Answer:
a. The rate constant = 0.0000030s^-1
b. The half life = 32000secs
Explanation:Please see attachment for explanation
(A) The rate constant for the reaction at 600 K has been [tex]\rm 3.01\;\times\;10^-^6\;s^-^1[/tex]
(B) The half life of the reaction at 320 degree Celsius has been [tex]\rm 3.15\;\times\;10^4\;s[/tex].
Half-life has been given as the time required by the substance to reduce to half of its initial concentration.
(A) The half life of a first order reaction has been given as:
[tex]\rm t\frac{1}{2}=\dfrac{0.693}{k}[/tex]
Where, the half life for the process is given as, [tex]\rm t\frac{1}{2}=2.3\;\times\;10^5\;s[/tex]
Substituting the values for the rate constant (k) of the reaction:
[tex]\rm 2.3\;\times\;10^5\;s=\dfrac{0.693}{k}\\k=\dfrac{0.693}{2.3\;\times\;10^5}\\k=3.01\;\times\;10^-6\;s^-^1[/tex]
The rate constant for the reaction at 600 K has been [tex]\rm 3.01\;\times\;10^-^6\;s^-^1[/tex].
(B) The rate constant (k) for the reaction at 320 degree Celsius has been [tex]\rm 2.2\;\times\;10^-^5\;s^-^1[/tex].
The half life ([tex]\rm t\frac{1}{2}[/tex]) for the reaction has been given by substituting the values as:
[tex]\rm t\frac{1}{2}=\dfrac{0.693}{2.2\;\times\;s^-^1}\\ t\frac{1}{2}=31500\;s\\t\frac{1}{2}=3.15\;\times\;10^4\;s[/tex]
The half life of the reaction at 320 degree Celsius has been [tex]\rm 3.15\;\times\;10^4\;s[/tex]
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