calculate the half-life of a first- order reaction if the concentration of the reactant is 0.0396 M at 12 seconds after the reaction starts and is 0.00579 M at 47 after the reaction starts. How long does it take for the reactant concentration to decrease to 0.00269 M
I worked this for you below.
To calculate the half-life of a first-order reaction, we can use the formula:
t₁/₂ = (ln 2) / k
where t₁/₂ is the half-life and k is the rate constant of the reaction.
In this case, we are given the concentrations of the reactant at different points in time. We can use this information to determine the rate constant (k) and then calculate the half-life.
First, let's find the rate constant (k):
ln (0.0396 M / 0.00579 M) = -k * (47 seconds - 12 seconds)
Simplifying this equation:
ln (6.831) = -k * 35 seconds
Now, let's solve for the rate constant (k):
k = -ln (6.831) / 35 seconds
Next, we can use the rate constant to calculate the half-life (t₁/₂):
t₁/₂ = (ln 2) / k
Substituting the value of k:
t₁/₂ = (ln 2) / (-ln (6.831) / 35 seconds)
Finally, we can calculate the time it takes for the reactant concentration to decrease to 0.00269 M by rearranging the equation for the half-life:
t = t₁/₂ * ln (Co / Cf)
where t is the time it takes, Co is the initial concentration (0.0396 M), and Cf is the final concentration (0.00269 M).
Substituting the values:
t = t₁/₂ * ln (0.0396 M / 0.00269 M)
Now, you can calculate the half-life and the time it takes for the reactant concentration to decrease to 0.00269 M using the given data and the equations provided.