Order and molecularity

Consider the reaction $\ce{aX -> bY}$, for which the rate constant at 30 °C is $1\times10^{-3}$ mol$^{-1}$ L s$^{-1}$. Which of the following statements are true ?

A. When concentration of 'X' is increased to four times, the rate of reaction becomes 16 times.

B. The reaction is a second order reaction.

C. The half-life period is independent of the concentration of X.

D. Decomposition of $\ce{N2O5}$ is an example of the above reaction.

E. The graph of $\ln\dfrac{[R_0]}{[R]}$ against time shown is valid for the above reaction.

Choose the correct answer from the options given below :

Consider the given graph showing variation of reactant concentration with time.

Three different reactions were started with identical initial concentration of reactants. Which of the following statement is correct?

For a reaction $\ce{A -> P}$ at T K, the half life ($t_{1/2}$) is plotted as a function of initial concentration $[\mathrm A]_o$ of A as given below.

The value of $x$ in the given figure is ________ s (Nearest integer)

Consider a reaction $A + R \longrightarrow \textit{Product}$. The rate of this reaction is measured to be $k[A][R]$. At the start of the reaction, the concentration of $R$, $[R]_0$, is 10-times the concentration of $A$, $[A]_0$. The reaction can be considered to be a pseudo first order reaction with assumption that $k[R] = k'$ is constant. Due to this assumption, the relative error (in %) in the rate when this reaction is 40 % complete, is _____.

[$k$ and $k'$ represent corresponding rate constants]

Consider the following reaction,

$$\ce{2H2(g) + 2NO(g) -> N2(g) + 2H2O(g)}$$

which follows the mechanism given below:

$$\ce{2NO(g)} \underset{k_{-1}}{\overset{k_1}{\rightleftharpoons}} \ce{N2O2(g)} \qquad \text{(fast equlibrium)}$$
$$\ce{N2O2(g) + H2(g)} \xrightarrow{k_2} \ce{N2O(g) + H2O(g)} \qquad \text{(slow reaction)}$$
$$\ce{N2O(g) + H2(g)} \xrightarrow{k_3} \ce{N2(g) + H2O(g)} \qquad \text{(fast reaction)}$$

The order of the reaction is _____.

Match the rate expressions in LIST-I for the decomposition of X with the corresponding profiles provided in LIST-II. $\mathrm X_s$ and k are constants having appropriate units.

At 345 K, the half life for the decomposition of a sample of a gaseous compound initially at 55.5 kPa was 340 s. When the pressure was 27.8 kPa, the half life was found to be 170 s. The order of the reaction is ______. [integer answer]

The half life for the decomposition of gaseous compound A is 240 s when the gaseous pressure was 500 Torr initially. When the pressure was 250 Torr, the half life was found to be 4.0 min. The order of the reaction is ______. (Nearest integer)

For a reaction A → 2B + C the half lives are 100 s and 50 s when the concentration of reactant A is 0.5 and 1.0 mol L$^{-1}$ respectively. The order of the reaction is ______. (Nearest Integer)

$$\mathrm{2NO+2H_2\rightarrow N_2+2H_2O}$$

The above reaction has been studied at 800°C. The related data are given in the table below

Reaction serial number	Initial Pressure of $\mathrm{H_2}$ / kPa	Initial Pressure of NO / kPa	Initial rate $\left(\dfrac{-dp}{dt}\right)$ / (kPa/s)
1	65.6	40.0	0.135
2	65.6	20.1	0.033
3	38.6	65.6	0.214
4	19.2	65.6	0.106

The order of the reaction with respect to NO is ______.

The reaction between X and Y is first order with respect to X and zero order with respect to Y.

Experiment	[X] / mol L$^{-1}$	[Y] / mol L$^{-1}$	Initial rate / mol L$^{-1}$ min$^{-1}$
I	0.1	0.1	$2\times10^{-3}$
II	L	0.2	$4\times10^{-3}$
III	0.4	0.4	$M\times10^{-3}$
IV	0.1	0.2	$2\times10^{-3}$

Examine the data of table and calculate ratio of numerical values of M and L. (Nearest Integer)

X → Y + Z

X decomposes at 700 K to give Y and Z. The results of two measurements are :

Initial concentration of X / (mol/L)	6.0	12.0
Half life / s	1.0	2.0

The rate constant for the reaction is _______ (in appropriate unit)

Consider the kinetic data given in the following table for the reaction $\ce{A + B + C -> Product}$.

The rate of the reaction for [A] = 0.15 mol dm⁻³, [B] = 0.25 mol dm⁻³ and [C] = 0.15 mol dm⁻³ is found to be $Y\times10^{-5}$ mol dm⁻³ s⁻¹. The value of $Y$ is ______

The decomposition reaction $\ce{2N2O5(g) ->[\Delta] 2N2O4(g) + O2(g)}$ is started in a closed cylinder under isothermal isochoric condition at an initial pressure of 1 atm. After $Y\times10^3$ s, the pressure inside the cylinder is found to be 1.45 atm. If the rate constant of the reaction is $5\times10^{-4}\ \mathrm{s^{-1}}$, assuming ideal gas behavior, the value of $Y$ is ______

The reaction of ozone with oxygen atoms in the presence of chlorine atoms can occur by a two step process shown below :

$\ce{O3(g) + Cl^.(g) -> O2(g) + ClO^.(g)}$ ...... (i) $k_i=5.2\times10^9$ L mol$^{-1}$ s$^{-1}$

$\ce{ClO^.(g) + O^.(g) -> O2(g) + Cl^.(g)}$ ...... (ii) $k_{ii}=2.6\times10^{10}$ L mol$^{-1}$ s$^{-1}$

The closest rate constant for the overall reaction $\ce{O3(g) + O^.(g) -> 2O2(g)}$ is :

Higher order (>3) reactions are rare due to :

For the elementary reaction $\ce{M -> N}$, the rate of disappearance of M increases by a factor of 8 upon doubling the concentration of M. The order of the reaction with respect to M is

For the non - stoichiometre reaction $\ce{2A + B -> C + D}$, the following kinetic data were obtained in three separate experiments, all at 298 K.

Initial Concentration (A)	Initial Concentration (B)	Initial rate of formation of C (mol L$^{-1}$ s$^{-1}$)
0.1 M	0.1 M	$1.2\times10^{-3}$
0.1 M	0.2 M	$1.2\times10^{-3}$
0.2 M	0.1 M	$2.4\times10^{-3}$

The rate law for the formation of C is :

In the reaction,
$$\ce{P + Q -> R + S}$$
the time taken for 75% reaction of P is twice the time taken for 50% reaction of P. The concentration of Q varies with reaction time as shown in the figure. The overall order of the reaction is

The concentration of R in the reaction R $\rightarrow$ P was measured as a function of time and the following data is obtained:

[R] (molar)	1.0	0.75	0.40	0.10
t (min.)	0.0	0.05	0.12	0.18

The order of the reaction is