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)

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.

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)

3
JEE Main 2024 (Online) 1st February Evening Shift
Numerical
+4
-1
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)
4
JEE Main 2024 (Online) 1st February Morning Shift
Numerical
+4
-1
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.