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If the initial concentration of NO2(g) is 0.050 M, what is the half-life of the reaction at 300°C given that the rate constant k is 0.54 M⁻¹s⁻¹?
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15. Chemical Kinetics
Half-Life
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In a first-order reaction, what fraction of the original reactant has been consumed after 4 half-lives?
A
7/8
B
1/4
C
1/8
D
15/16
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Recall that for a first-order reaction, the amount of reactant remaining after a certain number of half-lives is given by the formula: \(\left( \frac{1}{2} \right)^n\), where \(n\) is the number of half-lives elapsed.
Identify the number of half-lives given in the problem, which is 4 in this case.
Calculate the fraction of the reactant remaining after 4 half-lives using the formula: \(\left( \frac{1}{2} \right)^4\).
Determine the fraction of the reactant that has been consumed by subtracting the remaining fraction from 1: \(1 - \left( \frac{1}{2} \right)^4\).
Simplify the expression to find the fraction consumed, which corresponds to the answer.
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