## Numerical

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

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} ...

$$\mathrm{r}=\mathrm{k}[\mathrm{A}]$$ for a reaction, $$50 \%$$ of $$\mathrm{A}$$ is decomposed in 120 minutes. The time taken for $$90 \%$$ decomposi...

$$\mathrm{NO}_2$$ required for a reaction is produced by decomposition of $$\mathrm{N}_2 \mathrm{O}_5$$ in $$\mathrm{CCl}_4$$ as by equation
$$2 \math...

The rate of First order reaction is $$0.04 \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$$ at 10 minutes and $$0.03 \mathrm{~mol} \mathrm{~L}^{-1} \...

The half-life of radioisotope bromine - 82 is 36 hours. The fraction which remains after one day is ________ $$\times 10^{-2}$$.
(Given antilog $$0.20...

For a reaction taking place in three steps at same temperature, overall rate constant $$\mathrm{K}=\frac{\mathrm{K}_1 \mathrm{~K}_2}{\mathrm{~K}_3}$$....

Time required for completion of $$99.9 \%$$ of a First order reaction is ________ times of half life $$\left(t_{1 / 2}\right)$$ of the reaction....

Consider the following data for the given reaction
$$2 \mathrm{HI}_{(\mathrm{g})} \rightarrow \mathrm{H}_{2(\mathrm{~g})}+\mathrm{I}_{2(\mathrm{~g})}$...

For a reversible reaction $\mathrm{A} \rightleftharpoons \mathrm{B}$, the $\Delta \mathrm{H}_{\text{forward reaction}} = 20 \mathrm{~kJ} \mathrm{~mol}...

A(g) $$\to$$ 2B(g) + C(g) is a first order reaction. The initial pressure of the system was found to be 800 mm Hg which increased to 1600 mm Hg after ...

$$\mathrm{t}_{87.5}$$ is the time required for the reaction to undergo $$87.5 \%$$ completion and $$\mathrm{t}_{50}$$ is the time required for the rea...

The reaction $$2 \mathrm{NO}+\mathrm{Br}_{2} \rightarrow 2 \mathrm{NOBr}$$
takes places through the mechanism given below:
$$\mathrm{NO}+\mathrm{Br}_{...

$$\mathrm{KClO}_{3}+6 \mathrm{FeSO}_{4}+3 \mathrm{H}_{2} \mathrm{SO}_{4} \rightarrow \mathrm{KCl}+3 \mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3}+3 ...

The number of incorrect statement/s from the following is ___________
A. The successive half lives of zero order reactions decreases with time.
B. A s...

A molecule undergoes two independent first order reactions whose respective half lives are 12 min and 3 min. If both the reactions are occurring then ...

The number of given statement/s which is/are correct is __________.
(A) The stronger the temperature dependence of the rate constant, the higher is th...

$$\mathrm{A}$$ $$\rightarrow \mathrm{B}$$
The above reaction is of zero order. Half life of this reaction is $$50 \mathrm{~min}$$. The time taken for ...

A and B are two substances undergoing radioactive decay in a container. The half life of A is 15 min and that of B is 5 min. If the initial concentrat...

The rate constant for a first order reaction is $20 \mathrm{~min}^{-1}$. The time required for the initial concentration of the reactant to reduce to ...

A $$\to$$ B
The rate constants of the above reaction at 200 K and 300 K are 0.03 min$$^{-1}$$ and 0.05 min$$^{-1}$$ respectively. The activation energ...

An organic compound undergoes first-order decomposition. If the time taken for the $60 \%$ decomposition is $540 \mathrm{~s}$, then the time required ...

If compound A reacts with B following first order kinetics with rate constant $$2.011 \times 10^{-3} \mathrm{~s}^{-1}$$. The time taken by $$\mathrm{A...

For conversion of compound A $$\to$$ B, the rate constant of the reaction was found to be $$\mathrm{4.6\times10^{-5}~L~mol^{-1}~s^{-1}}$$. The order o...

