Derive the realtion between rate constant and half life peruod of zero order reaction
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Answer : The relation between the rate constant and the half life of zero order reaction is, Solution: Zero order reaction are those in which the rate is independent on the concentration of the reactant. It is directly proportional to the rate constant.
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Secondary SchoolChemistry 5+3 pts
Derive the relation between rate constant and half life period of zero order reaction?
Report by Devinandanatr 07.10.2018
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MohammdIInzy · Ambitious
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BarrettArcher Ambitious
Answer : The relation between the rate constant and the half life of zero order reaction is,
t_{1/2}=\frac{[A]_0}{2K}
Solution:
Zero order reaction are those in which the rate is independent on the concentration of the reactant. It is directly proportional to the rate constant.
For a reaction,
A → products
Rate expression for zero order reaction,
Rate = -\frac{d[A]}{dt}=K[A]^0 = K = constant
By rearranging the terms,
d[A] = - K dt ..........(1)
Integrating equation (1), we get
\int_{[A]_0}^{[A]}d[A]=\int_{0}^{t}-Kdt
At t = 0, the concentration of reactant [A] = [A]_0 which is the initial concentration.
[A]=[A]_0-Kt ........(2)
Half life of the reaction : It is the time required to reduce the concentration of the reactant to half of its initial value. It is represented by t_{1/2}.
Now, for half life reaction, the concentration of reactant become half.
[A]=\frac{1}{2}[A]_0 and t=t_{1/2}
By Using these conditions in equation (2), we get the relation between half life and the rate constant.
\frac{1}{2} [A]=[A]_0-Kt_{1/2}
t_{1/2}=\frac{[A]_0}{2K}
The relation between the rate constant and the half life of zero order reaction is,
t_{1/2}=\frac{[A]_0}{2K}