Advertisements
Advertisements
प्रश्न
Show that the time required for 99.9% completion of a first-order reaction is three times the time required for 90% completion.
Advertisements
उत्तर
For a first-order reaction,
`"t" = 2.303/"k" "log"_10 ["A"]_0/["A"]_"t"`
i. Time is taken for 99.9% completion:
Let the time taken for 99.9% completion of the reaction be t99.9%.
Let initial concentration, [A]0 = a
The final concentration, [A]t = a - 99.9% of a
= `"a" - (99.9/100 xx "a") = 0.001 "a"`
t99.9% = `2.303/"k" "log"_10 ["A"]_0/["A"]_"t"`
= `2.303/"k" "log"_10 "a"/(0.001 "a")`
= `2.303/"k" "log"_10 1000` ...(1)
ii. Time is taken for 90% completion:
Let the time taken for 90% completion of the reaction be t90%.
Let initial concentration, [A]0 = a
Then, final concentration, [A]t = a - 90% of a
= a - `(90/100 xx "a") = 0.1 "a"`
t90% = `2.303/"k" "log"_10 ["A"]_0/["A"]_"t" = 2.303/"k" "log"_10 "a"/(0.1 "a")`
= `2.303/"k" "log"_10 10` ...(2)
Dividing (1) by (2), we get
`("t"_99.9%)/("t"_90%) = (2.303/"k" "log"_10 1000)/(2.303/"k" "log"_10 10) = ("log"_10 1000)/("log"_10 10) = 3/1`
∴ `("t"_99.9%)/("t"_90%) = 3`
∴ t99.9% = 3 t90%
Therefore, for a first-order reaction, the time required for 99.9% completion is 3 times that required for 90% completion.
संबंधित प्रश्न
Sucrose decomposes in acid solution into glucose and fructose according to the first order rate law with t1/2 = 3 hours. What fraction of the sample of sucrose remains after 8 hours?
A first order reaction has a rate constant 1.15 × 10−3 s−1. How long will 5 g of this reactant take to reduce to 3 g?
The following data were obtained during the first order thermal decomposition of SO2Cl2 at a constant volume.
\[\ce{SO2Cl2_{(g)} -> SO2_{(g)} + Cl2_{(g)}}\]
| Experiment | Time/s–1 | Total pressure/atm |
| 1 | 0 | 0.5 |
| 2 | 100 | 0.6 |
Calculate the rate of the reaction when total pressure is 0.65 atm.
In a pseudo first order reaction in water, the following results were obtained:
| t/s | 0 | 30 | 60 | 90 |
| [A]/mol L−1 | 0.55 | 0.31 | 0.17 | 0.085 |
Calculate the average rate of reaction between the time interval 30 to 60 seconds.
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.
Following data are obtained for reaction :
N2O5 → 2NO2 + 1/2O2
| t/s | 0 | 300 | 600 |
| [N2O5]/mol L–1 | 1.6 × 10-2 | 0.8 × 10–2 | 0.4 × 10–2 |
1) Show that it follows first order reaction.
2) Calculate the half-life.
(Given log 2 = 0.3010, log 4 = 0.6021)
A first order reaction takes 20 minutes for 25% decomposition. Calculate the time when 75% of the reaction will be completed.
(Given : log = 2 = 0·3010, log 3 = 0·4771, log 4 = 0·6021)
Define order of reaction. How does order of a reaction differ from molecularity for a complex reaction?
State a condition under which a bimolecular reaction is kinetically first order reaction.
In the presence of acid, the initial concentration of cane sugar was reduced from 0.2 M to 0.1 Min 5 hours and to 0.05 Min 10 hours. The reaction must be of?
First order reaction is 50% complete in 1.26 × 1014s. How much time could it take for 100% completion?
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.
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 ______.
Gaseous cyclobutene isomerizes to butadiene in a first order process which has a 'k' value of 3.3 × 10−4 s−1 at 153°C. The time in minutes it takes for the isomerization to proceed 40% to completion at this temperature is ______. (Rounded-off to the nearest integer)
The decomposition of formic acid on gold surface follows first-order kinetics. If the rate constant at 300 K is 1.0 × 10−3 s−1 and the activation energy Ea = 11.488 kJ mol−1, the rate constant at 200 K is ______ × 10−5 s−1. (Round off to the Nearest Integer)
(Given R = 8.314 J mol−1 K−1)
The slope in the plot of ln[R] vs. time for a first order reaction is ______.
The slope in the plot of `log ["R"]_0/(["R"])` Vs. time for a first-order reaction is ______.
How will you represent first order reactions graphically?
What is the rate constant?
Define first-order reaction.
Slove: \[\ce{2NOBr -> 2NO_{2(g)} + Br_{2(g)}}\]
For the above reaction, the rate law is rate = k[NOBr]2. If the rate of reaction is 6.5 × 10−6 mol L−1 s−1 at 2 × 10−3 mol L−1 concentration of NOBr, calculate the rate constant k for the reaction.
The rate constant for the reaction:
\[\ce{2N2O_{(s)} ->2N2O4_{(g)}}\] is 4.98 × 10-4 s-1.
The order of the reaction is ______.
Show that `t_(1/2)= 0.693/k` for first reaction.
Write the unit of rate constant [k] for the first order reaction.
If the half-life (t1/2) for a first order reaction is 1 minute, then the time required for 99.9% completion of the reaction is closest to ______.
