Advertisements
Advertisements
Question
Derive an integrated rate law expression for first order reaction: A → B + C
Advertisements
Solution
Consider first order reaction, A → B + C
The differential rate law is given by
rate = −`("d"["A"])/"dt"` = k[A] .....(1)
where, [A] is the concentration of reactant at time t.
Rearranging Eq. (1)
`("d"["A"])/(["A"])` = - k dt ....(2)
Let [A]0 be the initial concentration of the reactant A at time t = 0.
Suppose [A]t is the concentration of A at time = t
The equation (2) is integrated between limits [A] = [A]0 at t = 0 and [A] = [A]t at t = t
`int_(["A"]_0)^(["A"]_"t") ("d"["A"])/(["A"]) = - "k" int_0^"t"`dt
On integration,
`["ln"["A"]]_(["A"]_0)^(["A"]_"t") = - "k" ("t")_0^"t"`
Substitution of limits gives
ln[A]t − ln[A]0 = –kt
or ln `["A"]_"t"/["A"]_0` = - kt ....(3)
or k = `1/"t"` ln `["A"]_0/["A"]_"t"`
Converting ln to log10, we write
k = `2.303/"t" log_10 ["A"]_0/["A"]_"t"` ....(4)
Eq. (4) gives the integrated rate law for the first order reactions.
APPEARS IN
RELATED QUESTIONS
Answer the following in one or two sentences.
Write the relationships between rate constant and half-life of the first order and zeroth-order reactions.
What are pseudo-first-order reactions?
Solve
A first-order reaction takes 40 minutes for 30% decomposition. Calculate its half-life.
The decomposition of phosphine (PH3) on tungsten at low pressure is a first-order reaction. It is because the
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 ____________.
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 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?
The time of completion of 90% of a first order reaction is approximately ____________.
Which among the following reaction is an example of a zero order reaction?
The rate constant of a reaction has same units as the rate of reaction. The reaction is of ____________.
For the first order reaction, plot of log10 [A]t against time 't' is a straight line with a negative slope equal to ____________.
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:
For a first order reaction, \[\ce{A -> B}\], if [A] = 1 M and rate is 4 × 10−2 M s−1. What is the rate constant of the reaction?
Which among the following is an example of pseudo first order reaction?
0.0210 M solution of N2O5 is allowed to decompose at 43°C. How long will it take to reduce to 0.0150 M?
(Given k = 6.0 × 10−4 sec−1)
Half-life of first order reaction is 20 minutes. What is the time taken to reduce the initial concentration of the reactant to `1/10`th?
What is the unit of rate constant for the zero order reaction?
For zero order reaction, when [A]t is plotted against time (t), the slope of the straight line obtained is equal to ______.
The rate constant and half-life of a first order reaction are related to each other as ______.
Which among the following reactions is an example of pseudo first order reaction?
A radioactive isotope decayed to 17/32 of its original mass after 60 minutes. Find the half-life of this radioisotope.
Which of the following correctly represents integrated rate law equation for a first order reaction in a gas phase?
A first order reaction takes 10 minute for 30% completion. Find rate constant of the reaction.
The plot that represents the zero order reaction is:
