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.
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.