Advertisements
Advertisements
Questions
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
Solution
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
RELATED QUESTIONS
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 brief.
Derive the integrated rate law for the first-order reaction.
Explain with the help of a potential energy diagram that the catalyst increases the rate of the reaction.
A zero-order reaction \[\ce{X -> Product}\], with an initial concentration 0.02 M has a half-life of 10 min. if one starts with concentration 0.04 M, then the half-life is
If 75% of a first order reaction was completed in 60 minutes, 50% of the same reaction under the same conditions would be completed in ____________.
Identify the order for the following reaction.
Radioactive disintegration of 92U238
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.
A first order reaction has a rate constant 0.00813 min-1. How long will it take for 60% completion?
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 ____________.
For first order reaction the concentration of reactant decreases from 0.2 to 0.1 M in 100 minutes. What is the rate constant of the reaction?
What is the order of reaction if the unit of rate constant (k) is mol dm−3 s−1?
If time required to decrease concentration of reactant from 0.8 M to 0.2 M is 12 hours, the half life of this first order reaction is ____________.
For the first order reaction, plot of log10 [A]t against time 't' is a straight line with a negative slope equal to ____________.
The rate and the rate constants of the reaction, \[\ce{A + 2B -> C + D}\] are 8 × 10−3 mol dm−3 s−1 and 2 × 10−3 s−1 respectively. The concentrations of A and B are 4 mol dm−3 each. The overall order of the reaction is ____________.
A first order reaction takes 40 minutes for 30% decomposition. What is the half-life of reaction?
In a reaction \[\ce{N2_{(g)} + 3H2_{(g)} -> 2NH3_{(g)}}\], if the rate of disappearance of N2(g) is 2.6 × 10−4 M/s, the rate of disappearance of H2(g) in M/s is ____________.
A certain zero order reaction has rate constant 0.025 M s-1. What will be the concentration of reactant 'A' after 15 seconds, if initial concentration is 0.50 M?
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?
Which of the following reactions is not of the first order?
What is the rate constant of a first order reaction if 0.08 mole of reactant reduces to 0.02 mole in 23.03 minutes?
The half-life of first order reaction is 1.7 hour. What is its rate constant?
The half-life period for the first order reaction is 1.7 hrs. How long will it take for 20% of the reactant to disappear?
The plot that represents the zero order reaction is:
