Advertisements
Advertisements
प्रश्न
Answer the following in brief.
Obtain the relationship between the rate constant and half-life of a first-order reaction.
Derive a relationship between the half-life and the rate constant for a first order reaction.
Advertisements
उत्तर
i. The integrated rate law for the first-order reaction is k = `2.303/t log_10 [A]_0/[A]_t`
Where [A]0 is the initial concentration of the reactant at t = 0. The concentration falls to [A]t at time t after the start of the reaction. The concentration of the reactant falls to `[A]_0/2` at time t1/2.
ii. The time required for [A]0 to become `[A]_0/2` is denoted as `t_(1/2)` or `[A]_t = [A]_0/2` at t = t1/2
Putting this condition in the integrated rate law we write
k = `2.303/t_(1/2) log_10 [A]_0/([A]_0/2)`
= `2.303/t_(1/2) log_10 2`
Substituting the value of `log_10 2`,
k = `2.303/t_(1/2) xx 0.3010`
∴ k = `0.693/t_(1/2)`
∴ `t_(1/2) = 0.693/k`
APPEARS IN
संबंधित प्रश्न
Answer the following in one or two sentences.
Write the relationships between rate constant and half-life of the first order and zeroth-order reactions.
Answer the following in one or two sentences.
How do the half-lives of the first order and zero-order reactions change with the initial concentration of reactants?
Solve
A first-order reaction takes 40 minutes for 30% decomposition. Calculate its half-life.
Write a mathematical expression for integrated rate law for zero-order reaction.
Derive an integrated rate law expression for first order reaction: A → B + C
The decomposition of phosphine (PH3) on tungsten at low pressure is a first-order reaction. It is because the
This reaction follows first-order kinetics. The rate constant at particular temperature is 2.303 × 10−2 hour−1. The initial concentration of cyclopropane is 0.25 M. What will be the concentration of cyclopropane after 1806 minutes? (log 2 = 0.3010)
From the following data, show that the decomposition of hydrogen peroxide is a reaction of the first order:
| t (min) | 0 | 10 | 20 |
| V (ml) | 46.1 | 29.8 | 19.3 |
Where t is the time in minutes and V is the volume of standard KMnO4 solution required for titrating the same volume of the reaction mixture.
What is the value of rate constant of first order reaction, if it takes 15 minutes for consumption of 20% of reactants?
The following reactions follow zero order kinetics, EXCEPT ____________.
The rate of the reaction \[\ce{A + B -> C}\] is 3.6 × 10−2 mol dm−3 s−1 when [A] = 0.3 mol dm−3 and [B] = 0.2 mol dm−3. Calculate k if reaction is first order in A and zero order in B.
A first order reaction completes its 10% in 20 minutes, then the time required to complete its 19% is ____________.
If [A]0 is the initial concentration, then the half life of zero order reaction is ____________.
The order of the reaction for which the unit of rate constant is s−1 is ____________.
Half-life period of a first order reaction, \[\ce{A -> product}\] is 3.0 hours. What is the value of rate constant?
For a zero order reaction, the plot of [A]t vs t is linear. The slope of the line is equal to ____________.
Which among the following is an example of zero order reaction?
For a first order reaction, \[\ce{A -> B}\], if [A] = 1 M and rate is 4 × 10−2 M s−1. What is the rate constant of the reaction?
Which among the following is an example of pseudo first order reaction?
A first order reaction takes 40 minutes for 30% completion. Calculate the half-life of reaction.
The time required to decompose SO2Cl2 to half of it's initial amount is 60 minutes. Calculate rate constant for this first order reaction.
Half-life of first order reaction is 20 minutes. What is the time taken to reduce the initial concentration of the reactant to `1/10`th?
Half-life of first-order reaction \[\ce{X -> Y + Z}\] is 3 minutes. What is the time required to reduce the concentration of 'X' by 90 % of it's initial concentration?
Rate constant for zero order reaction is 2 × 10-2 mol L-1 s-1. If the concentration of the reactant after 25 sec. is 0.5 M, what is the initial concentration of reactant?
The rate constant and half-life of a first order reaction are related to each other as ______.
Which of the following reactions is not of the first order?
Which is the relation between half life and rate constant for a zero order?
Calculate the time required to decrease the concentration of reactant of first order reaction from 0.8 M to 0.1 M if rate constant is 0.1155 hour−1.
