Chemical Kinetics Test

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Chemical Kinetics Test - 77

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Weekly Quiz Competition

Question 1
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Which option is valid for zero order reaction?

A
$$t_{1/2} = \dfrac {3}{2} t_{1/4}$$

B
$$t_{1/2} = \dfrac {4}{3} t_{1/4}$$

C
$$t_{1/2} = 2t_{1/4}$$

D
$$t_{1/4} = (t_{1/2})^{2}$$

Solution

For zero order
$$A = A_{0} - kt$$
$$t_{\dfrac {1}{2}} = \dfrac {A_{0}}{2k}$$
$$t_{\dfrac {1}{4}} = \dfrac {A_{0}}{4k}\ =\dfrac {t_{\dfrac {1}{2}}}{t_{\dfrac {1}{4}}} = \dfrac {2}{1}$$
Question 2
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Directions For Questions

Three flasks A, B, and C have equal volumes. A is maintained at $$300$$K, B at $$600$$K, and C at $$900$$K. Flask A contains $$H_2$$ gas, flask B contains $$CH_4$$ gas and flask C contains $$O_2$$ gas, and masses of all gases are the same. Assume ideal behavior of gases.

...view full instructions

Flask with greater mean free path for the molecules.($$r_{H_2}:r_{CH_4}:r_{O_2}=1:2:2$$)

A
A

B
B

C
C

D
Same for all

Solution

$$\lambda$$ (mean free path)$$=\dfrac{kT_A}{\sqrt{2\pi}\sigma^2_Ap_A}$$

$$\dfrac{\lambda_A}{\lambda_B}=\left(\dfrac{T_A}{T_B}\right)\left(\dfrac{\sigma^2_B}{\sigma^2_A}\right)\left(\dfrac{P_B}{P_A}\right)=\left(\dfrac{300}{600}\right)\left(\dfrac{2}{1}\right)^2\left(\dfrac{1}{4}\right)$$

$$\dfrac{\lambda_A}{\lambda_B}=\dfrac{1}{2}$$

similarly,

$$\dfrac{\lambda_B}{\lambda_C}=\dfrac{1}{4}$$

$$\therefore \lambda_C > \lambda_B > \lambda_A$$

$$\therefore$$ Mean free path of C is highest
Option C is the correct answer.
Question 3
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The number of collisions of Ar atoms with the walls of container per unit time?

A
Increases when the temperature increases

B
Remains the same when $$CO_2$$ is added to the container at constant temperature

C
Increases when $$CO_2$$ is added to the container at constant temperature

D
Decreases, when the average kinetic energy per molecule is decreased

Solution

Number of effective collisions, $$z=\dfrac{1}{4}N$$ $$u_{avg}$$
also $$u_{avg}=\sqrt{\dfrac{8RT}{M}}$$, $$N=\dfrac{pv}{RT}$$
$$z=\dfrac{1}{4}\dfrac{pv}{RT}\times\sqrt{\dfrac{8RT}{m}}$$
$$\Rightarrow z\propto \dfrac{1}{\sqrt{T}}$$
So if temperature is constant, 'Z' will be same
Option B.
Question 4
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Directions For Questions

Three flasks A, B, and C have equal volumes. A is maintained at $$300$$K, B at $$600$$K, and C at $$900$$K. Flask A contains $$H_2$$ gas, flask B contains $$CH_4$$ gas and flask C contains $$O_2$$ gas, and masses of all gases are the same. Assume ideal behavior of gases.

...view full instructions

Flask with greater number of collisions with the walls per unit area per unit time.

A
A

B
B

C
C

D
Same for all

Solution

Effective no. of collision: $$z=\dfrac{1}{4}\times N\times u_{avg}$$

$$=\dfrac{1}{4}\times N\times \sqrt{\dfrac{8RT}{nm}}$$

$$\Rightarrow Z\propto \dfrac{1}{\sqrt{M}}$$

Lower mass means higher Z

$$\therefore$$ A $$(H_2)$$ option A.
Question 5
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If X is the total number of collisions which a gas molecule registers with other molecules per unit time under particular conditions, then the collision frequency of the gas containing N molecules per unit volume is:

A
$$X/N$$

B
$$NX$$

C
$$2NX$$

D
$$NX/2$$

Solution

The collision frequency $$Z_{AA}=$$Total collision$$\times \dfrac{N}{2}$$

$$Z_{AA}=X\times \dfrac{N}{2}$$

$$=\dfrac{XN}{2}$$

Option D is correct.
Question 6
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When the temperature of an ideal gas is increased at constant pressure?

