Two isomers and of a given compound dimerize as follows both...

Two isomers ( and ) of a given compound dimerize as follows: Both processes are known to be second order in reactant, and is known to be 0.410 L/mol ⋅ s at 25ºC. In a particular experiment and were placed in separate containers at 25ºC, where and . It was found that after each reaction had progressed for 3.00 min, . In this case the rate laws are defined as a Question Content Area Calculate the concentration of after 3.00 min. Concentration = M

Transcript

00:01 So we have these two second order reactions, and the integrated rate law for a second order reaction is where we need to start because we need to relate the amounts at different times.

00:16 We're given the initial concentration, and we want the concentration of a 2 after three minutes.

00:33 I just realized that i've done this, calculated the concentration of a, but it'll be simple enough to calculate the concentration of a2.

00:42 So let's go on.

00:44 So we're going to calculate the concentration of a after three minutes, and that is kt.

00:50 So the k was given for the reaction of a after three minutes.

00:54 Notice that the k is given, the rate constant, is given as per molar per second.

01:04 Or the inverse of molar per second.

01:06 But our time is given in minutes, so we need to rationalize that with conversion to the seconds.

01:14 Plus 1 over a 0, the initial concentration was 1 times 10 to the minus 2.

01:20 And so these first three factors combine to give 45 per molar and 1 over 1 times 10 to minus 2 is 100.

01:31 So 1 over a, 1 over the concentration at 3 minutes is 45.

01:37 So the concentration at 3 minutes is 1 over 145.

01:44 So here's our concentration of a after 3 minutes.

01:47 So how much a was used up? so that was the change in concentration of a.

02:15 Well, what would be the concentration change for a2? that will be the concentration of a2.

02:23 At 3 minutes.

02:25 Well, that would be molar, change in concentration, decrease in concentration of a, and then 2 moles a for each, sorry, nope.

02:47 We want the, we want the a in the denominator, and so that's 1 mole a2 for each 2 moles of a.

03:06 And so the, the, uh, and so the, uh, answer for a2 at 3 minutes would be 0 .015.

03:20 That's the concentration of a2 at 3 minutes.

03:26 We calculated that from the change in concentration of a...

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