A first-order reaction has a rate constant of 0.547 min - 1. How long will it take a reactant concentration 0.14 M to decrease to 0.07 M?
Not sure how to do this!
k = 0.693/t1/2
Solve for k and substitute into the below equation.
Then ln(No/N) = kt
No = 0.14
N = 0.07
although you should be able to do this in your head with no equations.
Wrong, the answer is 1.267
To solve this problem, you can use the integrated rate law for a first-order reaction. The integrated rate law equation for a first-order reaction is:
ln([A]t / [A]0) = -kt
Where:
- [A]t is the final concentration of the reactant (0.07 M)
- [A]0 is the initial concentration of the reactant (0.14 M)
- k is the rate constant (0.547 min^-1)
- t is the time it takes for the concentration to decrease from [A]0 to [A]t (what we need to find)
To find the time required for the reactant concentration to decrease from 0.14 M to 0.07 M, we need to rearrange the equation:
ln(0.07 / 0.14) = -0.547t
Now we can solve for t:
t = ln(0.07 / 0.14) / -0.547
Using a calculator, we can calculate the value of t:
t ≈ 0.693 / 0.547
t ≈ 1.270 min
Therefore, it will take approximately 1.270 minutes for the reactant concentration to decrease from 0.14 M to 0.07 M in a first-order reaction with a rate constant of 0.547 min^-1.