A
Collision number increases

B
Collision frequency increases

C
Mean free path increases

D
Number of molecules per unit volume increases
Solution
Collision frequency is exceed to
$$z=\sigma \times \bar{c}ra\times \dfrac{PNA}{RT}$$

$$z=\sigma\times \bar{c}ra\times \dfrac{p}{RBT}$$
so when temperature $$\uparrow =\downarrow$$
Mean path is equal to

$$\lambda =\dfrac{RT}{\sqrt{2}na^2NAD}$$

so it will depend upon temperature so it will increases
(D) No of the molecule will be the same collision
No, the collision number increases because proper orientation also will be required.
So, the answer is C.
Question 7
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In a closed flask of $$5$$ litres $$1.0\ g$$ of $$H_2$$ is heated from $$300$$ to $$600\ K$$. Which statement is not correct?

A
Pressure of the gas increases

B
The rate of collisions increases

C
The number of moles of gas increases

D
The energy of gas molecules increases

Solution

Mass is fixed. It won't be effected by increase in temperature in a closed system. Therefore no. of moles of gas is also fixed.
Hence option C is an incorrect statement.
Question 8
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One mole of helium and one mole of neon are taken in a vessel. Which of the following statements are correct?

A
Molecules of helium strike the wall of vessel more frequently

B
Moles of neon apply more average force per collision on the wall of vessel

C
Molecules of helium have greater average molecular speed

D
Helium exerts higher pressure than neon

Solution

Helium gas has lower molecular mass and hence it moves faster than neon and strikes the wall more frequently.
$$μ_{av}=\sqrt{\dfrac{8RT}{\pi M}}$$

$$μ_{av}∝(\dfrac1M)^{1/2}$$

$$\text{Hence. He has higher speed than neon}$$
Question 9
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A container (cylindrical, base area$$=821cm^2$$) fitted with frictionless, massless piston consists of five valves-I, II, III, IV, and V. The distance of valves from the initial position of the piston is $$15, 30, 40, 45$$ and $$50$$cm, respectively. The initial height of the piston from the base of the container was $$60$$cm. These valves open automatically if pressure exceeds over $$1.5, 2.2, 2.5, 4.4$$, and $$4.8$$ atm, respectively. Under the given conditions(shown in the diagram), the system is in a state of equilibrium. The piston is now compressed(moved downward) slowly and isothermally. Neglect the volumes of valve connectors. Select the correct option(s).

A
Only the momentum of the molecules

B
Only the frequency of collision of molecules

C
Both momentum and frequency of collision of molecules

D
Neither momentum nor frequency of collision of molecules

Solution

As the piston (moved downward) slowly.
It does not change the pressure of the system.
$$\therefore \Delta P=0$$
$$\therefore$$ There is no change in momentum of molecule but as there is change in volume.
i.e., volume decreased.
$$\therefore$$ particles come closure & therefore particle collides with each other more frequently.
$$\therefore$$ As no. of collisions increases.
$$\therefore$$ Collision frequently changes
$$\therefore$$ There is change in frequency only.
Answer option B only.
Question 10
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The order of a reaction is zero. It will be definitely

A
exothermic

B
endothermic

C
elementary

D
complex

Solution

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Chemical Kinetics Test - 77

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Chemical Kinetics Test - 77

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Question 1

$$t_{1/2} = \dfrac {3}{2} t_{1/4}$$

$$t_{1/2} = \dfrac {4}{3} t_{1/4}$$

$$t_{1/2} = 2t_{1/4}$$

$$t_{1/4} = (t_{1/2})^{2}$$

Solution

Question 2

A

B

C

Same for all

Solution

Question 3

Increases when the temperature increases

Remains the same when $$CO_2$$ is added to the container at constant temperature

Increases when $$CO_2$$ is added to the container at constant temperature

Decreases, when the average kinetic energy per molecule is decreased

Solution

Question 4

A

B

C

Same for all

Solution

Question 5

$$X/N$$

$$NX$$

$$2NX$$

$$NX/2$$

Solution

Question 6

Collision number increases

Collision frequency increases

Mean free path increases

Number of molecules per unit volume increases

Solution

Question 7

Pressure of the gas increases

The rate of collisions increases

The number of moles of gas increases

The energy of gas molecules increases

Solution

Question 8

Molecules of helium strike the wall of vessel more frequently

Moles of neon apply more average force per collision on the wall of vessel

Molecules of helium have greater average molecular speed

Helium exerts higher pressure than neon

Solution

Question 9

Only the momentum of the molecules

Only the frequency of collision of molecules

Both momentum and frequency of collision of molecules

Neither momentum nor frequency of collision of molecules

Solution

Question 10

exothermic

endothermic

elementary

complex

Solution

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