Chemical Kinetics Test

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Chemical Kinetics Test - 24

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Question 1
1 / -0

In the decomposition of oxalic acid following data were obtained.
Time (second)
0
300
600
Volume of $$KMnO_4$$ used in mL
22.0
17.0
13.4
If reaction obeys 1st order kinetics then determine the rate constant K and half-life period:

A
$$8.43\times 10^{-4} sec, 13.7minute$$

B
$$86\times 10^{-4} sec, 134.3 minute$$

C
$$8.6\times 10^{-5} sec, 1.343 minute$$

D
None of these

Solution

Volume of $$KMnO_4$$ used is directly proportional to the oxalic acid concentration.
For the first order reaction, the integrated rate law expression is
$$\displaystyle k = \frac {2.303}{t} log \frac {a}{a-x} $$......(1)
For 300 seconds, the rate constant is
$$\displaystyle k = \frac {2.303}{300} log \frac {22.0}{17.0} = 0.0086 \: /s $$
For 600 seconds, the rate constant is
$$\displaystyle k = \frac {2.303}{600} log \frac {22.0}{13.4} = 0.0083 \: /s$$
The average value of k is $$\displaystyle \frac {0.0083+0.0086}{2} = 0.00843 \: /s = 8.43 \times 10^{-4} \: s$$
The half life period is $$\displaystyle t_{1/2} = \frac {0.693}{k} = \frac {0.693}{0.00843} = 822 \: s$$
Convert the half life period from seconds to minutes
$$\displaystyle t_{1/2} = \frac {822}{60} = 13.7 \: min$$
Question 2
1 / -0

For a reaction for which the activation energies of forward and reverse reactions are equal:

A
$$\Delta H=0$$

B
$$\Delta S=0$$

C
the order is zero

D
there is no catalyst

Solution

For a reaction for which the activation energies of forward and reverse reactions are equal, then both $$\Delta H$$ and $$\Delta S$$ are $$0$$.
The activation energy is the energy it takes to push the reactants up to the transition state.
For Exothermic reaction = negative $$\Delta H$$
Endothermic reaction = positive $$\Delta H$$
Question 3
1 / -0

The rate constant for an isomerisation reaction, $$A\rightarrow B$$ is $$4.5\times 10^{-3} min ^{-1}$$. If the initial concentration of A is 1 M, the rate of the reaction after 1 hr will be:

A
$$3.4354\times 10^{-3}$$

B
$$4.4554\times 10^{-3}$$

C
$$5.4364\times 10^{-3}$$

D
None of these

Solution

$$\underset {[A]_0=1 M}{A\rightarrow B} K=4.5\times 10^{-3} min^{-1}$$
For Ist order reaction, $$K=\frac {2.303}{t}log \frac {a}{(a-x)}$$ at $$t=60 min$$
$$4.5\times 10^{-3}=\frac {2.303}{60} log_{10}\frac {1}{(a-x)}$$
$$\therefore (a-x)=0.7634$$
Thus, rate after 60 minute $$=K(a-x)$$
$$=4.5\times 10^{-3}\times 0.7634$$
$$=3.4354\times 10^{-3}$$
Question 4
1 / -0

The activation energy for a chemical reaction depends upon:

A
reaction

B
nature of reacting species

C
frequency factor

D
concentration of reacting species

Solution

Activation energy is independent of temperature, concentration and collision frequency. Activation energy for a chemical reaction depends upon nature of reacting species.
Question 5
1 / -0

$$A\rightarrow B+2C$$

At $$100^oC$$, in above gaseous reaction, is observed to be of the first order. On starting with pure A, at the end of $$14$$ minutes, the total pressure found to be $$264$$ mm of Hg. After a long time, the total pressure of the system was $$450$$ mm of Hg.
Rate constant of the reaction is:

A
$$6.455\times 10^{-2} min^{-1}$$

B
$$3.415\times 10^{-2} min^{-1}$$

C
$$5.575\times 10^{-2} min^{-1}$$

D
none of these

Solution

To provide a long time or heating to a reaction mixture means that reaction has gone to completion.

$$A\rightarrow B+2C$$

Mole before dissociation a 0 0
Mole after dissociation a-x x 2x
Mole after complete dissociation 0 a 2a
$$\because$$ Total mole at a time $$\propto$$ pressure at that time

$$a\propto P_0 {\;};\ t=0$$ ......(i)

$$a+2X\propto 264 {\;};\ t=14\ minutes$$ ....(ii)

$$3a = 450 {\;};\ t=\infty$$ .....(iii)

$$\because$$ By Eqs. (i), (ii) and (iii) we get $$X= 57; \ a=150.$$

$$K=\dfrac {2.303}{14}log \dfrac {150}{150-57}=3.415\times 10^{-2}\ min^{-1}$$

Hence, the correct option is $$B$$.
Question 6
1 / -0

At room temperature, the reaction between $$NO$$ and $$O_2$$ to give $$NO_2$$ is fast, while that between $$CO$$ and $$O_2$$ is slow. It is due to:

A
CO is smaller in size than that of NO

B
CO is poisonous

C
the activation energy for the reaction, $$2NO+O_2\rightarrow 2NO_2$$ is less than $$2CO+O_2\rightarrow 2CO_2$$

