The rate constant for the reaction is 0.710 M–1·s–1 at 200 °C.
A ---> products
If the initial concentration of A is 0.00390 M, what will be the concentration after 595 s?
Well, if I were a clown in a chemistry lab, I'd probably be juggling beakers and adding a dash of comedy to the reactions!
But since I'm just a bot, let me calculate that for you. We can use the first-order rate equation, which is ln(A0 / At) = kt. Rearranging it to solve for At, we get At = A0 * e^(-kt).
Now, plugging in the given values, we have A0 = 0.00390 M, k = 0.710 M–1·s–1, and t = 595 s. Plugging these values into the equation, we get:
At = 0.00390 M * e^(-0.710 M–1·s–1 * 595 s)
And using a calculator, At = 0.00171 M. So, after 595 seconds, the concentration of A will be approximately 0.00171 M.
To solve this problem, we can use the integrated rate law for a first-order reaction:
ln([A]t/[A]0) = -kt
Where:
[A]t = concentration of A at time t
[A]0 = initial concentration of A
k = rate constant
t = time
Rearranging the equation, we get:
[A]t = [A]0 * e^(-kt)
Now, let's plug in the given values:
[A]0 = 0.00390 M
k = 0.710 M^(-1)·s^(-1)
t = 595 s
[A]t = 0.00390 M * e^(-0.710 M^(-1)·s^(-1) * 595 s)
Using a calculator, we can calculate the exponent first:
e^(-0.710 M^(-1)·s^(-1) * 595 s) = e^(-421.95)
Now, we can calculate the final concentration:
[A]t = 0.00390 M * e^(-421.95)
[A]t ≈ 3.06 x 10^(-6) M
Therefore, the concentration of A after 595 s will be approximately 3.06 x 10^(-6) M.
To find the concentration of A after a specific time, we can use the integrated rate equation for a first-order reaction:
ln([A]t / [A]0) = -kt
Where:
[A]t is the concentration of A at time t
[A]0 is the initial concentration of A
k is the rate constant for the reaction
t is the time
Rearranging the equation, we get:
[A]t = [A]0 * e^(-kt)
Now we can plug in the given values:
[A]0 = 0.00390 M (initial concentration of A)
k = 0.710 M^(-1) * s^(-1) (rate constant)
t = 595 s (time)
[A]t = 0.00390 * e^(-0.710 * 595)
Calculating the value, we find that the concentration of A after 595 seconds is approximately 0.00118 M.