MHT CET · Chemistry · Chemical Kinetics
In a first order reaction, concentration of reactant is reduced to \((1 / 8)^{\text {th }}\) of concentration in 23.03 minutes. What is half-life period of reaction?
- A \(25 \mathrm{~min}\)
- B \(7.7 \mathrm{~min}\)
- C \(15 \mathrm{~min}\)
- D \(30 \mathrm{~min}\)
Answer & Solution
Correct Answer
(B) \(7.7 \mathrm{~min}\)
Step-by-step Solution
Detailed explanation
Initial concentration \(\mathrm{a}_0=\mathrm{a}\) (let)
Final concentration \(a_t=\frac{a}{8}\)
\(1^{\text {st }}\) order reaction
\(
\begin{aligned}
& \mathrm{k}=\frac{2.303}{\mathrm{t}} \log \frac{\mathrm{a}_0}{\mathrm{a}_{\mathrm{t}}}=\frac{2.303}{23.03} \log \frac{\mathrm{a}}{\mathrm{a} / 8} \\
& \mathrm{k}=\frac{1}{10} \log 8=\frac{3}{10} \log 2=0.3 \log 2
\end{aligned}
\)
Half -life \(\mathrm{t}_{1 / 2}=\frac{2.303 \log 2}{\mathrm{k}}\)
\(
\begin{aligned}
& =\frac{2.303 \times \log }{0.3 \log 2} \\
& =7.7 \mathrm{~min}
\end{aligned}
\)
Final concentration \(a_t=\frac{a}{8}\)
\(1^{\text {st }}\) order reaction
\(
\begin{aligned}
& \mathrm{k}=\frac{2.303}{\mathrm{t}} \log \frac{\mathrm{a}_0}{\mathrm{a}_{\mathrm{t}}}=\frac{2.303}{23.03} \log \frac{\mathrm{a}}{\mathrm{a} / 8} \\
& \mathrm{k}=\frac{1}{10} \log 8=\frac{3}{10} \log 2=0.3 \log 2
\end{aligned}
\)
Half -life \(\mathrm{t}_{1 / 2}=\frac{2.303 \log 2}{\mathrm{k}}\)
\(
\begin{aligned}
& =\frac{2.303 \times \log }{0.3 \log 2} \\
& =7.7 \mathrm{~min}
\end{aligned}
\)
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
- Glucose gives silver mirror with ammoniacal silver nitrate because it hasMHT CET 2007 Easy
- What is the volume of one particle in BCC structure if 'a' is edge length?MHT CET 2024 Easy
- Calculate amount of methane formed by liberation of \(149.6 \mathrm{~kJ}\) of heat using following equation.
\( \mathrm{C}_{(\mathrm{s})}+2 \mathrm{H}_{2(\mathrm{~g})} \longrightarrow \mathrm{CH}_{4(\mathrm{~g})} \quad \Delta \mathrm{H}\) \(=-74.8 \mathrm{~kJ} / \mathrm{mol} \)MHT CET 2023 Medium - Which of the following species is NOT isoelectronic with neon?MHT CET 2023 Easy
- Calculate the number of unit cells in 0.4 g metal if the product of density and volume of unit cell is \(1.2 \times 10^{-22} \mathrm{~g}\).MHT CET 2024 Easy
- Calculate the molar mass of non volatile solute when 1 g of it is dissolved in 100 g solvent decreases its freezing point by 0.2 K .
\(\left[\mathrm{K}_{\mathrm{f}}=1.2 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right.\) ]MHT CET 2024 Easy
More PYQs from MHT CET
- If \(A=\left[\begin{array}{cc}1 & \cot \frac{\theta}{2} \\ -\cot \frac{\theta}{2} & 1\end{array}\right]\) then \(A^{-1}=\)MHT CET 2025 Medium
- The ratio of the specific heats \(\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}=\gamma\) in terms of degrees of freedom 'n' is given byMHT CET 2020 Easy
- If \(\int \frac{\sin x}{3+4 \cos ^2 x} \mathrm{~d} x=\mathrm{A} \tan ^{-1}(\mathrm{~B} \cos x)+\mathrm{C}\), (where \(\mathrm{c}\) is a constant of integration), then the value of \(\mathrm{A}+\mathrm{B}\) isMHT CET 2023 Medium
- The value of \(m\), such that \(\frac{x-4}{1}=\frac{y-2}{1}=\frac{2 z-m}{3}\) lies in the plane \(2 x-5 y+2 z=7\), isMHT CET 2024 Easy
- The area of the region bounded by the curve \(y=\sin x\) between \(x=-\pi\) and
\(x=\frac{3 \pi}{2}\) isMHT CET 2020 Easy - The equation of normal to the curve \(x=\theta+\sin \theta, y=1+\cos \theta\) at \(\theta=\frac{\pi}{2}\) isMHT CET 2024 Hard