A first order reaction ABC → AB + C has a rate constant of 0.0125 /s. If the initial concentration of ABC is 0.500 M, what is the concentration of ABC after 5 minutes? Note: do not include units in your answer, do not use scientific notation.
ln(Ao/A) = kt
If you use k as listed than t is 5 min x (60 s/min) = 300 s.
Solve for A
0.012
To solve this problem, we can use the integrated rate law for a first-order reaction, which is:
ln(A/A₀) = -kt
Where:
A₀ is the initial concentration of the reactant (ABC).
A is the concentration of the reactant at a given time.
k is the rate constant.
t is the time.
In this case, we want to find the concentration of ABC after 5 minutes, so we need to solve for A.
Rearranging the integrated rate law equation, we have:
ln(A/A₀) = -kt
Let's plug in the given values:
k = 0.0125 /s
t = 5 minutes = 5 * 60 = 300 seconds
A₀ = 0.500 M
Now we can solve for A:
ln(A/0.500) = -0.0125 * 300
To isolate A, we exponentiate both sides of the equation:
A/0.500 = e^(-0.0125 * 300)
Finally, we multiply both sides by 0.500 to solve for A:
A = 0.500 * e^(-0.0125 * 300)
Calculating this expression, we find that the concentration of ABC after 5 minutes is approximately 0.275 M.