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
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 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?
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?
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).
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 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)
The slope in the plot of ln[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?
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.
The rate constant for the reaction:
\[\ce{2N2O_{(s)} ->2N2O4_{(g)}}\] is 4.98 × 10-4 s-1.
The order of the reaction is ______.
Write the equation for integrated rate law for a first order reaction.
Write the unit of rate constant [k] for the first order reaction.
