Respuesta :
Answer:
15.9 KJ/mol
Explanation:
Given data:
Temperature = T1 = 307 K
Temperature = T2 = 343 K
Gas constant R= 8.314 J/(mol • K)
rate constant = k2/K1 = 89
To find:
Activation energy (in kJ/mol) = Ea = ?
Formula:
The Arrhenius equation gives the relation between temperature and reaction rates:
[tex]ln\frac{K2}{K1} = \frac{Ea}{R} (\frac{1}{T1} - \frac{1}{T2})[/tex]
here, in this equation
k = the rate constant
Ea = the activation energy
R = the Universal Gas Constant
T= the temperature
Solution:
[tex]ln\frac{89 K1}{K1} = \frac{Ea}{8.314 J/mol . k\\} (\frac{1}{307 K} - \frac{1}{343 K})[/tex]
ln 89 = Ea / 8.314 J/mol.K x (0.0325 - 0.00291)
ln 89 = Ea / 8.314 J/mol.K x (2.95 x 10^2 )
4.488 = Ea / 8.314 J/mol.K x (2.95 x 10^2)
Ea = 4.488 x (2.95 x 10^2) / 8.314 J/mol.K
= 0.1324 / 8.314
Ea = 0.0159
Ea = 1.59 x 10^2 J/mol
= 15.9 KJ/mol
The least quantity of energy needed by the reactants to start a chemical reaction and result in products is called activation energy.
Activation energy can be given by the Arrhenius equation:
[tex]\text{k} & = \text{Ae} ^{ \dfrac{\text{- Ea}}{\text{RT}} }[/tex]
Where Ea is the activation energy.
The activation energy needed is 15.9 KJ/mol.
This can be calculated by:
Given,
- Temperature (T1) = 307 K
- Temperature (T2) = 343 K
- Gas constant (R) = 8.314 J/(mol • K)
- rate constant = [tex]\frac{\text{K}2}{\text{K}1} = 89[/tex]
To calculate the activation energy (Ea):
[tex]\text{ln} \;\dfrac{\text{K2}}{\text{K1}} & = \dfrac{\text{Ea}}{\text{R}} \;(\dfrac{1}{\text{T}1} \;- \dfrac{1}{\text{T2}})[/tex]
Where, Ea is the activation energy, k is the rate constant, R is the Universal Gas Constant and T is the temperature.
[tex]\text{ln} \;\dfrac{\text{89 K1}}{\text{K1}} & = \dfrac{\text{Ea}}{\text{8.314 J/mol.K }} \;(\dfrac{1}{\text{307 K}} \;- \dfrac{1}{\text{343 K}})[/tex]
[tex]\text{ln} 89 = {\frac {\text{Ea}} { 8.314 \text{J/mol.K}} \times (0.0325 - 0.00291)[/tex]
[tex]\text{ln} 89 = {\frac {\text{Ea}} { 8.314 \text{J/mol.K}} \times (2.95 \times 10^{2} )[/tex]
[tex]4.488= {\frac {\text{Ea}} { 8.314 \text{J/mol.K}} \times (2.95 \times 10^{2} )[/tex]
[tex]\text{Ea} = \dfrac{4.488 \times (2.95 \times 10^{2} )}{ 8.314 \text{J/mol.K}}[/tex]
[tex]= \dfrac{0.1324}{8.314}[/tex]
Ea = 0.0159
Ea = 1.59 x 10² J/mol
Therefore, the required activation energy is 15.9 KJ/mol.
To learn more about activation energy refer to the link:
https://brainly.com/question/16464672