D
none of the above

Solution

At room temperature, the reaction between $$NO$$ and $$O_2$$ to give $$NO_2$$ is fast, while that between $$CO$$ and $$O_2$$ is slow. It is due to the activation energy for the reaction, $$2NO+O_2\rightarrow 2NO_2$$ is less than $$2CO+O_2\rightarrow 2CO_2$$.
Reactions having lower energy of activation occurs more fast under similar experimental conditions.
Question 7
1 / -0

For a first-order reaction, $$A\rightarrow Product$$, the initial concentration of A is 0.1M and after 40 minutes it becomes 0.025 M. Calculate the rate of reaction at reactant concentration of 0.01 M:

A
$$3.47\times 10^{-4} M .min^{-1}$$

B
$$3.47\times 10^{-5} M. min^{-1}$$

C
$$1.735\times 10^{-6} M. min^{-1}$$

D
$$1.735\times 10^{-4} M. min^{-1}$$

Solution

As we know,

$$K=\frac {2.303}{40}log\frac {[0.1]}{[0.025]}$$

$$\therefore K=0.03466\ min^{-1}$$

$$\therefore rate=K\times 0.01=0.03466\times 0.01=3.47\times 10^{-4} M min^{-1}$$
Question 8
1 / -0

The maximum value of activation energy is equal to:

A
zero

B
heat of reaction

C
threshold energy

D
none of these

Solution

Option (D) is correct.
Activation energy may be greater than heat of reaction or lesser than threshold energy.At room temperature, most of the molecules have less than the threshold value. Hence, if energy is supplied to the reactant molecules in the form of light or heat, they absorb that energy and reach a higher energy level which is equal to or greater than the threshold energy level, is called as activation energy.

Activation energy ($$E_a$$) = Threshold energy - Average kinetic energy of molecules
Question 9
1 / -0

In a first order reaction the concentration of reactant decreases from 800 $$mol/dm^3$$ to $$50\ mol/dm^3$$ in $$2\times 10^4 sec$$. The rate constant of reaction in $$sec^{-1}$$ is:

A
$$2.000\times 10^{4}$$

B
$$3.415\times 10^{-5}$$

C
$$1.386\times 10^{-4}$$

D
$$2.000\times 10^{-4}$$

Solution

As we know,

$$t=\frac {2.303}{K} \times log \frac {N_0}{N}$$

$$\therefore K=\frac {2.303}{2\times 10^{4}}\times log \frac {800}{50}=1.386\times 10^{-4} sec^{-1}$$
Question 10
1 / -0

Which of the following is not correct reason for the substantially lower rate of reaction than the collision frequency?

A
All the collisions do not attain threshold energy level

B
The activated complex formed is short lived

C
All the collisions do not have proper orientation

D
Effective collision are lesser in number than all collisions

Solution

Option (B) is correct.
If there is substantially lower rate of reaction than the collision frequency then the activated complex formed will be long-lived and the reaction will proceed at a slower rate. Because of low energy, the activated complex exists for an extremely long period of time and activated complex will neither reforms to form products.

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Time (second)	0	300	600
Volume of $$KMnO_4$$ used in mL	22.0	17.0	13.4

Mole before dissociation	a	0	0
Mole after dissociation	a-x	x	2x
Mole after complete dissociation	0	a	2a

Chemical Kinetics Test - 24

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Chemical Kinetics Test - 24

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Question 1

$$8.43\times 10^{-4} sec, 13.7minute$$

$$86\times 10^{-4} sec, 134.3 minute$$

$$8.6\times 10^{-5} sec, 1.343 minute$$

None of these

Solution

Question 2

$$\Delta H=0$$

$$\Delta S=0$$

the order is zero

there is no catalyst

Solution

Question 3

$$3.4354\times 10^{-3}$$

$$4.4554\times 10^{-3}$$

$$5.4364\times 10^{-3}$$

None of these

Solution

Question 4

reaction

nature of reacting species

frequency factor

concentration of reacting species

Solution

Question 5

$$6.455\times 10^{-2} min^{-1}$$

$$3.415\times 10^{-2} min^{-1}$$

$$5.575\times 10^{-2} min^{-1}$$

none of these

Solution

Question 6

CO is smaller in size than that of NO

CO is poisonous

the activation energy for the reaction, $$2NO+O_2\rightarrow 2NO_2$$ is less than $$2CO+O_2\rightarrow 2CO_2$$

none of the above

Solution

Question 7

$$3.47\times 10^{-4} M .min^{-1}$$

$$3.47\times 10^{-5} M. min^{-1}$$

$$1.735\times 10^{-6} M. min^{-1}$$

$$1.735\times 10^{-4} M. min^{-1}$$

Solution

Question 8

zero

heat of reaction

threshold energy

none of these

Solution

Question 9

$$2.000\times 10^{4}$$

$$3.415\times 10^{-5}$$

$$1.386\times 10^{-4}$$

$$2.000\times 10^{-4}$$

Solution

Question 10

All the collisions do not attain threshold energy level

The activated complex formed is short lived

All the collisions do not have proper orientation

Effective collision are lesser in number than all collisions

Solution

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