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Test: Zero, First, Second and Third Order reactions - Chemistry MCQ


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15 Questions MCQ Test Physical Chemistry - Test: Zero, First, Second and Third Order reactions

Test: Zero, First, Second and Third Order reactions for Chemistry 2024 is part of Physical Chemistry preparation. The Test: Zero, First, Second and Third Order reactions questions and answers have been prepared according to the Chemistry exam syllabus.The Test: Zero, First, Second and Third Order reactions MCQs are made for Chemistry 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Zero, First, Second and Third Order reactions below.
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Test: Zero, First, Second and Third Order reactions - Question 1

A first-order reaction is 50 percent complete in 30 minutes. Calculate the time taken for completion of 87.5 percent of the reaction.

Detailed Solution for Test: Zero, First, Second and Third Order reactions - Question 1

To calculate the time taken for 87.5% completion of a first-order reaction, we can use the following concepts:

For a first-order reaction, the time required to complete a certain percentage of the reaction is given by the first-order rate equation:

where:

  • ttt is the time taken for the reaction to reach a certain completion.
  • kkk is the rate constant.
  • [R]0[R]_0[R]0​ is the initial concentration of the reactant.
  • [R][R][R] is the concentration of the reactant at time ttt.

The rate constant kkk for a first-order reaction can be determined from the half-life using the relation:

 

The other solution can be:-

Reaction is 50 percent complete in 30 minutes. Hence, t1/2 = 30 minutes
75 percent of the reaction is completed in two half-lives. Hence, t = 2 × 30 = 60 minutes
87.5 percent of the reaction is completed in three half-lives. Hence, t = 3 × 30 = 90 minutes.

Test: Zero, First, Second and Third Order reactions - Question 2

For the reaction X → Y + Z, the rate constant is 0.00058 s-1. What percentage of X will be decomposed in 50 minutes?

Detailed Solution for Test: Zero, First, Second and Third Order reactions - Question 2

Given, rate constant k= 0.00058 s-1
Time t= 50 minutes = 50 × 60 = 3000 seconds
First-order integrated rate equation, k = 

a=82.44 percent.

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Test: Zero, First, Second and Third Order reactions - Question 3

 first-order reaction was 70 percent complete in 20 minutes. What is the rate constant of the reaction?

Detailed Solution for Test: Zero, First, Second and Third Order reactions - Question 3

Given, the reaction is 70 percent complete so, a = 70
Time t = 20 minutes
First order integrated rate equation, k = 

Test: Zero, First, Second and Third Order reactions - Question 4

What is the formula to calculate the time taken for the completion of a zero-order reaction?

Detailed Solution for Test: Zero, First, Second and Third Order reactions - Question 4

The time taken for the zero-order reaction to complete can be calculated as follows:
When the reaction is complete, [A]0 = 0
Therefore, k = [A]0/t or t100% = [A]0/k.

Test: Zero, First, Second and Third Order reactions - Question 5

For a certain reaction the values of Arrhenius factor and Activation energy are 4 x 1013 collision/sec and 98.6KJ/mol at 303K. Calculate the rate constant if reaction is 1st order?( R=8.341mol-1K-1)

Detailed Solution for Test: Zero, First, Second and Third Order reactions - Question 5

Given,
Arrhenius factor(A) = 4 x 1013 collisions/sec
Activation energy (Ea)=98.6KJ/mol=98.6 x 103J/mol, T=303 K
log K = log A – (Ea/2.303RT)
log K = log (4 x 1013) – (98.6 x 103)/(2.303 x 8.314 x 303)
log K = 13.6020 – (98.6 x 103/5801.584)
log k = -3.39
K = 10-3.39
K = 4.07 x 10-4.

Test: Zero, First, Second and Third Order reactions - Question 6

A zero-order reaction is 25% complete in 30seconds. What time does it take for 50% completion?

Detailed Solution for Test: Zero, First, Second and Third Order reactions - Question 6

t25% = (1-0.75)/K
K = 0.25/30
t50% = (1 x 30)/(2 x 0.25)
t50% = 15/0.25
t50% = 60s.

