Respuesta :
Answer:
66.5 min does it take for 82.3% of the compound to decompose.
Explanation:
Using integrated rate law for first order kinetics as:
[tex][A_t]=[A_0]e^{-kt}[/tex]
Where,
[tex][A_t][/tex] is the concentration at time t
[tex][A_0][/tex] is the initial concentration
Given:
25.5 % is decomposed which means that 0.255 of [tex][A_0][/tex] is decomposed. So,
[tex]\frac {[A_t]}{[A_0]}[/tex] = 1 - 0.255 = 0.745
t = 11.3 min
[tex]\frac {[A_t]}{[A_0]}=e^{-k\times t}[/tex]
[tex]0.745=e^{-k\times 11.3}[/tex]
k = 0.02605 min⁻¹
Also,
Given:
82.3 % is decomposed which means that 0.823 of [tex][A_0][/tex] is decomposed. So,
[tex]\frac {[A_t]}{[A_0]}[/tex] = 1 - 0.823 = 0.177
t = ?
[tex]\frac {[A_t]}{[A_0]}=e^{-k\times t}[/tex]
[tex]0.177=e^{-0.02605\times t}[/tex]
t = 66.5 min
66.5 min does it take for 82.3% of the compound to decompose.
66.5 min will take 82.3% of the compound to decompose.
What is the first-order reaction?
The first-order reaction rate depends on the concentration of one reactant.
By the first-order integrated rate law
[tex]\rm [At]= [A_0]e^-^k^t[/tex]
where [tex]\rm [A_0][/tex] is the initial concentration
[tex]\rm [At][/tex] is the concentration at time t
25.5% of a compound decomposes in 11.3 min.
So [tex]\rm [A_0][/tex] is 0.255
[tex]\rm \dfrac{[At]}{[A_0]} = 1- 0.255 = 0.745[/tex]
Time is 11.3 min.
[tex]\rm \dfrac{[At]}{[A_0]} =e^-^k^t\\\\\\\rm 0.745 =e^-^k^ \times^1^1^.^3\\\\k = 0.02605\; min^-^1[/tex]
82.3% of the compound to decompose
k =0.02605
t=?
[tex]\rm \dfrac{[At]}{[A_0]} = 1 - 0.823 = 0.177\\\\\rm \dfrac{[At]}{[A_0]} =e^-^k^t\\\\\\\rm 0.177 =e^-^0^.^0^2^6^0^5^ \times^t\\\\t = 66.5\; min^-^1[/tex]
Thus, 66.5 min will take 82.3% of the compound to decompose.
Learn more about first-order reaction, here:
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