Calculate the initial concentration of a reactant if it took 4.7 minutes for it to reach a final concentration of 0.15m. The rate constants K is 0.0025m/s^-1

Answer 1

To calculate the initial concentration of the reactant, we can use the first-order reaction equation:

ln(Cf/Ci) = -Kt

Where:
- Cf is the final concentration of the reactant (0.15 M)
- Ci is the initial concentration of the reactant (unknown)
- K is the rate constant (0.0025 M/s^-1)
- t is the time taken for the reaction to reach the final concentration (4.7 minutes)

Rearranging the equation to solve for Ci:

ln(Cf/Ci) = -Kt
ln(Ci/Cf) = Kt
Ci/Cf = e^(Kt)
Ci = Cf * e^(Kt)

Plugging in the values:

Ci = 0.15 M * e^(0.0025 M/s^-1 * 4.7 min)

First, we need to convert the time from minutes to seconds, as the rate constant is given in M/s:

t = 4.7 min * 60 s/min = 282 s

Ci = 0.15 M * e^(0.0025 M/s^-1 * 282 s)

Now we can calculate the initial concentration of the reactant by plugging in the values:

Ci = 0.15 M * e^(0.0025 M/s^-1 * 282 s)
Ci = 0.15 M * e^(0.705 M)
Ci ≈ 0.15 M * 2.027
Ci ≈ 0.305 M

Therefore, the initial concentration of the reactant is approximately 0.305 M.