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Explanation of Zero-Order Reaction and Half-Life
Zero-Order Reaction
In a zero-order reaction, the rate of the reaction is independent of the concentration of reactants. This means that the rate of the reaction remains constant over time, even as the concentration of reactants decreases. The rate law for a zero-order reaction is:
Rate = k
where k is the rate constant.
Half-Life
The half-life of a reaction is the amount of time it takes for the concentration of a reactant to decrease to half of its initial value. The half-life of a zero-order reaction can be calculated using the following equation:
t1/2 = [A]0 / 2k
where t1/2 is the half-life, [A]0 is the initial concentration of reactant A, and k is the rate constant.
Time Taken for Concentration to Reduce to One Fourth
If the half-life of a reaction is 50 minutes, then we can calculate the rate constant k using the equation:
k = 0.693 / t1/2 = 0.693 / 50 = 0.01386 min-1
Now we can use the rate law for a zero-order reaction to calculate the concentration of A at any given time:
[A] = [A]0 - kt
If we want to know the time it takes for the concentration of A to reduce to one fourth of its initial value, we can substitute the appropriate values into this equation:
[A] = [A]0/4 = [A]0 - kt
Solving for t, we get:
t = ([A]0 - [A]0/4) / k = 3/4([A]0) / k = 3/4(50 min) = 37.5 min
Therefore, it takes 37.5 minutes for the concentration of A to reduce to one fourth of its initial value.