Respuesta :
Answer:
A) 577.6 years
B) 1580.9 years
Explanation:
You can know the order of a reaction given the units of the rate constant:
- For a 0 order reaction are M/s=(mol/L*s)
- For a 1 order reaction are 1/s
- For a 2 order reaction are 1/M*s=(L/mol*s)
Then we know that this is a first order reaction because years is a unit of time as well as seconds. The half life of a first order reaction is given by:
[tex]t_{1/2}=\frac{ln(2)}{k}[/tex]
Here you can solve for the half life:
[tex]t_{1/2}=\frac{ln(2)}{0.0012 years^-1}=577.6 years[/tex]
Now for the rate law for a first order reaction is:
[tex][A]=[A_{o} ]*e^{-kt}[/tex]
Then, if you want to know how long does it take to reach a certain value you solve for time:
[tex]t=-ln([A]/[A]_{o}) *1/k[/tex]
The 15% of its original value is [tex]0.15*[A_{o}][/tex]
You solve for time:
[tex]t=-ln(0.15) *1/0.0012 years^-1=1580.9 years[/tex]
Hope it helps!
In the Decomposition reaction, a reactant gets split into two or more products. The half-life of the reaction is 577.6 years and the time taken to reach 15% of the original is 1580.9 years.
What is half-life?
Half-life is the time taken by the radioactive isotope to decay one-half of its total amount.
From the units of the rate of the reaction, the order can be estimated as, for a first-order reaction unit is 1/s.
The half-life of the reaction can be given as,
[tex]\rm t\dfrac{1}{2} = \dfrac{\rm ln (2)}{k}[/tex]
The rate constant (k) for the decomposition reaction is 0.0012 per year.
Substituting values in the above equation:
[tex]\begin{aligned} \rm t\dfrac{1}{2} &= \dfrac{\rm ln (2)}{0.0012}\\\\&= 577.6\;\rm years\end{aligned}[/tex]
The rate law of the first-order reaction is given as,
[tex]\begin{aligned}\rm [A] = [A_{o}] \times e^{-kt}\\\\\rm t = -ln ([A][A_{o}]) \times \dfrac{1}{k}\end{aligned}[/tex]
Solving for time (t):
[tex]\begin{aligned}\rm t &= \rm -ln (0.15) \times \dfrac{1}{0.0012}\\\\& = 1580.9\;\rm years\end{aligned}[/tex]
Therefore, the half-life is 577.6 years and the time taken is 1580.9 years.
Learn more about half-life here:
https://brainly.com/question/18802932
