Answer : The value of rate constant is, [tex]0.3607s^{-1}[/tex]
Explanation :
The Arrhenius equation is written as:
[tex]K=A\times e^{\frac{-Ea}{RT}}[/tex]
Taking logarithm on both the sides, we get:
[tex]\ln k=-\frac{Ea}{RT}+\ln A[/tex] ............(1)
where,
k = rate constant
Ea = activation energy = 249 kJ/mol = 249000 kJ/mol
T = temperature = 896 K
R = gas constant = 8.314 J/K.mole
A = pre-exponential factor or frequency factor = [tex]1.60\times 10^{14}s^{-1}[/tex]
Now we have to calculate the value of rate constant by putting the given values in equation 1, we get:
[tex]\ln k=-\frac{249000J/mol}{8.314J/K.mol\times 896K}+\ln (1.60\times 10^{14}s^{-1})[/tex]
[tex]\ln k=-1.0198[/tex]
[tex]k=0.3607s^{-1}[/tex]
Therefore, the value of rate constant is, [tex]0.3607s^{-1}[/tex]
Ethyl chloride vapor decomposes by the first-order reaction. Given the activation energy is 249 kJ/mol and the frequency factor is 1.60 × 10¹⁴ s⁻¹, the rate constant at 896 K is 0.4870 s⁻¹.
A first-order reaction is a chemical reaction in which the rate of reaction is directly proportional to the concentration of the reacting substance.
Let's consider the first-order reaction for the decomposition of ethyl chloride.
C₂H₅Cl → C₂H₄ + HCl
The activation energy is 249 kJ/mol and the frequency factor is 1.60 × 10¹⁴ s⁻¹. We can find the value of the rate constant at 896 K using the Arrhenius equation.
[tex]k = A \times e^{-Ea/R \times T} \\\\k = (1.60 \times 10^{14}s^{-1} ) \times e^{-(249 \times 10^{3} J/mol)/(8.314 J/mol.K) \times 896K} = 0.4870 s^{-1}[/tex]
where,
Ethyl chloride vapor decomposes by the first-order reaction. Given the activation energy is 249 kJ/mol and the frequency factor is 1.60 × 10¹⁴ s⁻¹, the rate constant at 896 K is 0.4870 s⁻¹.
Learn more about first-order reactions here: https://brainly.com/question/518682
