Advertisements
Advertisements
प्रश्न
Answer the following in brief.
Obtain the relationship between the rate constant and half-life of a first-order reaction.
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"`
संबंधित प्रश्न
Answer the following in one or two sentences.
What are the units for rate constants for zero-order and second-order reactions if time is expressed in seconds and concentration of reactants in mol/L?
How will you represent first order reactions graphically.
Answer the following in brief.
What are the units of the rate constant?
Rate constant of a reaction is 3.6 × 10–3 s–1. The order of reaction is ______.
Write a mathematical expression for integrated rate law for zero-order reaction.
For the reaction 2NOBr → 2NO2 + Br2, the rate law is rate = k[NOBr]2. If the rate of a reaction is 6.5 × 10–6 mol L–1 s–1, when the concentration of NOBr is 2 × 10–3 mol L–1. What would be the rate constant of the reaction?
Define half life of a 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
The rate constant of a reaction is 5.8 × 10−2 s−1. The order of the reaction is ____________.
The time for half change in a first order decomposition of a substance A is 60 seconds. Calculate the rate constant. How much of A will be left after 180 seconds?
A first order reaction is 40% complete in 50 minutes. Calculate the value of the rate constant. In what time will the reaction be 80% complete?
The following reactions follow zero order kinetics, EXCEPT ____________.
The time of completion of 90% of a first order reaction is approximately ____________.
If [A] is the concentration of A at any time t and [A]0 is the concentration at t = 0, then for the 1st order reaction, the rate equation can be written as ____________.
The rate constant of a first order reaction is 3 × 10−6 per s. If the initial concentration is 0.10 mol dm−3, the initial rate of reaction is ____________.
Which of the following represents the expression for `(3/4)^"th"` life of 1st order reaction?
The order of the reaction for which the unit of rate constant is s−1 is ____________.
A first order reaction is 75% completed in 60 minutes, the time required for it's 50% completion is ____________.
In the reaction \[\ce{2SO2 + O2 -> 2SO3}\] the rate of appearance of SO3 is 4 × 10−4 M/s, the rate of disappearance of O2 is ____________.
The slope of a graph, log [A]t versus 't' for a first order reaction is −2.5 × 10−3 s−1. The rate constant for the reaction is ____________.
For a zero order reaction, the plot of [A]t vs t is linear. The slope of the line is equal to ____________.
The half-life of a first order reaction is 6.0 hour. How long will it take for the concentration of reactant to decrease from 0.4 M to 0.12 M?
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?
Which one of the following reactions is a true first-order reaction?
If the rate constant for a first-order reaction is k, the time (t) required for the completion of 99% of the reaction is given by:
The rate constant and half-life of a first order reaction are related to each other as ______.
The rate constant for a first order reaction is 7.0 × 10-4 s-1. If initial concentration of reactant is 0.080 M, what is the half-life of reaction?
Which is the relation between half life and rate constant for a zero order?
