Advertisements
Advertisements
प्रश्न
Derive an expression for the relation between half-life and rate constant for first-order reaction.
With the help of integrated rate law, derive an expression for the half-life of a first order reaction.
Advertisements
उत्तर
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 reactant at t = 0. It falls to [A]t at time t after the start of the reaction.
The time required for [A]0 to become `[A]_0/2` is denoted as t1/2 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]_t/([A]_0/2)`
= `2.303/t_(1//2) log_10 2`
Substituting value of log102,
k = `2.303/t_(1//2) xx 0.3010`
∴ k = `0.693/t_(1//2)`
∴ `t_(1//2) = 0.693/k`
The half-life of a first-order reaction is independent of the initial reactant concentration.
APPEARS IN
संबंधित प्रश्न
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?
Answer the following in brief.
Obtain the relationship between the rate constant and half-life of a first-order reaction.
Answer the following in brief.
What is a zeroth-order reaction?
Answer the following in brief.
Give one example and explain why it is pseudo-first-order.
The rate of catalysed reaction is large than the uncatalysed reaction as _______.
Explain pseudo first order reaction with a suitable example.
For a first order reaction \[\ce{A ->Product}\] with initial concentration x mol L−1, has a half life period of 2.5 hours. For the same reaction with initial concentration `("x"/2)` mol L−1 the half life is
For a first-order reaction, the rate constant is 6.909 min−1 the time taken for 75% conversion in minutes is
The rate constant of a reaction is 5.8 × 10−2 s−1. The order of the reaction is ____________.
Describe the graphical representation of first order reaction.
The integrated rate law is a direct relationship between ____________ and ____________.
How long would it take to electroplate a spoon with 0.1 mol of silver (108 g/mol) at a constant current of 2.0 A using AgNO3?
A first order reaction is 25% completed in 40 minutes. What is the rate constant k tor the reaction?
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 ____________.
What is the order of reaction if the unit of rate constant (k) is mol dm−3 s−1?
A first order reaction is 75% completed in 60 minutes, the time required for it's 50% completion is ____________.
The initial concentration of reactant (A) is 2 mol dm−3 for a zero order reaction \[\ce{A -> B}\]. The rate constant (k) is related to its half-life `("t"_(1//2))` by the equation:
A first order reaction takes 40 minutes for 30% decomposition. What is the half-life of reaction?
For the first order reaction A → B, the rate constant is 0.25 s-1, if the concentration of A is reduced to half, the value of rate constant will be ________.
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?
The integrated rate law is a direct relationship between time and ______
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:
Consider the following reaction.
\[\ce{SO2(g) + 1/2 O2(g) <=>[K1] SO3(g)}\]
\[\ce{2SO3(g)<=>[K2] 2SO2(g) + O2(g)}\]
What is the relation between K1 and K2?
A radioactive isotope decayed to 17/32 of its original mass after 60 minutes. Find the half-life of this radioisotope.
A first order reaction takes 10 minute for 30% completion. Find rate constant of the reaction.
For a first order reaction, the plot of log k against 1/T is a straight line. The slope of the line is equal to ______.
