1
JEE Main 2024 (Online) 4th April Evening Shift
Numerical
+4
-1

Consider the following reaction, the rate expression of which is given below

$$\begin{aligned} & \mathrm{A}+\mathrm{B} \rightarrow \mathrm{C} \\ & \text { rate }=\mathrm{k}[\mathrm{A}]^{1 / 2}[\mathrm{~B}]^{1 / 2} \end{aligned}$$

The reaction is initiated by taking $$1 \mathrm{~M}$$ concentration of $$\mathrm{A}$$ and $$\mathrm{B}$$ each. If the rate constant $$(\mathrm{k})$$ is $$4.6 \times 10^{-2} \mathrm{~s}^{-1}$$, then the time taken for $$\mathrm{A}$$ to become $$0.1 \mathrm{~M}$$ is _________ sec. (nearest integer)

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2
JEE Main 2024 (Online) 4th April Morning Shift
Numerical
+4
-1

Consider the following transformation involving first order elementary reaction in each step at constant temperature as shown below.

JEE Main 2024 (Online) 4th April Morning Shift Chemistry - Chemical Kinetics and Nuclear Chemistry Question 8 English

Some details of the above reactions are listed below.

Step Rate constant (sec$$^{-1}$$) Activation energy (kJ mol$$^{-1}$$)
1 $$\mathrm{k_1}$$ 300
2 $$\mathrm{k_2}$$ 200
3 $$\mathrm{k_3}$$ $$\mathrm{Ea_3}$$

If the overall rate constant of the above transformation (k) is given as $$\mathrm{k=\frac{k_1 k_2}{k_3}}$$ and the overall activation energy $$(\mathrm{E}_{\mathrm{a}})$$ is $$400 \mathrm{~kJ} \mathrm{~mol} \mathrm{~m}^{-1}$$, then the value of $$\mathrm{Ea}_3$$ is ________ integer)

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3
JEE Main 2024 (Online) 1st February Evening Shift
Numerical
+4
-1
Change Language
The following data were obtained during the first order thermal decomposition of a gas A at constant volume :

$\mathrm{A}(\mathrm{g}) \rightarrow 2 \mathrm{~B}(\mathrm{~g})+\mathrm{C}(\mathrm{g})$

S.No. Time /s Total pressure /(atm)
1. 0 0.1
2. 115 0.28

The rate constant of the reaction is ________ $\times 10^{-2} \mathrm{~s}^{-1}$ (nearest integer)
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4
JEE Main 2024 (Online) 1st February Morning Shift
Numerical
+4
-1
Change Language
The ratio of $\frac{{ }^{14} \mathrm{C}}{{ }^{12} \mathrm{C}}$ in a piece of wood is $\frac{1}{8}$ part that of atmosphere. If half life of ${ }^{14} \mathrm{C}$ is 5730 years, the age of wood sample is ________ years.
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