in the mole proportion of \(1: 2\). The mole fraction of \(A\) in the vapour phase of the solution will beKCET 2012 Easy
- In chrysoberyl, a compound containing beryllium, aluminium and oxygen, oxide ions form cubic close packed structure. Aluminium ions occupy \(\frac{1}{4}\) th of octahedral voids. The formula of the compound isKCET 2021 Medium
More PYQs from KCET
- Two events \( A \) and \( B \) will be independent ifKCET 2017 Medium
- If \(\overrightarrow{\mathbf{a}}, \overrightarrow{\mathbf{b}}\) and \(\overrightarrow{\mathbf{c}}\) are unit vectors, such that \(\overrightarrow{\mathbf{a}}+\overrightarrow{\mathbf{b}}+\overrightarrow{\mathbf{c}}=\overrightarrow{\mathbf{0}}\), then \(3 \overrightarrow{\mathbf{a}} \cdot \overrightarrow{\mathbf{b}}+2 \overrightarrow{\mathbf{b}} \cdot \overrightarrow{\mathbf{c}}+\overrightarrow{\mathbf{c}} \cdot \overrightarrow{\mathbf{a}}\) isKCET 2010 Medium
- The length of DNA helix in a typical nucleosome isKCET 2020 Hard
- In the expansion of \((1+x)^n\)
\(\frac{C_1}{C_0}+2 \frac{C_2}{C_1}+3 \frac{C_3}{2}+\ldots+n \frac{C_n}{C_{n-1}}\) is equal toKCET 2024 Medium - Current in a coil changes from \(4 \mathrm{~A}\) to zero in \(0.1 \mathrm{~s}\) and the emf induced is \(100 \mathrm{~V}\). The self inductance of the coil isKCET 2007 Easy
- The feasible region of an LPP is shown in the figure. If \(z=11 x+7 y\), then the maximum value of \(Z\) occurs at
KCET 2020 Medium