Advertisements
Advertisements
Question
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?
Advertisements
Solution
Given: t1/2 = 3 Hours
Now we know that,
k = `0.693/t_(1//2)`
= `0.693/3`
= 0.231 hr−1
Put the above value in the formula of a first-order reaction.
k = `2.303/8 log [R]_0/([R])`
⇒ 0.231 = `2.303/8 log [R]_0/([R])`
⇒ `log [R]_0/([R]) = (0.231 xx 8)/2.303`
= `1.848/2.303`
⇒ `log [R]_0/([R])` = 0.8024
⇒ `[R]_0/([R])` = antilog 0.8024
= 6.3445
`[R]/([R]_0) = 1/6.3445`
= 0.158
∴ The fraction of the sample of sucrose remaining after 8 hours is 0.158.
RELATED QUESTIONS
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?
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.
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.
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.
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)
A first order reaction is 50% complete in 25 minutes. Calculate the time for 80% completion of the reaction.
Show that the time required for 99.9% completion of a first-order reaction is three times the time required for 90% completion.
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.
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?
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?
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.
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).
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 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 `log ["R"]_0/(["R"])` Vs. time for a first-order reaction is ______.
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 ______.
Write the equation for integrated rate law for a first order reaction.
Show that `t_(1/2)= 0.693/k` for first 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 ______.
