Respuesta :
Answer : The activation energy for the reaction is, [tex]8.39\times 10^4J[/tex]
Explanation :
According to the Arrhenius equation,
[tex]K=A\times e^{\frac{-Ea}{RT}}[/tex]
Taking logarithm on both side, we get:
[tex]\ln K=\frac{-Ea}{RT}+\ln A[/tex]
where,
[tex]Ea[/tex] = activation energy for the reaction
R = gas constant = 8.314 J/mole.K
T = temperature
K = rate constant
A = pre-exponential factor
The linear equation expression is:
y = mx + c
Plot of ln (K) versus (1/T) gives a straight line with a slope is equal to, [tex]\frac{-Ea}{R}[/tex]
As we are given that:
Slope = [tex]-1.01\times 10^4K[/tex]
So,
[tex]Slope=\frac{-Ea}{R}=-1.01\times 10^4K[/tex]
[tex]-Ea=-1.01\times 10^4K\times R[/tex]
[tex]Ea=1.01\times 10^4K\times 8.314J/mol.K[/tex]
[tex]Ea=83971.4J=8.39\times 10^4J[/tex]
Thus, the activation energy for the reaction is, [tex]8.39\times 10^4J[/tex]