For certain chemical reaction $$X\to Y$$, the rate of formation of product is plotted against the time as shown in the figure. The number of $$\mathrm...

A first order reaction has the rate constant, $$\mathrm{k=4.6\times10^{-3}~s^{-1}}$$. The number of correct statement/s from the following is/are ____...

For the first order reaction A $$\to$$ B, the half life is 30 min. The time taken for 75% completion of the reaction is _________ min. (Nearest intege...

The number of correct statement/s from the following is __________
A. Larger the activation energy, smaller is the value of the rate constant.
B. The ...

Assuming $$1 \,\mu \mathrm{g}$$ of trace radioactive element X with a half life of 30 years is absorbed by a growing tree. The amount of X remaining i...

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

For a reaction, given below is the graph of $$\ln k$$ vs $${1 \over T}$$. The activation energy for the reaction is equal to ____________ $$\mathrm{ca...

For the given first order reaction
$$\mathrm{A} \rightarrow \mathrm{B}$$
the half life of the reaction is $$0.3010 \mathrm{~min}$$. The ratio of the i...

$$\matrix{
{[A]} & \to & {[B]} \cr
{{\mathop{\rm Reactant}\nolimits} } & {} & {{\mathop{\rm Product}\nolimits} } \cr
} $$
If formation o...

$$2 \mathrm{NO}+2 \mathrm{H}_{2} \rightarrow \mathrm{N}_{2}+2 \mathrm{H}_{2} \mathrm{O}$$
The above reaction has been studied at $$800^{\circ} \mathrm...

For a reaction $$\mathrm{A} \rightarrow 2 \mathrm{~B}+\mathrm{C}$$ the half lives are $$100 \mathrm{~s}$$ and $$50 \mathrm{~s}$$ when the concentratio...

For the decomposition of azomethane.
CH3N2CH3(g) $$\to$$ CH3CH3(g) + N2(g), a first order reaction, the variation in partial pressure with time at 600...

The half life for the decomposition of gaseous compound $$\mathrm{A}$$ is $$240 \mathrm{~s}$$ when the gaseous pressure was 500 Torr initially. When t...

For the reaction P $$\to$$ B, the values of frequency factor A and activation energy EA are 4 $$\times$$ 1013 s$$-$$1 and 8.3 kJ mol$$-$$1 respectivel...

The equation k = (6.5 $$\times$$ 1012s$$-$$1)e$$-$$26000K/T is followed for the decomposition of compound A. The activation energy for the reaction is...

The activation energy of one of the reactions in a biochemical process is 532611 J mol$$-$$1. When the temperature falls from 310 K to 300 K, the chan...

A radioactive element has a half life of 200 days. The percentage of original activity remaining after 83 days is ___________. (Nearest integer)
(Give...

For a first order reaction A $$\to$$ B, the rate constant, k = 5.5 $$\times$$ 10$$-$$14 s$$-$$1. The time required for 67% completion of reaction is x...

It has been found that for a chemical reaction with rise in temperature by 9 K the rate constant gets doubled. Assuming a reaction to be occurring at ...

The rate constant for a first order reaction is given by the following equation:
$$\ln k = 33.24 - {{2.0 \times {{10}^4}\,K} \over T}$$
The activation...

Catalyst A reduces the activation energy for a reaction by 10 kJ mol$$-$$1 at 300 K. The ratio of rate constants, $${{{}^kT,\,Catalysed} \over {{}^kT,...

A flask is filled with equal moles of A and B. The half lives of A and B are 100 s and 50 s respectively and are independent of the initial concentrat...

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 h...

For a given chemical reaction
$$\gamma$$1A + $$\gamma$$2B $$\to$$ $$\gamma$$3C + $$\gamma$$4D
Concentration of C changes from 10 mmol dm$$-$$3 to 20 m...

The rate constants for decomposition of acetaldehyde have been measured over the temperature range 700 - 1000 K. The data has been analysed by plottin...

For the reaction A $$\to$$ B, the rate constant k(in s$$-$$1) is given by$${\log _{10}}k = 20.35 - {{(2.47 \times {{10}^3})} \over T}$$The energy of a...

