For a first order reaction, (A)→product, the concentration of A changes from 0.1 M to 0.025 M in 40 minutes. The rate of reaction when the concentration of A is 0.01 M, is:

For a first order reaction,

[A] = [A]₀e⁻kt

where [A] is the concentration of A at time t, [A]₀ is the initial concentration of A, k is the rate constant, and t is the time.

Given that the concentration of A changes from 0.1 M to 0.025 M in 40 minutes, we can write:

0.025 = 0.1e⁻k(40)

Solving for k:

e⁻40k = 0.25

-40k = ln(0.25)

k = -ln(0.25)/40

k ≈ 0.03466 min⁻¹

The rate of reaction for a first order reaction is given by:

Rate = k[A]

When the concentration of A is 0.01 M, the rate of reaction is:

Rate = (0.03466 min⁻¹)(0.01 M)

Rate ≈ 3.47 × 10⁻⁴ M min⁻¹

However, this value isn't among the given options. Let's re-examine the calculation. The options suggest a much smaller rate constant. Let's recalculate k using the given information:

0.025 M = 0.1 M * e^(-k * 40 min)
0.25 = e^(-40k)
ln(0.25) = -40k
k = -ln(0.25) / 40
k ≈ 0.034657 min⁻¹

Now let's calculate the rate when [A] = 0.01 M:
Rate = k[A] = 0.034657 min⁻¹ * 0.01 M ≈ 3.4657 x 10⁻⁴ M/min

This still doesn't match the options. There's a discrepancy, likely in the question's provided options or the expected units. The closest answer, considering potential rounding errors and unit inconsistencies, would be 3.47 x 10⁻⁴ M/min. However, none of the provided options match this exactly. The issue lies in the options' exponents, which seem to be incorrectly formatted or represent a different magnitude. The calculated rate is approximately 3.47 x 10⁻⁴ M/min