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.
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?
Answer the following in brief.
How will you represent the zeroth-order reaction graphically?
Derive the integrated rate law for the zeroth order reaction.
Write order of the following reaction:
\[\ce{2NH_{3(g)} -> N_{2(g)} + 3H_{2(g)}}\]
Write a mathematical expression for integrated rate law for zero-order reaction.
What is half life of first order reaction if time required to decrease concentration of reactants from 0.8 M to 0.2 M is 12 hours?
Explain with the help of a potential energy diagram that the catalyst increases the rate of the reaction.
Derive an integrated rate law expression for first order reaction: A → B + C
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
Assertion: rate of reaction doubles when the concentration of the reactant is doubles if it is a first-order reaction.
Reason: rate constant also doubles.
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?
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 reaction that is of the first order with respect to reactant A has a rate constant 6 min−1. If we start with [A]0 = 0.5 mol dm−3, when would [A] reach the value 0.05 mol dm−3?
The time of completion of 90% of a first order reaction is approximately ____________.
The activation energy of a reaction is zero. Its rate constant at 280 K is 1.6 × 10-6 s-1, the rate constant at 300 K is ______.
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 ____________.
In a first order reaction, the concentration of the reactant, decreases from 0.8 mol dm−3 to 0.4 mol dm−3 in 15 minutes. The time taken for the concentration to change from 0.1 mol dm−3 to 0.025 mol dm−3 is ____________.
Half-life period of a first order reaction, \[\ce{A -> product}\] is 3.0 hours. What is the value of rate constant?
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 expression to calculate time required for completion of zero order reaction is ______.
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.
The half-life of first order reaction is 1.7 hour. What is its rate constant?