For a first order reaction, the ratio of the time for 75% completion of a reaction to the time for 50% completion is ____________. (Integer answer)

According to the following figure, the magnitude of the enthalpy change of the reactionA + B $$\to$$ M + N in kJ mol$$-$$ is equal to ___________. (In...

The first order rate constant for the decomposition of CaCO3 at 700 K is 6.36 $$\times$$ 10$$-$$3s$$-$$1 and activation energy is 209 kJ mol$$-$$1. It...

The reaction that occurs in a breath analyser, a device used to determine the alcohol level in a person's blood stream is $$2{K_2}C{r_2}{O_7} + 8{H_2}...

The following data was obtained for chemical reaction given below at 975 K.2NO(g) + 2H2(g) $$\to$$ N2(g) + 2H2O(g)The order of the reaction with respe...

For the first order reaction A $$\to$$ 2B, 1 mole of reactant A gives 0.2 moles of B after 100 minutes. The half life of the reaction is __________ mi...

For a chemical reaction A $$\to$$ B, it was found that concentration of B is increased by 0.2 mol L$$-$$ in 30 min. The average rate of the reaction i...

$${N_2}{O_{5(g)}} \to 2N{O_{2(g)}} + {1 \over 2}{O_{2(g)}}$$In the above first order reaction the initial concentration of N2O5 is 2.40 $$\times$$ 10$...

$$PC{l_5}(g) \to PC{l_3}(g) + C{l_2}(g)$$In the above first order reaction the concentration of PCl5 reduces from initial concentration 50 mol L$$-$$1...

The inactivation rate of a viral preparation is proportional to the amount of virus. In the first minute after preparation, 10% of the virus is inacti...

A reaction has a half life of 1 min. The time required for 99.9% completion of the reaction is _________ min. (Round off to the Nearest Integer). [Use...

2NO(g) + Cl2(g) $$\rightleftharpoons $$ 2NOCl(s) This reaction was studied at $$-$$10$$^\circ$$ and the following data was obtained
Run
$$...

The reaction 2A + B2 $$ \to $$ 2AB is an elementary reaction.For a certain quantity of reactants, if the volume of the reaction vessel is reduced by a...

For a certain first order reaction 32% of the reactant is left after 570s. The rate constant of this reaction is _________ $$\times$$ 10$$-$$3 s$$-$$1...

A and B decompose via first order kinetics with half-lives 54.0 min and 18.0 min respectively. Starting from an equimolar non reactive mixture of A an...

The decomposition of formic acid on gold surface follows first order kinetics. If the rate constant at 300 K is 1.0 $$\times$$ 10$$-$$3 s$$-$$1 and th...

If the activation energy of a reaction is 80.9 kJ mol$$-$$1, the fraction of molecules at 700 K, having enough energy to react to form products is e$$...

The rate constant of a reaction increases by five times on increase in temperature from 27$$^\circ$$C to 52$$^\circ$$C. The value of activation energy...

For the reaction, aA + bB $$ \to $$ cC + dD, the plot of log k vs $${1 \over T}$$ is given below :The temperature at which the rate constant of the re...

Sucrose hydrolyses in acid solution into glucose and fructose following first order rate law with a half-life of 3.33 h at 25$$^\circ$$C. After 9 h, t...

Gaseous cyclobutene isomerises to butadiene in a first order process which has a 'k' value of 3.3 $$ \times $$ 10-4 s-1 at 153°C. The time in minutes ...

The rate of a reaction decreased by 3.555
times when the temperature was changed
from 40oC to 30oC. The activation energy
(in kJ mol–1) of the reactio...

The number of molecules with energy greater
than the threshold energy for a reaction
increases five fold by a rise of temperature
from 27oC to 42oC. I...

If 75% of a first order reaction was completed
in 90 minutes, 60% of the same reaction would
be completed in approximately (in minutes)
_______.
(Take...

A sample of milk splits after 60 min. at 300 K
and after 40 min. at 400 K when the population
of lactobacillus acidophilus in it doubles. The
activa t...

