Advertisements
Advertisements
Question
Which of the following correctly represents integrated rate law equation for a first order reaction in a gas phase?
Options
k = `2.303/t xx log_10 P_i/(P_i - P)`
k = `2.303/t xx log_10 P_i/(2P_i - P)`
k = `2.303/t xx log_10 (2P_i)/(P_i - P)`
k = `2.303/t xx log_10 (P_i - P)/(2P_i)`
Advertisements
Solution
`bb(k = 2.303/t xx log_10 P_i/(2P_i - P))`
Explanation:
For the gas phase reaction,
\[\ce{A(g) -> B(g) + C(g)}\]
Let initial pressure of A be Pi that decreases by x within time t.
Pressure of reactant A at time t
PA = Pi – x .....(i)
The pressures of products B and C at time t are
PB = PC = x
The total pressure at time t is then
P = Pi – x + x + x
= Pi + x
Hence, x = P – Pi ........(ii)
Pressure of A, PA at time t is obtained by substitution of equation (ii) into the (i) equation. Thus
PA = Pi – (P – Pi)
= Pi – P + Pi
= 2Pi – P
The integrated rate law turns out to be
k = `2.303/t log_10 [A]_0/[A]_t`
The concentration is now expressed in terms of pressures.
Thus, [A]0 = Pi and [A]t = PA = 2Pi – P
Substitution gives in above
k = `2.303/t log_10 P_i/(2P_i - P)` .....(iii)
P is the total pressure of the reaction mixture at time t.
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.
Answer the following in brief.
Derive the integrated rate law for the first-order reaction.
The rate of catalysed reaction is large than the uncatalysed reaction as _______.
Write order of the following reaction:
\[\ce{2NH_{3(g)} -> N_{2(g)} + 3H_{2(g)}}\]
Explain pseudo first order reaction with a suitable example.
Explain with the help of a potential energy diagram that the catalyst increases the rate of the reaction.
The decomposition of phosphine (PH3) on tungsten at low pressure is a first-order reaction. It is because the
In a first order reaction \[\ce{x -> y}\]; if k is the rate constant and the initial concentration of the reactant x is 0.1 M, then, the half life is
The rate constant of a reaction is 5.8 × 10−2 s−1. The order of the reaction is ____________.
Write the rate law for the following reaction.
A reaction that is second order in NO and first order in Br2.
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?
What is the value of rate constant of first order reaction, if it takes 15 minutes for consumption of 20% of reactants?
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 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 ______.
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 ____________.
For a zero order reaction, the plot of [A]t vs t is linear. The slope of the line is equal to ____________.
The half-life of a first order reaction is 6.0 hour. How long will it take for the concentration of reactant to decrease from 0.4 M to 0.12 M?
A first order reaction takes 40 minutes for 30% decomposition. What is the half-life of reaction?
A first order reaction, A → B takes 100 minutes for it's 90% completion. What is the rate constant of reaction?
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?
For zero order reaction, when [A]t is plotted against time (t), the slope of the straight line obtained is equal to ______.
Define the half-life of a first-order reaction.
Half-life of a first order reaction is 30 minutes and initial concentration of reactant is 0.1 M.
What is half-life of the reaction if initial concentration of reactant is doubled?
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?
What are integrated rate laws?
