The decomposition of IBr(g)into I2 (g) and Br2 (g) is first order in IBr with k = 0.00255/sec.

(a)Starting with [IBr] = 1.50M, what will [IBr] become after 2.50 minutes?

(b)How long, in minutes, will it take for [IBr] to go from 0.500M to 0.100M?

(c)What is the half-life for this reaction in seconds?

(d)Enough IBr is added to an evacuated container to make [IBr] = 0.350M. How long will it take [I2] = 0.100M?
(e) The following mechanism has been proposed for the reaction above:

(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)

Based on the rate law described above, which step is the rate-determining step? ______________

What is the molecularity of the rate-determining step? _____________________

a)

ln(No/N) = akt
No = 1.5M
solve for N
a = 2
k = 0.00255
t = 2.5 min changed to seconds.

b)
same as in (a) but solve for t.

c)
Make No = 1.5 and
N = 1/2 that, solve for t.

0.490mol {\rm mol} magnesium fluoride

To answer these questions, we need to use the rate law and apply the concepts of first-order reactions and rate-determining steps. Let's go through each question step by step.

(a) To determine what [IBr] will become after 2.50 minutes, we need to use the first-order rate equation:
ln([IBr]₀/[IBr]) = -kt

Where [IBr]₀ is the initial concentration and [IBr] is the concentration at a given time. Rearranging the equation, we get:
[IBr] = [IBr]₀ * e^(-kt)

Given [IBr]₀ = 1.50 M, k = 0.00255 sec^(-1), and t = 2.50 minutes (which needs to be converted to seconds), we can now calculate [IBr]:
[IBr] = 1.50 * e^(-0.00255 * (2.50 * 60))

(b) To find the time it takes for [IBr] to go from 0.500 M to 0.100 M, we need to use the same formula:
[IBr] = [IBr]₀ * e^(-kt)

Rearranging the equation to solve for time, we have:
t = (ln([IBr]₀/[IBr])) / k

Plugging in [IBr]₀ = 0.500 M, [IBr] = 0.100 M, and k = 0.00255 sec^(-1), we can now calculate the time required.

(c) The half-life of a first-order reaction can be determined using the formula:
t_1/2 = ln(2) / k

Plugging in k = 0.00255 sec^(-1), we can calculate the half-life.

(d) To find the time it takes for [I2] to reach 0.100 M, we'll need to consider the rate law and stoichiometry of the reaction.

From the balanced equation, we can see that 2 moles of IBr yields 1 mole of I2. So, the rate of the reaction is equal to the rate of change of IBr, but multiplied by 2 to account for the stoichiometry.

Using the rate law for the decomposition of IBr (first-order in IBr):
rate = k[IBr]

We can set up the equation:
rate = -d[IBr]/dt = d[I2]/dt

Rearrange the equation to solve for time:
dt = -d[IBr]/(k * [IBr])

Using [IBr] = 0.350 M, [I2] = 0.100 M, and k = 0.00255 sec^(-1), we can calculate the time required.

(e) To determine the rate-determining step, we need to compare the overall rate law with the individual rate laws of each proposed step. The slowest step is the rate-determining step.

From the rate law described (first-order in IBr), we can see that the rate-determining step should have IBr as a reactant. Comparing the proposed mechanism, we see that step 2 involves IBr as a reactant. Therefore, step 2 is the rate-determining step.

Regarding the molecularity of the rate-determining step, molecularity refers to the number of reactant molecules involved in the rate-determining step. As step 2 involves IBr and Br as reactants, it is bimolecular (molecularity of 2).

Note: The answers provided depend on the information given in the question.