For a reaction 2 H 2 O 2 2 H 2 O 2 → Alkaline medium I - 2 H 2 O + O 2 The proposed mechanism is as given below: 1. H 2 O 2 + I - → H 2 O + IO - (slow) 2. H 2 O 2 + IO - → H 2 O + I - + O 2 (fast) Out of steps (1) and (2), which one is rate-determining step?

In chemical kinetics, the overall reaction rate is often approximately determined by the slowest step, known as the rate-determining step or rate-limiting step. If the first step is the slowest, and the entire reaction must wait for it, then it is the rate-determining step. The slowest step in a reaction mechanism is known as the rate-determining step. Step number (1) is the slowest among two steps, hence this is the rate-determining step. i.e., H 2 O 2 + I - → H 2 O + IO - (slow).

The probability of finding a green signal on a busy crossing X is 30 % . What is the probability of finding a green signal on X on two consecutive days out of three?

Let A be the event of finding a green signal on a busy crossing X The probability of finding a green signal on a busy crossing X is 30 % . P A = 30 100 = 3 10 The probability of not finding a green signal on a busy crossing X is P A ¯ = 1 - 3 10 = 7 10 . The probability of finding a green signal on X on two consecutive days out of three = P A P A P A ¯ + P A ¯ P A P A = 3 10 × 3 10 × 7 10 + 7 10 × 3 10 × 3 10 = 63 500 .

If A and B are two independent events such that P ( A ) = 0 . 3 and P ( A ∪ B ¯ ) = 0 . 8 . Find P ( B ) .

Given that A and B are two independent events then P A ∩ B = P A . P B Since we know addition theorem of probability P ( A ∪ B ) = P ( A ) + P ( B ) - P ( A ∩ B ) ∴ P ( A ∪ B ¯ ) = P ( A ) + P ( B ¯ ) - P ( A ∩ B ¯ ) Now put the given values in the above formula,we get ⇒ 0 . 8 = 0 . 3 + [ 1 - P ( B ) ] - P ( A ) P ( B ¯ ) ⇒ 0 . 5 = 1 - P ( B ) - 0 . 3 [ 1 - P ( B ) ] ⇒ 0 . 5 = 1 - P ( B ) - 0 . 3 + 0 . 3 P ( B ) ⇒ 0 . 5 = 0 . 7 - P ( B ) [ 1 - 0 . 3 ] ⇒ 0 . 7 P ( B ) = 0 . 2 ⇒ P ( B ) = 0 . 2 0 . 7 = 2 7 .

If A and B are two independent events, then write P ( A ∩ B ¯ ) in terms of P ( A ) and P B .

If A and B are two independent events then P A ∩ B = P A × P B . ∴ P A ∩ B ¯ = P A × P B ¯ ∴ P A ∩ B ¯ = P A 1 - P B ∵ P ( B ¯ ) + P B = 1 ∴ P ( A ∩ B ¯ ) = P A - P A × P B .

Three numbers are chosen from 1 to 20 . Find the probability that they are consecutive.

Let A is the occurrence of an event. Given numbers are 1 , 2 , 3 . . . 20 . From 20 numbers we have chosen 3 . ∴ Total possible outcomes n ( S ) = 20 C 3 The three Consecutive numbers are ( 1 , 2 , 3 ) , ( 2 , 3 , 4 ) … ( 18 , 19 , 20 ) . ∴ Total favourable cases are n ( A ) = 18 Hence, the required probability is P ( A ) = n ( A ) n ( S ) = 18 C 3 20 .

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Important Questions on Chemical Kinetics

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Four persons can hit a target correctly with probabilities

\frac{1}{2}, \frac{1}{3}, \frac{1}{4}

and

\frac{1}{8}

respectively. If all hit at the target independently, then the probability that the target would be hit, is

EASY

Chemistry>Physical Chemistry>Chemical Kinetics>Molecularity of a Reaction

For a reaction $2 H_{2} O_{2}$

$2 H_{2} O_{2} \to_{Alkaline medium}^{I^{-}} 2 H_{2} O + O_{2}$

The proposed mechanism is as given below:

1. $H_{2} O_{2} + I^{-} \to H_{2} O + {IO}^{-}$ (slow)

2. $H_{2} O_{2} + {IO}^{-} \to H_{2} O + I^{-} + O_{2}$ (fast)

Out of steps (1) and (2), which one is rate-determining step?