During the nuclear explosion, one of the products is 90Sr with half life of 6.93 years. If 1 $$\mu $$ g of 90Sr was absorbed in the bones of newly bor...

## MCQ (Single Correct Answer)

Integrated rate law equation for a first order gas phase reaction is given by (where $$\mathrm{P}_{\mathrm{i}}$$ is initial pressure and $$\mathrm{P}_...

For a chemical reaction $$\mathrm{A}+\mathrm{B} \rightarrow$$ Product, the order is 1 with respect to $$\mathrm{A}$$ and $$\mathrm{B}$$.
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The correct reaction profile diagram for a positive catalyst reaction.

Consider the following reaction that goes from A to B in three steps as shown below:
Choose the correct option...

A student has studied the decomposition of a gas AB$$_3$$ at 25$$^\circ$$C. He obtained the following data.
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For kinetic study of the reaction of iodide ion with $$\mathrm{H}_{2} \mathrm{O}_{2}$$ at room temperature :
(A) Always use freshly prepared starch so...

At $$30^{\circ} \mathrm{C}$$, the half life for the decomposition of $$\mathrm{AB}_{2}$$ is $$200 \mathrm{~s}$$ and is independent of the initial conc...

For a first order reaction, the time required for completion of 90% reaction is 'x' times the half life of the reaction. The value of 'x' is
(Given : ...

Which one of the following given graphs represents the variation of rate constant (k) with temperature (T) for an endothermic reaction?

For a reaction of order n, the unit of the rate constant is :

For the following graphs,Choose from the options given below, the correct one regarding order of reaction is :...

Isotope(s) of hydrogen which emits low energy $$\beta$$$$-$$ particles with t1/2 value > 12 years is/are

Consider the following reactions
A $$ \to $$ P1 ; B $$ \to $$ P2 ; C $$ \to $$ P3 ; D $$ \to $$ P4,
The order of the above reactions are a, b, c,
and ...

The rate constant (k) of a reaction is measured at differenct temperatures (T), and the data are
plotted in the given figure. The activation energy of...

A flask contains a mixture of compounds A and
B. Both compounds decompose by first-order
kinetics. The half-lives for A and B are 300 s
and 180 s, res...

For the reaction 2A + 3B +
$${3 \over 2}$$C
$$ \to $$ 3P, which
statement is correct ?

It is true that :

The results given in the below table were
obtained during kinetic studies of the following
reaction
2A + B $$ \to $$ C + D
X and Y in the given table...

For the following reactions
$$A\buildrel {700K} \over
\longrightarrow {\mathop{\rm Product}\nolimits} $$
$$A\mathrel{\mathop{\kern0pt\longrightarrow}...

Consider the following plots of rate constant
versus $${1 \over T}$$ for four different reactions. Which
of the following orders is correct for the
ac...

The rate of a certain biochemical reaction at physiological temperature (T) occurs 106 times faster with
enzyme than without. The change in the activa...

For the reaction 2H2(g) + 2NO(g) $$ \to $$ N2(g) + 2H2O(g) the observed rate expression is, rate = Kf[NO]2[H2]. The rate expression for the reverse re...

NO2 required for a reaction is produced by the decomposition of N2O5 in CCl4 as per the equation,
2N2O5(g) $$ \to $$ 4NO2(g) + O2(g).
The initial conc...

In the following reaction; xA $$ \to $$ yB
$${\log _{10}}\left[ { - {{d\left[ A \right]} \over {dt}}} \right] = {\log _{10}}\left[ {{{d\left[ B \right...

For the reaction of H2 with I2, the rate constant is 2.5 × 10–4 dm3
mol–1s–1
at 327°C and 1.0 dm3
mol–1
at
527°C. The activation energy for the re...

A bacterial infection in an internal wound grows as N'(t) = N0 exp(t), where the time t is in hours. A does of antibiotic, taken orally, needs 1 hour ...