Test: Zero, First, Second and Third Order reactions - Question 7

The rate constant of a reaction is 0.01s-1, how much time does it take for 2.4 mol L-1 concentration of reactant reduced to 0.3 mol L-1?

Detailed Solution for Test: Zero, First, Second and Third Order reactions - Question 7

Given,
K = 0.01s-1
t1/2 = 0.693/0.01
t1/2 = 69.3s
[R] = [R]0/2n
2n = [R]0/[R]
2n = 2.4/0.3
2n = 8
n = 3 (number of half-lives)
For 1 half-life t1/2 = 69.3s
For 3 half-life 3t1/2 = 3 x 69.3s = 207.9s.

Test: Zero, First, Second and Third Order reactions - Question 8

What is the time required for 75 percent completion of a first-order reaction?

Detailed Solution for Test: Zero, First, Second and Third Order reactions - Question 8

Given, the reaction is 75 percent complete so, a = 75
We know, t = 

t75 = 2 × t50.

Test: Zero, First, Second and Third Order reactions - Question 9

What is the time taken to complete 75 percent of the reaction if the rate of the first-order reaction is 0.023 min-1?

Detailed Solution for Test: Zero, First, Second and Third Order reactions - Question 9

Given, the reaction is 75 complete so, a=75
Rate of the reaction k=0.023 min-1
First-order integrated rate equation, k = 

Test: Zero, First, Second and Third Order reactions - Question 10

The half-life of a given reaction is doubled if the initial concentration of the reactant is doubled. What is the order of the reaction?

Detailed Solution for Test: Zero, First, Second and Third Order reactions - Question 10

Half-life (t1⁄2) is the time required for a quantity to reduce to half of its initial value. The half-life of a zero-order reaction is directly proportional to its initial concentration. They are related as:
t1/2 = [R]0/2k.

Test: Zero, First, Second and Third Order reactions - Question 11

The decomposition of N2O5 in CCl4 solution was studied. N2O5 → 2NO2 + 1/2O2. The rate constant of the reaction is 6.2 x 10-4 sec-1. Calculate the rate when the concentration of N2O5 is 1.25 molar.

Detailed Solution for Test: Zero, First, Second and Third Order reactions - Question 11

Given,
N2O5 → 2NO2 + 1/2 O2
Rate = k[N2O5] 1
Rate =6.25 x 10-4 x [1.25]
Rate = 7.75 x 10-4.

Test: Zero, First, Second and Third Order reactions - Question 12

What is the integrated rate equation for a first order reaction?

Detailed Solution for Test: Zero, First, Second and Third Order reactions - Question 12

A reaction is said to be of the first order if the rate of the reaction depends upon one concentration term only. The integrated rate equation for a first order reaction in exponential form is [A] = [A]0e-kt.

Test: Zero, First, Second and Third Order reactions - Question 13

What time does it take for reactants to reduce to 3/4 of initial concentration if the rate constant is 7.5 x 10-3 s-1?

Detailed Solution for Test: Zero, First, Second and Third Order reactions - Question 13

Given,
K=7.5 x 10-3 s-1
K = (2.303/t) x log([R]0/[R])
t = (2.303/7.5 x 10-3) x log([100]/[25])
t = (2.303/7.5 x 10-3) x 0.6
t = 38.4s.

Test: Zero, First, Second and Third Order reactions - Question 14

The unit of the rate constant of a zero-order reaction and second-order reaction is same.

Detailed Solution for Test: Zero, First, Second and Third Order reactions - Question 14

The unit of the rate constant k for a zero-order reaction is mol L-1 s-1. For a first-order reaction, the unit of k is s-1. The unit of the rate constant k for a second-order reaction is mol-1 L s-1.

Test: Zero, First, Second and Third Order reactions - Question 15

The unit of rate constant of a first-order reaction is s-1.

Detailed Solution for Test: Zero, First, Second and Third Order reactions - Question 15

The rate constant is defined as the proportionality constant which explains the relationship between the molar concentration of the reactants and the rate of a chemical reaction. It is denoted by k.
For a first-order reaction, the unit of k is s-1.

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