The decomposition reaction, x-->products, is second-order with rate constant k=0.0183 L/(s)(mol).
How long will it take for the decomposition to be 95% complete, if the intitial concentration of X is 1.25mol/L?
Thanks
(1/A) - (1/Ao) = akt
Let Ao = 100; A = 5; a = 1
To find the time it takes for the decomposition reaction to be 95% complete, we can use the following second-order rate equation:
Rate = k [X]^2
First, let's calculate the initial rate of decomposition. At t=0, the concentration of X is 1.25 mol/L, so we can substitute this into the rate equation:
Rate = k [X]^2
Rate = (0.0183 L/(s)(mol)) * (1.25 mol/L)^2
Calculating this gives us the initial rate of decomposition.
Once we have the initial rate, we can determine the time it takes for the concentration of X to decrease to 95% of its initial concentration. This can be done by using the integrated rate law for a second-order reaction:
1/[X] = 1/[X]0 + kt
We can rearrange this equation to solve for time:
t = (1/[X] - 1/[X]0) / k
Since we are given that the concentration of X decreases to 95% of its initial concentration, we can substitute the values into the equation:
t = (1/0.95[X]0 - 1/[X]0) / k
Substituting the values [X]0 = 1.25 mol/L and k = 0.0183 L/(s)(mol):
t = (1/0.95*1.25 - 1/1.25) / 0.0183
Calculating this expression will give you the time it takes for the decomposition to be 95% complete.