To calculate the first order rate constant (k), use the formula k = ln([A]₀/[A]t) / t with any two data points, solve for ln([A]₀/[A]t), and then divide by the time interval. An example calculation using the first and last data points gives an estimated k of 0.0001245 s⁻¹.
To calculate the first-order constant (k), we'll use data from a kinetic study where the concentration of a reactant ([A]) is measured at different times (t). For first-order reactions, the relationship between concentration and time is given by the formula:
ln([A]₀/[A]t) = kt
where:
[A]₀ is the initial concentration,
[A]t is the concentration at time t,
k is the first order rate constant, and
t is time.
To find k, we can rearrange the equation to solve for it:
k = ln([A]₀/[A]t) / t
Using the provided data, we can select two points to calculate the rate constant. For simplicity, let's use the initial time and the last time given:
t₁ = 0 s, [A]₁ = 1
t₂ = 10000 s, [A]₂ = 0.803
Now, calculate k:
k = ln([A]₁/[A]₂) / (t₂ - t₁)
k = ln(1/0.803) / (10000 - 0) s
Upon calculation,
k = ln(1.245)/10000 s
k = 0.0001245 s⁻¹
This is the estimated first-order rate constant based on the provided kinetic data.