Question
$A \rightarrow B$
The molecule A changes into its isomeric form B by following a first order kinetics at a temperature of 1000 K . If the energy barrier with respect to reactant energy for such isomeric transformation is $191.48 kJ mol ^{-1}$ and the frequency factor is $10^{20}$, the time required for $50 \%$, molecules of A to become B is _________ picoseconds (nearest integer).
$
\left[R=8.314 J K^{-1} mol^{-1}\right]
$

Answer

(69)
$
\begin{array}{l}Sol.\
t_{1 / 2}=\frac{0.693}{K} \\
K=Ae^{-EaRT} \\
=10^{20} \times e^{-\frac{199.48 \times 10^3}{8.314 \times 1000}} \\
=10^{20} \times e^{-23.031}=10^{20} \times-e^{\ln 10 \times 10} \\
=\frac{10^{20}}{10^{10}}=10^{10} sec \\
t_{1 / 2}=\frac{0.693}{10^{10}}=6.93 \times 10^{-11} \\
=69.3 \times 10^{-12} sec .
\end{array}
$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

The compound formed by the reaction of ethanal with semicarbazide contains ________ number of nitrogen atoms.
The oxidation number of $Mn$ in $MnO_4^{ - 1}$ is
Wavenumber for a radiation having $5800 \mathring A$ wavelength is $x \times 10 \mathrm{~cm}^{-1}$. The value of $x$ is. . . . . . . . 
A $2.0 \,g$ sample containing $MnO _{2}$ is treated with $HCl$ liberating $Cl _{2}$. The $Cl _{2}$ gas is passed into a solution of $KI$ and $60.0\, mL$ of $0.1\, M\, Na _{2} S _{2} O_{3}$ is required to titrate the liberated iodine. The percentage of $MnO _{2}$ in the sample is $.....$ (Nearest integer)

[Atomic masses (in $u$) $Mn =55 ; Cl =35.5 ; O =16, I =127, Na =23, K =39, S =32]$

3-Methylhex-2-ene on reaction with HBr in presence of peroxide forms an addition product (A). The number of possible stereoisomers for ' A ' is _________________ .
The total number of reagents from those given below, that can convert nitrobenzene into aniline is ..... . (Integer answer)

$I.$ ${Sn}-{HCl}$       $II.$ ${Sn}-{NH}_{4} {OH}$         $III.$ ${Fe}-{HCl}$        ${IV} . {Zn}-{HCl}$               $V.$ ${H}_{2}-{Pd}$               $VI.$ ${H}_{2}-$ રેની નિકલ

Liquids $A$ and $B$ form ideal solution over the entire range of composition. At temperature T, equimolar binary solution of liquids $A$ and $B$ has vapour pressure $45$ Torr. At the same temperature, a new solution of $A$ and $B$ having mole fractions $x _{ A }$ and $x _{ B }$, respectively, has vapour pressure of $22.5$ Torr. The value of $x_A / x_B$ in the new solution is . . . . . that the vapour pressure of pure liquid $A$ is $20$ Torr at temperature $T$ )
If $1.2\, g$ of metal displace $1.12\, litre$ hydrogen at normal temperature and pressure ,equivalent weight of metal would be
The difference in oxidation state of chromium in chromate and dichromate salts is .... .
At which value of $n$ the formation of six membered ring takes place ?