Advertisements
Advertisements
प्रश्न
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
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`
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?
In a first-order reaction, the concentration of the reactant decreases from 20 mmol dm−3 to 8 mmol dm−3 in 38 minutes. What is the half-life of reaction?
Solve
A first-order reaction takes 40 minutes for 30% decomposition. Calculate its half-life.
Derive the integrated rate law for the zeroth order reaction.
Rate constant of a reaction is 3.6 × 10–3 s–1. The order of reaction is ______.
For first order reaction, the rate constant for the decomposition of N2O5 is 6 × 10–4 s –1. The half-life period for decomposition in seconds is ______.
The rate of catalysed reaction is large than the uncatalysed reaction as _______.
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?
Describe the graphical representation of first order reaction.
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.
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?
The rate constant of a reaction has same units as the rate of reaction. The reaction is of ____________.
If [A]0 is the initial concentration, then the half life of zero order reaction is ____________.
The integrated rate equation for first-order reaction, A → product, is ______.
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 ____________.
The order of the reaction for which the unit of rate constant is s−1 is ____________.
For first order reaction the slope of the graph of log10 [A]t Vs. time is equal to ____________.
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 ____________.
Which among the following is an example of pseudo first order reaction?
A first order reaction is 50% completed in 16 minutes. The percentage of reactant that will react in 32 minutes 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?
The integrated rate equation is Rt = log C0 – log Ct, then the straight-line graph is obtained by plotting.
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?
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?
Which of the following equations exhibits the integrated rate law equation for first order reaction?
Calculate half life of reaction if rate constant of first order reaction is 0.0178 minute−1.
