Respuesta :
Answer : The initial concentration of the ethylene chloride is, 0.219 M
Explanation :
First we have to calculate the rate constant.
The expression used for first order kinetics is:
[tex]K=\frac{1}{t_2-t_1}\times \ln (\frac{[C_2H_5Cl]_{initial}}{[C_2H_5Cl]_{final}})[/tex]
[tex]K=\frac{1}{t_2-t_1}\times (\ln [C_2H_5Cl]_{initial}-\ln [C_2H_5Cl]_{final})[/tex]
Given:
[tex]t_2[/tex] = final time = 2.0 s
[tex]t_1[/tex] = initial time = 1.0 s
[tex]\ln [C_2H_5Cl]_{initial}[/tex] = initial concentration = -1.625 M
[tex]\ln [C_2H_5Cl]_{final}[/tex] = final concentration = -1.735 M
Now put all the given values in the above expression, we get:
[tex]K=\frac{1}{2.0-1.0}\times [(-1.625)-(-1.735)][/tex]
[tex]K=0.11s^{-1}[/tex]
The value of rate constant is, 0.11 s⁻¹
Now we have to calculate the initial concentration of the ethylene chloride.
At t = 1, [tex]\ln [C_2H_5Cl]_{final}[/tex] = -1.625 M
At t = 0, [tex]\ln [C_2H_5Cl]_{initial}[/tex] = ?
[tex]K=\frac{1}{t_2-t_1}\times (\ln [C_2H_5Cl]_{initial}-\ln [C_2H_5Cl]_{final})[/tex]
[tex]0.11=\frac{1}{1-0}\times (\ln [C_2H_5Cl]_{initial}-(-1.625)][/tex]
[tex]\ln [C_2H_5Cl]_{initial}=-1.515[/tex]
[tex][C_2H_5Cl]_{initial}=0.219M[/tex]
Thus, the initial concentration of the ethylene chloride is, 0.219 M
