Advertisements
Advertisements
Question
Solve
The energy of activation for a first-order reaction is 104 kJ/mol. The rate constant at 25°C is 3.7 × 10–5 s –1. What is the rate constant at 30°C? (R = 8.314 J/K mol)
Advertisements
Solution
Given:
Activation energy (Ea) = 104 kJ mol-1 = 104 × 103 J mol-1
Rate constant (k1) = `3.7 xx 10^-5 "s"^-1`
Temperatures; T1 = 25 + 273 = 298 K, T2 = 30 + 273 = 303 K
R = 8.314 J K-1 mol-1
To find:
Rate constant (k2) at 30°C
Formula:
`"log"_10 "k"_2/"k"_1 = "E"_"a"/(2.303"R") (("T"_2 - "T"_1)/("T"_2"T"_1))`
Calculation:
`"log"_10 "k"_2/(3.7 xx 10^-5 "s"^-1) = (104 xx 10^3 "J" "mol"^-1)/(2.303 xx 8.314 "J" "K"^-1 "mol"^-1) ((303 "K" - 298 "K")/(303 "K" xx 298 "K"))`
∴ `"log"_10 "k"_2/(3.7 xx 10^-5 "s"^-1) = 104000/(2.303 xx 8.314) xx 5/(303 xx 298)`
∴ `"log"_10 "k"_2/(3.7 xx 10^-5 "s"^-1) = 0.301`
∴ `"k"_2/(3.7 xx 10^-5 "s"^-1)` = antilog(0.301) = 2.00
k2 = `2.00 xx 3.7 xx 10^-5 "s"^-1 = 7.4 xx 10^-5 "s"^-1`
The rate constant of the reaction is `7.4 xx 10^-5 "s"^-1`.
APPEARS IN
RELATED QUESTIONS
Answer the following in one or two sentences.
Write the Arrhenius equation and explain the terms involved in it.
Explain with the help of the Arrhenius equation, how do the rate of reaction changes with temperature.
Answer the following in brief.
How will you determine activation energy graphically using the Arrhenius equation?
The rate constant of a reaction at 500°C is 1.6 × 103 M−1 s−1. What is the frequency factor of the reaction if its activation energy is 56 kJ/mol?
Solve
What fraction of molecules in a gas at 300 K collide with an energy equal to the activation energy of 50 kJ/mol?
How will you determine activation energy from rate constants at two different temperatures?
Explain with the help of the Arrhenius equation, how do the rate of reaction changes with activation energy.
A catalyst lowers the activation energy of a certain reaction from 83.314 to 75 kJ mol−1 at 500 K. What will be the rate of reaction as compared to uncatalysed reaction? Assume other things are equal.
Slope of the straight line obtained by plotting log10k against represents what term?
Explain with the help of Arrhenius equation, how does the rate of reaction changes with temperature.
Explain, with the help of the Arrhenius equation, how does the rate of reaction changes with temperature.
Explain with the help of Arrhenius equation, how does the rate of reaction changes with temperature.
Explain with the help of the Arrhenius equation, how do the rate of reaction changes with activation energy.
Explain with the help of Arrhenius equation, how does the rate of reaction changes with temperature.
Explain with the help of Arrhenius equation, how does the rate of reaction changes with activation energy.
Explain with the help of Arrhenius equation, how does the rate of reaction changes with temperature.
Explain with the help of Arrhenius equation, how does the rate of reaction changes with activation energy.
Explain with the help of Arrhenius equation, how does the rate of reaction changes with temperature.
Explain with the help of Arrhenius equation, how does the rate of reaction changes with activation energy.