EASY

Chemistry>Physical Chemistry>Chemical Kinetics>Molecularity of a Reaction

A certain reaction occurs in two steps as:

(i)

2 {SO}_{2} (g) + 2 {NO}_{2} (g) \to 2 {SO}_{3} (g) + 2 NO (g)

(ii)

2 {NO}_{} (g) + O_{2} (g) \to 2 {NO}_{2} (g)

In the reaction,

EASY

Chemistry>Physical Chemistry>Chemical Kinetics>Molecularity of a Reaction

The ratio of mass densities of nuclei of

^{40} C a

and

^{16} O

is close to:

EASY

Chemistry>Physical Chemistry>Chemical Kinetics>Molecularity of a Reaction

The probability of finding a green signal on a busy crossing

X

30 %

. What is the probability of finding a green signal on

X

on two consecutive days out of three?

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2 M e V

neutron is emitted in a fission reactor. If it looses half of its kinetic energy in each collision with a moderator atom, how many collisions must it undergo to achieve thermal energy of

0.039 e V

HARD

Chemistry>Physical Chemistry>Chemical Kinetics>Molecularity of a Reaction

Explain the principle and working of a nuclear reactor with the help of a labelled diagram.

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Chemistry>Physical Chemistry>Chemical Kinetics>Molecularity of a Reaction

A die marked

1, 2, 3

in red

4, 5, 6

in green tossed. Let

A

be the event "number is even" and

B

be the event "number is marked red". Find whether the events

A

and

B

are independent or not.

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Chemistry>Physical Chemistry>Chemical Kinetics>Molecularity of a Reaction

A problem in mathematics is given to three students

A, B, C

and their respective probability of solving the problem is

\frac{1}{2}, \frac{1}{3}

and

\frac{1}{4}

, the probability that the problem will be solved is

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Chemistry>Physical Chemistry>Chemical Kinetics>Molecularity of a Reaction

An unbiased die with face marked

1, 2, 3, 4, 5, 6

is rolled four times. Out of

4

face values obtained, find the probability that the minimum face value is not less than

2

and the maximum face value is not greater than

5

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It is given that the probability that

A

can solve a given problem is

\frac{3}{5}

and the probability that

B

can solve the same problem is

\frac{2}{3}

. The probability that at least one of

A

and

B

can solve a problem is

HARD

Chemistry>Physical Chemistry>Chemical Kinetics>Molecularity of a Reaction

A

and

B

are two independent events such that

P (A) = 0.3

and

P (A \cup \bar{B}) = 0.8

. Find

P (B)

EASY

Chemistry>Physical Chemistry>Chemical Kinetics>Molecularity of a Reaction

A

and

B

are two independent events, then write

P (A \cap \bar{B})

in terms of

P (A)

and

P (B)

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A

and

B

are events such that

P (A) = \frac{1}{2}

P (B) = \frac{7}{12}

and

P (A^{'} \cup B^{'}) = \frac{3}{4}

, then

A

and

B

are

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Chemistry>Physical Chemistry>Chemical Kinetics>Molecularity of a Reaction

Three numbers are chosen from

1

20

. Find the probability that they are consecutive.

EASY

Chemistry>Physical Chemistry>Chemical Kinetics>Molecularity of a Reaction

A

and

B

are mutually exclusive events such that

P (A) = 0.4, P (B) = x

and

P (A \cup B) = 0.5,

then

x = ?

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6

boys and

6

girls sit in a row at random. Find the probability that all the girls sit together.

HARD

Chemistry>Physical Chemistry>Chemical Kinetics>Molecularity of a Reaction

A

and

B

are two events such that

P (A \cup B) = \frac{5}{6}, P (A \cap B) = \frac{1}{3} and P (B) = \frac{1}{2}

, then the events

A

and

B

are

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Chemistry>Physical Chemistry>Chemical Kinetics>Molecularity of a Reaction

A

and

B

are independent events such that

P (A) = 0.4

P (B) = x

and

P (A \cup B) = 0.5

, then find the value of

x

HARD

Chemistry>Physical Chemistry>Chemical Kinetics>Molecularity of a Reaction

The probabilities of

A, B

and

C

of solving a problem are

\frac{1}{6}, \frac{1}{5} and \frac{1}{3}

, respectively. What is the probability that the problem is solved?

In which year did the first war between India and Pakistan take place after independence?

Important Questions on Chemical Kinetics

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