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.
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
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 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 hydrolysis of ester 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.
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?
A first order reaction is 50% complete in 25 minutes. Calculate the time for 80% completion of the reaction.
Straight line graph for first order reaction is obtained between ____________.
A first order reaction is 50% completed in 1.26 × 1014 s. How much time would it take for 100% completion?
Which of the following graphs is correct for a first order reaction?
State a condition under which a bimolecular reaction is kinetically first order reaction.
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?
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.
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-
Observe the graph shown in figure and answer the following questions:
- What is the order of the reaction?
- What is the slope of the curve?
- Write the relationship between k and t1/2 (half life period).
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 ______.
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?
Define first-order reaction.
The following data were obtained during the decomposition of SO2Cl2 at the constant volume. SO2Cl2 →SO2(g) + Cl2(g)
| Time (s) | Total Pressure (bar) |
| 0 | 0.5 |
| 100 | 0.6 |
Calculate the rate constant of the 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.
Write the unit of rate constant [k] for the first order reaction.
