The rate constant for a zero-order reaction is 0.54 M/s. What is the half-life of this reaction if the initial concentration is 0.49 M?

Question

BlackTom AI · Accepted Answer

The problem asks for the half-life of a zero-order reaction given k = 0.54 M/s and [A]0 = 0.49 M. For a zero-order process, the half-life is t1/2 = [A]0 / (2k).

Option 1: 0.45 s. If we compute t1/2 = 0.49 / (2 × 0.54) = 0.49 / 1.08 ≈ 0.4537 s, which rounds to 0.45 s. This value closely matches the calculated result, so it is consistent with the zero-order half-life formula.

Option 2: 2.6 s. This is far larger than the calculated 0.454 s, indicating a misunderstanding of the k value or an incorrect formula. It would imply a much slower decay than the given rate constant would produce.

Option 3: 0.90 s. While closer than option 2, 0.90 s corresponds to a calculation using a different multiplier or a higher concentration value; it does not fit t1/2 = [A]0/(2k) with the provided numbers.

Option 4: 0.11 s. This is about a quarter of the correct half-life and would result from using an erroneously large denominator or misapplying the factor of 2. It deviates significantly from the proper expression.

Option 5: 1.1 s. This is roughly double the correct value and suggests either forgetting the factor of 2 in the denominator or using an incorrect k value in the calculation.

To distinguish correctly among the choices, apply the zero-order half-life formula t1/2 = [A]0/(2k) and substitute the given numbers: t1/2 = 0.49/(2 × 0.54) ≈ 0.4537 s, which aligns with the first option when rounded. The other options arise from applying the formula incorrectly or mixing up units or factors, leading to results that are either too large or too small relative to the proper calculation.

The rate constant for a zero-order reaction is 0.54 M/s. What is the half-life of this reaction if the initial concentration is 0.49 M?单项选择题

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