A certain first-order reaction A--->B is 25% complete in 42 min at 25 degrees C. What is the rate constant?
ln(No/N) = kt
Call No = 100.
Solve for k.
a first order reaction takes 69.3 minutes for 59% completion how much time will be needed for 80% completion.
To determine the rate constant of a first-order reaction, we can use the integrated rate law for a first-order reaction:
ln([A]t/[A]0) = -kt
Where:
[A]t is the concentration of reactant A at time t
[A]0 is the initial concentration of reactant A
k is the rate constant
t is the time
In this case, we are given that the reaction is 25% complete, so the concentration of reactant A at this time is 75% of the initial concentration. Therefore, [A]t/[A]0 = 0.75.
Let's plug in the given values and solve for k:
ln(0.75) = -k * 42 min
First, we need to convert the time to seconds:
42 min * 60 sec/min = 2520 sec
Now, let's solve for k:
ln(0.75) = -k * 2520 sec
To isolate k, divide both sides by -2520 sec:
k = -ln(0.75)/2520 sec
Calculating this value, we find:
k ≈ 0.000766 sec^-1
Therefore, the rate constant for the reaction is approximately 0.000766 sec^-1.
To calculate the rate constant for a first-order reaction, we first need to determine the reaction rate constant. The reaction rate constant is related to the time required for the reaction to proceed by the equation:
ln([A]₀/[A]) = kt
where [A]₀ is the initial concentration of reactant A, [A] is the concentration of reactant A at a given time t, k is the reaction rate constant, and ln() denotes the natural logarithm.
In this case, the reaction is 25% complete after 42 minutes, so the concentration of reactant A at this time is 75% of the initial concentration, [A]₀. Thus, [A] = 0.75[A]₀.
Substituting this into the equation above, we have:
ln([A]₀/0.75[A]₀) = k(42 min)
Simplifying:
ln(1/0.75) = k(42 min)
Using a calculator, we can evaluate the natural logarithm of 1/0.75, which is approximately -0.2877:
-0.2877 = k(42 min)
Finally, we rearrange the equation to solve for k:
k = -0.2877 / 42 min
Evaluating this expression, we find:
k ≈ -0.006846 min⁻¹
So, the rate constant for the first-order reaction A → B is approximately -0.006846 min⁻¹ at 25 degrees C.