Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
t = `2.303/k_1 log [R]_0/(90/100 [R]_0)`
t = `2.303/k_2 log [R]_0/(75/100 [R]_0)`
t = `2.303/k_1 log 10/9`,
t = `2.303/k_2 log 4/3`
`2.303/k_1 log 10/9 = 2.303/k_2 log 4/3`
`=> k_2/k_1 = (log(4/3))/(log(10/9))`
= `log 1.333/log 1.111`
= `0.1249/0.0457`
= 2.733
`log k_2/k_1 = E_a/(2.303 R)((T_2 - T_1)/(T_1 T_2))`
⇒ log 2.733 = `E_a/(2.303 xx 8.314) ((308 - 298)/(298 xx 308))`
Ea = `(2.303 xx 8.314 xx 308 xx 298)/10 xx 0.4367`
= `(19.147 xx 308 xx 298)/10 xx 0.4367`
= 76.75 kJ mol−1
ln k = ln A `- E_a/(RT)`
log k = `log A - E_a/(2.303 RT)`
= `log (4 xx 10^10) - (76.75 xx 1000)/(2.303 xx 8.314 xx 318)`
= `10.6021 - 76750/6088.791`
= 10.6021 − 12.6051
= −2.003
k = Antilog (−2.003) = 9.93 × 10−3
Notes
The answer in the textbook is incorrect.
संबंधित प्रश्न
Sucrose decomposes in acid solution into glucose and fructose according to the first order rate law with `t_(1/2)` = 3 hours. What fraction of the sample of sucrose remains after 8 hours?
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.
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?
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.
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)
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.
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 ______.
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 ______%.
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.
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 ______.
Write the unit of rate constant [k] for the first order reaction.
