JEE MainsJEE AdvanceBITSAT

JEE Mains | PYQ

The half-life of radioisotope bromine – \( 82 \) is \( 36 \, \text{hours} \). The fraction which remains after one day is ___ \( \times 10^{-2} \). (Given \( \text{antilog } 0.2006 = 1.587 \))

Consider the two different first order reactions given below
\( \mathrm{A + B \rightarrow C} \) \( \text{(Reaction 1)} \)
\( \mathrm{P \rightarrow Q} \) \( \text{(Reaction 2)} \)
The ratio of the half life of Reaction \( 1 : \) Reaction \( 2 \) is \( 5 : 2 \). If \( t_1 \) and \( t_2 \) represent the time taken to complete \( \dfrac{2}{3} \)rd and \( \dfrac{4}{5} \)th of Reaction 1 and Reaction 2, respectively, then the value of the ratio \( t_1 : t_2 \) is ______ \( \times 10^{-1} \) (nearest integer)
[Given: \( \log_{10}(3) = 0.477 \) and \( \log_{10}(5) = 0.699 \)]

The following data were obtained during the first order thermal decomposition of a gas A at constant volume: \( \mathrm{A(g)} \rightarrow 2\mathrm{B(g)} + \mathrm{C(g)} \)

Time required form completion of \( 99.9\% \) of a First order reaction is ____________ times of half life \(( t_{1/2}) \) of the reaction.

Time required for \( 99.9\% \) completion of a first order reaction is ________ times the time required from completion of \( 90\% \) reaction. (nearest integer):

For a reaction \( \mathrm{A} \xrightarrow{k_{1}} \mathrm{B} \xrightarrow{k_{2}} \mathrm{C} \) If the rate of formation of \( \mathrm{B} \) is set to be zero then the concentration of \( \mathrm{B} \) is given by:

Consider the following data for the given reaction
\( 2\text{HI}(g) \rightarrow \text{H}_2(g) + \text{I}_2(g) \)

The order of the reaction is __________.

Consider the following single step reaction in gas phase at constant temperature.
\( 2A_{(g)} + B_{(g)} \rightarrow C_{(g)} \)
The initial rate of the reaction is recorded as \( r_1 \) when the reaction starts with \( 1.5 \, \text{atm} \) pressure of \( A \) and \( 0.7 \, \text{atm} \) pressure of \( B \). After some time, the rate \( r_2 \) is recorded when the pressure of \( C \) becomes \( 0.5 \, \text{atm} \). The ratio \( r_1 : r_2 \) is ______ \( \times 10^{-1} \). (Nearest integer).

Integrated rate law equation for a first order gas phase reaction is given by (where \( P_i \) is initial pressure and \( P_t \) is total pressure at time \( t \))

\( r = k[A] \) for a reaction, \( 50\% \) of \( A \) is decomposed in \( 120 \) minutes. The time taken for \( 90\% \) decomposition of \( A \) is ______ minutes.

Given below are two statements:
Statement I: The rate law for the reaction \( \text{A} + \text{B} \rightarrow \text{C} \) is rate \( (r) = k[\text{A}]^{2}[\text{B}] \). When the concentration of both \( \text{A} \) and \( \text{B} \) is doubled, the reaction rate is increased "x" times.
Statement II:

The figure is showing " the variation in concentration against time plot" for a "y" order reaction.

The value of \( x + y \) is __________.

Consider the following first order gas phase reaction at constant temperature
\( \text{A(g)} \rightarrow 2\text{B(g)} + \text{C(g)} \)
If the total pressure of the gases is found to be \( 200 \, \text{torr} \) after \( 23 \, \text{sec} \) and \( 300 \, \text{torr} \) upon the complete decomposition of \( \text{A} \) after very long time, then the rate constant of the given reaction is ______ \( \times 10^{-2} \, \text{s}^{-1} \) (nearest integer)
[Given: \( \log_{10}(2) = 0.301 \)]

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.

If the overall rate constant of the above transformation (\( k \)) is given as \( k = \dfrac{k_1 k_2}{k_3} \) and the overall activation energy (\( E_a \)) is \( 400 \, \text{kJ mol}^{-1} \), then the value of \( E_{a3} \) is ______ \( \text{kJ mol}^{-1} \) (nearest integer)

The rate of first order reaction is \( 0.04 \, \text{mol} \, \text{L}^{-1}\, \text{s}^{-1} \) at \( 10 \) minutes and \( 0.03 \, \text{mol} \, \text{L}^{-1}\, \text{s}^{-1} \) at \( 20 \) minutes after initiation. Half life of the reaction is __________ minutes. (Given \( \log 2 = 0.3010 \), \( \log 3 = 0.4771 \) )

The ratio of $\frac{^{14}\text{C}}{^{12}\text{C}}$ in a piece of word is $\frac{1}{8}$ part that of atmosphere. If half life of $^{14}\text{C}$ is 5730 years, the age of wood sample is ______ years.

Consider the following reaction \( \mathrm{A + B \rightarrow C} \).
The time taken for \( \mathrm{A} \) to become $1/4^{\text{th}}$ of its initial concentration is twice the time taken to become \( \tfrac{1}{2} \) of the same. Also, when the change of concentration of \( \mathrm{B} \) is plotted against time, the resulting graph gives a straight line with a negative slope and a positive intercept on the concentration axis. The overall order of the reaction is ______.

\( \mathrm{NO_2} \) required for a reaction is produced by decomposition of \( \mathrm{N_2O_5} \) in \( \mathrm{CCl_4} \) as by equation \( 2\mathrm{N_2O_{5(g)}} \rightarrow 4\mathrm{NO_{2(g)}} + \mathrm{O_{2(g)}} \).
The initial concentration of \( \mathrm{N_2O_5} \) is \( 3 \, \mathrm{mol\, L^{-1}} \) and it is \( 2.75 \, \mathrm{mol\, L^{-1}} \) after \( 30 \, \text{minutes} \).
The rate of formation of \( \mathrm{NO_2} \) is \( x \times 10^{-3} \, \mathrm{mol\, L^{-1}\, min^{-1}} \), value of \( x \) is _______. (nearest integer).

For a reaction taking place in three steps at same temperature, overall rate constant \( K = \frac{k_1 k_2}{k_3} \). If \( E_{a1}, E_{a2} \) and \( E_{a3} \) are \( 40 \), \( 50 \) and \( 60 \, \mathrm{kJ/mol} \) respectively, the overall \( E_a \) is _________ \( \mathrm{kJ/mol} \).

During Kinetic study of reaction \( 2A + B \rightarrow C + D \), the following results were obtained:

Based on above data, overall order of the reaction is _______________.

Consider the following reaction, the rate expression of which is given below
\( \mathrm{A} + \mathrm{B} \rightarrow \mathrm{C} \)
\( \text{rate} = k[\mathrm{A}]^{1/2}[\mathrm{B}]^{1/2} \)
The reaction is initiated by taking \( 1\,\mathrm{M} \) concentration of A and B each. If the rate constant \( (k) \) is \( 4.6 \times 10^{-2}\ \mathrm{s^{-1}} \), then the time taken for A to become \( 0.1\,\mathrm{M} \) is __________ sec.