Consider the given plot of enthalpy of the
following reaction between A and B.
A+ B $$ \to $$ C + D
Identify the incorrect statement.
...

The given plots represent the variation of the
concentration of a reactant R with time for two
different reactions (i) and (ii). The respective
orders...

For a reaction scheme $$A\buildrel {{k_1}} \over
\longrightarrow B\buildrel {{k_2}} \over
\longrightarrow C$$,
if
the rate of formation of B is set...

For the reaction 2A + B $$ \to $$ C, the values of initial rate at diffrent reactant concentrations are
given in the table below. The rate law for the...

For a reaction consider the plot of $$\ell $$n k versus 1/T given in the figure. If the rate constant of this reaction at 400 K is 10–5 s–1, then the ...

Decomposition of X exhibits a rate constant of 0.05 $$\mu $$g/year. How many year are required for the decomposition of 5$$\mu $$g of X into 2.5 $$\mu...

The reaction 2X $$ \to $$ B is a zeroth order reaction. If the initial concentration of X is 0.2 M, the half-life is 6 h. When the initial concentrati...

If a reaction follows the Arrhenius equation, the plot ln k vs $${1 \over {\left( {RT} \right)}}$$ gives straight line with a gradient ($$-$$ y) unit....

For an elementary chemical reaction,
the expression for $${{d\left[ A \right]} \over {dt}}$$ is ...

Consider the given plots for a reaction obeying Arrhenius equation (0oC < T < 300oC) : (K and Ea are rate constant and activation energy, respec...

For the reaction, 2A + B $$ \to $$ products, when the concentrations of A and B both were doubled, the rate of the reaction increased from 0.3 mo...

The following results were obtained during kinetic studies of the reaction ;
2A + B $$ \to $$ Products
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If 50% of a reaction occurs in 100 second and 75% of the reaction occurs in 200 secod, the order of this reaction is :

At 518oC the rate of decomposition of a sample of gaseous acetaldehyde initially at a pressure of 363 Torr,
was 1.00 Torr s–1 when 5% had reacted and ...

For a first order reaction, A $$ \to $$ P, t1/2 (half-life) is 10 days The time required for $${1 \over 4}$$th conversion of A (in days) is : (ln 2 = ...

N2O5 decomposes to NO2 and O2 and follows first order kinetics. After 50 minutes, the pressure inside the vessel increases from 50 mmHg to 87.5 mmHg. ...

The rate of a reaction quadruples when the temperature changes from 300 to 310 K. The activation energy of this reaction is :
(Assume activation energ...

The rate of a reaction A doubles on increasing the temperature from 300 to 310 K. By how much, the temperature of reaction B should be Increased from ...

Two reactions R1 and R2 have identical pre-exponential factors. Activation energy of R1 exceeds that of R2 by 10 kJ mol–1. If k1 and k2 are rate const...

The rate law for the reaction below is given by the expression k [A] [B]
A + B $$ \to $$ Product
If the concentration of B is increased from 0.1 to 0....

The reaction of ozone with oxygen atoms in the presence of chlorine atoms can occur
by a two step process shown below :
O3(g) + Cl$${^ \bullet }$$ (g)...

Decomposition of H2O2 follows a first order reaction. In fifty minutes the concentration of H2O2 decreases
from 0.5 to 0.125 M in one such decompositi...

Higher order (>3) reactions are rare due to

For the non – stoichiometre reaction 2A + B $$\to$$ C + D, the following kinetic data were obtained in three
separate experiments, all at 298 K.
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The rate of a reaction doubles when its temperature changes from 300K to 310K. Activation energy of such
a reaction will be:(R = 8.314 JK–1 mol–1 and ...

For a first order reaction, (A) $$\to$$ products, the concentration of A changes from 0.1 M to 0.025 M in 40
minutes. The rate of reaction when the co...

The rate of a chemical reaction doubles for every 10oC rise of temperature. If the temperature is raised
by 50oC , the rate of the reaction increases ...

The time for half life period of a certain reaction A $$\to$$ products is 1 hour. When the initial
concentration of the reactant ‘A’, is 2.0 mol L–1, ...

