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 brief.
Obtain the relationship between the rate constant and half-life of a first-order reaction.
How will you represent first order reactions graphically.
Solve
A first-order reaction takes 40 minutes for 30% decomposition. Calculate its half-life.
Answer the following in brief.
What are the units of the rate constant?
Derive the integrated rate law for the zeroth order reaction.
Write order of the following reaction:
\[\ce{2NH_{3(g)} -> N_{2(g)} + 3H_{2(g)}}\]
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?
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
The decomposition of phosphine (PH3) on tungsten at low pressure is a first-order reaction. It is because the
The rate constant of a reaction is 5.8 × 10−2 s−1. The order of the reaction is ____________.
Identify the order for the following reaction.
Radioactive disintegration of 92U238
A zero order reaction is 20% complete in 20 minutes. Calculate the value of the rate constant. In what time will the reaction be 80% complete?
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.
The integrated rate law is a direct relationship between ____________ and ____________.
The following reactions follow zero order kinetics, EXCEPT ____________.
A first order reaction has rate constant 1 × 10−2 s−1. What time will, it take for 20 g or reactant to reduce to 5 g?
A first order reaction completes its 10% in 20 minutes, then the time required to complete its 19% is ____________.
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 ______.
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 ____________.
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 ____________.
What is the unit of rate constant for the zero order reaction?
The integrated rate equation is Rt = log C0 – log Ct, then the straight-line graph is obtained by plotting.
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 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?
Calculate half life of reaction if rate constant of first order reaction is 0.0178 minute−1.
If the half-life of a first-order reaction is 10 minutes, find the time required to decrease the concentration of the reactant from 0.08 M to 0.02 M.
