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
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.
To calculate the initial concentration of a reactant, you need to use the first-order reaction rate equation:
ln(Ct/C0) = -Kt
Where:
Ct = final concentration = 0.15 M
C0 = initial concentration (unknown)
K = rate constant = 0.0025 s^-1
t = time = 4.7 minutes = 4.7 * 60 s = 282 s
Rearranging the equation, we have:
ln(C0/Ct) = Kt
Substituting the values into the equation, we get:
ln(C0/0.15) = 0.0025 * 282
Now, solve for C0:
ln(C0/0.15) = 0.705
C0/0.15 = e^(0.705)
C0 = 0.15 * e^(0.705)
Using a calculator, you can find that C0 is approximately 0.383 M (rounded to three decimal places).
Therefore, the initial concentration of the reactant is approximately 0.383 M.
To calculate the initial concentration of a reactant, we can use the first-order reaction rate equation:
ln(Cf/Ci) = -kt
Where:
- Cf is the final concentration of the reactant (0.15 M in this case),
- Ci is the initial concentration of the reactant (what we're trying to find),
- k is the rate constant (0.0025 s^-1 in this case),
- t is the time it took for the reactant to reach the final concentration (4.7 minutes or 280 seconds in this case).
Rearranging the equation, we get:
Ci = Cf * e^(kt)
Now we can calculate the initial concentration Ci:
Ci = 0.15 M * e^(-0.0025 s^-1 * 280 s)
Ci = 0.15 M * e^(-0.7)
Ci ≈ 0.15 M * 0.4966
Ci ≈ 0.0745 M
Therefore, the initial concentration of the reactant is approximately 0.0745 M.