Consider the reaction :
Cl2(aq) + H2S(aq) → S(s) + 2H+ (aq) + 2Cl– (aq)
The rate equation for this reaction is rate = k [Cl2] [H2S]
Which of these mec...

The half life period of a first order chemical reaction is 6.93 minutes. The time required for the
completion of 99% of the chemical reaction will be ...

For a reaction $${1 \over 2}A \to 2B$$ rate of disappearance of ‘A’ is related to the rate of appearance of ‘B’ by the
expression

The energies of activation for forward and reverse reactions for A2 + B2 $$\leftrightharpoons$$ 2AB are 180 kJ mol−1
and 200 kJ mol−1 respectively. Th...

Consider the reaction, 2A + B $$\to$$ products. When concentration of B alone was doubled, the half-life did not change. When the concentration of A
a...

A radioactive element gets spilled over the floor of a room. Its half-life period is 30 days. If the initial
activity is ten times the permissible val...

Which of the following nuclear reactions will generate an isotope?

A reaction was found to be second order with respect to the concentration of carbon monoxide. If the
concentration of carbon monoxide is doubled, with...

In the transformation of $${}_{92}^{238}U$$ to $${}_{92}^{234}U$$, if one emission is an α-particle, what should be the other
emission(s)?

Rate of a reaction can be expressed by Arrhenius equation as:
$$$k = A\,{e^{ - E/RT}}$$$
In this equation, E represents

The following mechanism has been proposed for the reaction of NO with Br2 to form NOBr:
NO(g) + Br2 (g) $$\leftrightharpoons$$ NOBr2 (g)
NOBr2 (g) ...

Hydrogen bomb is based on the principle of

A reaction involving two different reactants can never be

The photon of hard gamma radiation knocks a proton out of $${}_{12}^{24}Mg$$ nucleus to form

t1/4 can be taken as the time taken for the concentration of a reactant to drop to $$3 \over 4$$ of its initial value. If the rate constant for a firs...

A schematic plot of $$ln$$ $${K_{eq}}$$ versus inverse of temperature for a reaction is shown below
The reaction must be ...

In a first order reaction, the concentration of the reactant decreases from 0.8 M to 0.4 M in 15
minutes. The time taken for the concentration to chan...

Consider the following nuclear reactions
$${}_{92}^{238}M \to {}_Y^XN + 2{}_2^4He$$
$${}_Y^XN \to {}_B^AL + 2{\beta ^ + }$$
The number of neutrons in ...

The rate equation for the reaction 2A + B $$\to$$ C is found to be: rate k[A][B]. The correct
statement in relation to this reaction is that the

The half – life of a radioisotope is four hours. If the initial mass of the isotope was 200 g, the
mass remaining after 24 hours undecayed is

The radionucleide $${}_{90}^{234}Th$$ undergoes two successive $$\beta$$ -decays followed by one $$\alpha$$-decay. The atomic number
and the mass numb...

The half-life of a radioactive isotope is three hours. If the initial mass of the isotope were 256 g, the mass of
it remaining undecayed after 18 hour...

In respect of the equation k = Ae-Ea/RT in chemical kinetics, which one of the following statements is correct?

The rate law for a reaction between the substances A and B is given by Rate = k[A]n [B]m On doubling the concentration of A and halving the concentrat...

For the reaction system:
2NO(g) + O2(g) $$\to$$ 2NO2(g) volume is suddenly reduce to half its value by increasing the pressure on it. If the reaction...

Units of rate constant of first and zero order reactions in terms of molarity M unit are respectively

For the reaction A + 2B $$\to$$ C, rate is given by R = [A] [B]2 then the order of the reaction is

The differential rate law for the reaction H2 + I2 $$\to$$ 2HI is

If half-life of a substance is 5 yrs, then the total amount of substance left after 15 years, when initial amount is 64 grams is

The integrated rate equation is Rt = log C0 - log Ct . The straight line graph is obtained by
plotting

$$\beta$$ - particle is emitted in radioactivity by