Respuesta :
Explanation:
(a) The given data is as follows.
Frequency factor A = [tex]1.60 \times 10^{14} s^{-1}[/tex]
Activation energy ([tex]E_{a}[/tex]) = 249 kJ/mol
Gas constant = 8.314 J/mol K
Temperature (T) = 876 K
Hence, calculate the specific rate constant as follows.
K = [tex]Ae^{\frac{-E_{a}}{RT}}[/tex]
= [tex]1.60 \times 10^{14} s^{-1} e^{\frac{249000 J/mol}{8.314 J/mol K \times 876 K}}[/tex]
= [tex]1.60 \times 10^{14} s^{-1} \times 1.034[/tex]
= [tex]1.128 \times 10^{29}[/tex]
Hence, the value of specific rate constant K is [tex]1.6544 \times 10^{14}[/tex].
(b) It is given that time is 20 minutes. As there are 60 seconds present in 1 min. Therefore, seconds present in 20 minutes are as follows.
[tex]20 min \times \frac{60 sec}{1 min}[/tex]
= 1200 sec
Hence, for the first order reaction the fraction remaining is as follows.
[tex]\frac{C}{C_{o}} = e^{-kt}[/tex]
= [tex]e^{-1.6544 \times 10^{14} \times 1200 sec}[/tex]
= 0
Hence, fraction decomposed = 1 - 0 = 1
Therefore, the fraction of the ethyl chloride that decomposes in 20 minutes at this temperature is 1.
The rate constant of the first order reaction is 0.227.
What is a first order reaction?
A first order reaction is that in which the rate of reaction depends on the concentration of one reactant.
Using the Arrhenius equation;
k=A e^-Ea/RT
k = rate constant
A = frequency factor
Ea = activation energy
R = gas constant
T = temperature
k = 1.60 * 10^14e^-249 * 10^3/8.314 * 876
k =0.227
We know that;
N=Noe^-kt
Where;
N = amount ptresent at time t
No = amount initially present
k = rate constant
t = time
N/No =e^-kt
N/No =e^-(0.227 * 20 * 60)
= 0
Learn more about first order reaction: https://brainly.com/question/26463975?
