particular reactant decomposes with a half?life of 147 s when its initial concentration is 0.294 m. the same reactant decomposes with a half?life of 215 s when its initial concentration is 0.201 m.

Answer:

The first reactant takes approximately 147 seconds to reach half its initial concentration, while the second reactant takes approximately 214.5 seconds for the same reduction, based on their half-lives and initial concentrations.

Step-by-step explanation:

The rate constant (k) for a first-order reaction can be calculated using the formula:

k = (0.693) / t_half

For the first set of data:

k₁ = (0.693) / 147 s ≈ 0.00472 s⁻¹

For the second set of data:

k₂ = (0.693) / 215 s ≈ 0.00322 s⁻¹

Now, you can use these rate constants to calculate the time it takes for each reactant to reach a certain concentration. For example, if you want to find the time it takes for the first reactant (initial concentration = 0.294 M) to reduce to 0.147 M (half its initial concentration), you can use the following equation for a first-order reaction:

ln(C_t / C₀) = -kt

Where:

C_t = concentration at time t

C₀ = initial concentration

k = rate constant

t = time

For the first reactant:

ln(0.147 / 0.294) = -0.00472t

Solving for t:

t ≈ 147 seconds

For the second reactant (initial concentration = 0.201 M) to reduce to 0.1005 M (half its initial concentration):

ln(0.1005 / 0.201) = -0.00322t

Solving for t:

t ≈ 214.5 seconds

So, it takes approximately 147 seconds for the first reactant to reach half its initial concentration, and approximately 214.5 seconds for the second reactant to do the same, based on their respective half-lives and initial concentrations.