Answer :
Final answer:
In a first-order reaction for a substance with a rate constant of 9.05 × 10⁻⁴ s⁻¹, it approximately takes 8.00 seconds for 23.0% of the substance to decompose.
Explanation:
This question relates to the concept of first-order reactions in chemistry. In a first-order reaction, the rate of decomposition is directly proportional to the concentration of the substance, which decays over time at a rate that can be calculated by the equation t = ln((100% - percentage decomposed%)/100%)/(-k).
In this case, for a substance with a rate constant (k) of 9.05 × 10⁻⁴ s⁻¹ decomposing by 23.0%, we can plug in these values to find the time it takes for this decomposition to occur. This gives us t = ln((100% - 23%)/100)/(-9.05 × 10⁻⁴ s⁻¹) which approximately equals 8.00 seconds.
So, D. 8.00 seconds is the correct answer for how long it takes for 23.0% of the substance to decompose.
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