The rate constants for a first order decay reaction are found to be:
k287.3∘C=1 x 10−4 s−1
k327.4∘C=19.2 x 10−4 s−1
a) Determine the value, in s-1 of k250∘C
(b) How long will it take, at 350 ∘C, for the reactant to decay to 1% of its original concentration? Express your answer in seconds.
a-4.2623*10^-6
b-536.42
thanks a lotttttttt
To determine the value of k at 250°C, we can use the Arrhenius equation, which relates the rate constant to temperature:
k = Ae^(-Ea/RT)
Where:
- k is the rate constant
- A is the pre-exponential factor
- Ea is the activation energy
- R is the gas constant (8.314 J/(mol K))
- T is the temperature in Kelvin
Since we know the rate constants at 287.3°C and 327.4°C, we can set up two equations using the Arrhenius equation:
k287.3∘C = A e^(-Ea/RT287.3)
k327.4∘C = A e^(-Ea/RT327.4)
To find the value of k at 250°C, we need to know the activation energy and the pre-exponential factor. Unfortunately, this information is not provided in the question. Without those values, we cannot determine the value of k at 250°C.
Now, let's move on to part b of the question.
To find the time it takes for the reactant to decay to 1% of its original concentration at 350°C, we can use the first-order decay reaction equation:
ln(Ct/C0) = -kt
Where:
- Ct is the concentration at time t
- C0 is the initial concentration
- k is the rate constant
- t is the time
In this case, we want to find the time when Ct is 1% of C0. So we have:
ln(0.01) = -k * t
Rearranging this equation to solve for t:
t = ln(0.01) / -k
Now, we can substitute the given rate constant into the equation to find the time:
k = 19.2 x 10^(-4) s^(-1)
t = ln(0.01) / -(19.2 x 10^(-4))
Calculating this, we can find the time in seconds.