(a) To determine [IBr] after 2.50 minutes, we need to use the first-order rate equation:
ln([IBr]t/[IBr]0) = -kt
Where [IBr]t is the concentration of IBr at time t, [IBr]0 is the initial concentration of IBr, k is the rate constant, and t is the time.
Substituting the given values into the equation:
ln([IBr]t/1.50M) = -(0.00255/sec)(2.50 min x 60 sec/min)
Solving for [IBr]t:
[IBr]t = (1.50M) * e^(-0.00255/sec*2.50 min x 60 sec/min)
(b) To find the time it takes for [IBr] to go from 0.500M to 0.100M, we can again use the first-order rate equation:
ln([IBr]t/[IBr]0) = -kt
Rearrange the equation:
t = (1/k) * ln([IBr]t/[IBr]0)
Substitute the given values:
t = (1/0.00255/sec) * ln(0.100M/0.500M)
(c) The half-life of a first-order reaction can be calculated using the following equation:
t1/2 = (ln(2))/k
Substitute the given value of k:
t1/2 = ln(2)/(0.00255/sec)
(d) To find the time it takes for [I2] to reach 0.100M, we need to set up a ratio using the stoichiometry of the balanced chemical equation:
IBr(g) --> I2 (g) + Br2 (g)
From the equation, we can see that the ratio of moles of I2 to moles of IBr is 1:1. Therefore, the time it takes for [I2] to reach 0.100M will be the same as the time it takes for [IBr] to decrease by the same amount.
Use the first-order rate equation to find the time:
ln([IBr]t/[IBr]0) = -kt
Solve for t when [IBr]t = 0.100M.
(e) To determine the rate-determining step and its molecularity, we need to examine the rate law for the reaction:
rate = k[IBr]^x
Based on the proposed mechanism:
(step 1) IBr (g) --> I (g) + Br (g)
(step 2) IBr(g) + Br(g) --> Br2(g) + I(g)
(step 3) I(g) + I(g) --> I2(g)
The rate-determining step is typically the slowest step in the reaction mechanism and determines the overall rate of the reaction. The rate law for the reaction is determined by the species involved in the rate-determining step.
From the rate law for the overall reaction, we can deduce that the species involved in the rate-determining step are included in the rate law. In this case, the rate law is first order in IBr.
Comparing the rate law to the proposed mechanism, we see that step 1 is the only step that involves IBr, indicating that it is the rate-determining step.
The molecularity of a reaction step refers to the number of reactant species involved in that step. In this case, step 1 involves only one reactant species, IBr. Therefore, the molecularity of the rate-determining step is unimolecular.