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
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?
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.
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 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.
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?
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.
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 ______.
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).
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)
A definite volume of H2O2 undergoing spontaneous decomposition required 22.8 c.c. of standard permanganate solution for titration. After 10 and 20 minutes respectively the volumes of permanganate required were 13.8 and 8.25 c.c. The time required for the decomposition to be half completed is ______ min.
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?
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.
Show that `t_(1/2)= 0.693/k` for first reaction.
Write the unit of rate constant [k] for the first order reaction.
