Iodine combines to form I2 in liquid propane solvent with a constant of 1,5 x 10^10 L/mol. The rate is 2nd order. Since the reaction occurs quickly, a flash of light creates an I concentration of .0100M. How long will it take for 95% of the atoms to form I2?
This must use a second order rate equation, but I cannot get 1.0x10^-7 which is the answer
1.0 x 10^-7 WHAT?
Sorry it is 1.0x10^10 seconds.
Any idea how to obtain this answer?
To solve this problem, we need to use the second order rate equation:
1 / [A] = kt + 1 / [A₀]
Where:
[A] = concentration of A at time t
[A₀] = initial concentration of A
k = rate constant
t = time
Given that the reaction is second order, we can rewrite the equation as:
1 / [A] = kt + 1 / [A₀]
Since the reaction occurs quickly, we can assume that the initial concentration of I is equal to the concentration obtained from the flash of light, which is 0.0100 M. Therefore, [A₀] = 0.0100 M.
We are also given the rate constant, which is 1.5 x 10^10 L/mol.
To find the time required for 95% of the atoms to form I2, we need to solve for t when [A] is equal to 0.05 * [A₀] (95% conversion to I2).
Let's plug the values into the equation:
1 / (0.05 * [A₀]) = (1.5 x 10^10 L/mol) * t + 1 / [A₀]
To simplify the equation, we can first find the reciprocal:
20 / [A₀] = (1.5 x 10^10 L/mol) * t + 1 / [A₀]
Next, we can multiply both sides by [A₀] to eliminate the denominators:
20 = (1.5 x 10^10 L/mol) * t * [A₀] + 1
Since [A₀] = 0.0100 M, we can substitute the value into the equation:
20 = (1.5 x 10^10 L/mol) * t * 0.0100 M + 1
Now we can solve for t:
(1.5 x 10^10 L/mol) * t * 0.0100 M = 19
t = 19 / [(1.5 x 10^10 L/mol) * 0.0100 M]
Calculating this expression, we get:
t ≈ 1.06 x 10^-7 seconds
Therefore, it will take approximately 1.06 x 10^-7 seconds for 95% of the atoms to form I2 in this reaction.
It seems that the answer you mentioned, 1.0 x 10^-7, is close to the correct answer. There might be a small rounding error in the calculations.