Advertisements
Advertisements
Question
For the decomposition of azoisopropane to hexane and nitrogen at 543 K, the following data are obtained.
| t (sec) | P(mm of Hg) |
| 0 | 35.0 |
| 360 | 54.0 |
| 720 | 63.0 |
Calculate the rate constant.
Advertisements
Solution
Azoisopropane decomposes according to the following equation:
\[\ce{(CH3)2CHN = NCH(CH3)2_{(g)} -> N2_{(g)} + C6H14_{(g)}}\]
This action is a first-order reaction.
Initial pressure (P0) = 35.0 mm Hg
Decrease in pressure of azoisopropane after time t is P.
Increase in N2 pressure = `P_(N_2)`
Increase in the pressure of hexane = `P_(C_6H_14)`
Total pressure of the mixture (Pt) = `P_A + P_(N_2) + P_(C_6H_14)`
Pt = (P0 – P) + P + P
Pt = P0 + P
P = Pt – P0
PA = P0 – (Pt – P0) = 2P0 – Pt
But PA ∝ a − x and P0 ∝ Pt
k = `2.303/t log P_0/(2P_0 - P_t)`
When t = 360 s,
k = `2.303/360 log 35/(2 xx 35 - 54)`
= `2.303/360 log 35/16`
= `2.303/360 log 2.1875`
= `2.303/360 xx 0.339`
k = 2.17 × 10–3 s–1
When, t = 720 s,
k = `2.303/720 log 35/(2 xx 35 - 63)`
= `2.303/720 log 35/7`
= `2.303/720 (log 35 - log 7)`
= `2.303/720 (1.544 - 0.845)`
= `2.303/720 xx 0.699`
k = 2.23 × 10–3 s–1
Rate constant = `((2.17 + 2.23))/2 xx 10^-3 s^-1`
= 2.20 × 10–3 s–1
RELATED QUESTIONS
Time required to decompose SO2Cl2 to half of its initial amount is 60 minutes. If the decomposition is a first order reaction, calculate the rate constant of the reaction.
The rate constant for a first order reaction is 60 s−1. How much time will it take to reduce the initial concentration of the reactant to its `1/16`th value?
The time required for 10% completion of a first order reaction at 298 K is equal to that required for its 25% completion at 308 K. If the value of A is 4 × 1010 s−1. Calculate k at 318 K and Ea.
Show that the time required for 99.9% completion of a first-order reaction is three times the time required for 90% completion.
A first order reaction is 50% completed in 1.26 × 1014 s. How much time would it take for 100% completion?
With the help of an example explain what is meant by pseudo first order reaction.
The rate constant of a first order reaction is 6.9 × 10–3s–1. How much time will it take to reduce the initial concentration to its 1/8th value?
A first order reaction is 50% complete in 20 minute What is rate constant?
In the first order reaction, half of the reaction is complete in 100 seconds. The time for 99% of the reaction to occurs will be
The reaction X → product
Follow first order of kinetics. In 40 minutes the concentration of 'X' changes from 0.1 m to 0.025. M. The rate of reaction when concentration of X is 0.01 m is.
Time required to decompose SO2Cl2 to half of its initial concentration is 60 minutes. If the de-composite is a first order reaction, calculated the rate constant of the reaction-
In a first order reaction the concentration of reactants decreases from 400mol L-1 to 25 mol L-1 in 200 seconds. The rate constant for the reaction is ______.
The reaction \[\ce{SO2Cl2(g) -> SO2(g) + Cl2(g)}\] is a first-order gas reaction with k = 2.2 × 10−5 sec−1 at 320°C. The percentage of SO2Cl2 is decomposed on heating this gas for 90 min, is ______%.
For a first order reaction, the ratio of the time for 75% completion of a reaction to the time for 50% completion is ______. (Integer answer)
Radioactive decay follows first-order kinetics. The initial amount of two radioactive elements X and Y is 1 gm each. What will be the ratio of X and Y after two days if their half-lives are 12 hours and 16 hours respectively?
Write the unit of rate constant [k] for the first order reaction.
