A first-order reaction has a rate constant of 0.025 s^-1. Calculate the time it takes for the concentration of the reactant to decrease to one-fourth of its initial value.
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A first-order reaction follows the equation:
ln(C/C0) = -kt
Where:
C is the final concentration of the reactant
C0 is the initial concentration of the reactant
k is the rate constant
t is the time
We want to find the time it takes for the concentration of the reactant to decrease to one-fourth of its initial value, which means C = C0/4.
Substituting these values into the equation, we get:
ln(C0/4/C0) = -0.025t
Simplifying, we have:
ln(1/4) = -0.025t
ln(1/4) is equal to -ln(4), so the equation becomes:
-ln(4) = -0.025t
Taking the natural logarithm of both sides:
ln(4) = 0.025t
Dividing both sides by 0.025:
t = ln(4)/0.025
Using a calculator, we find:
t ≈ 27.73 s
Therefore, it takes about 27.73 seconds for the concentration of the reactant to decrease to one-fourth of its initial value.
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