It's probably not a bad idea to keep that reaction cold when you're adding the H2SO4 to make your HBr. The orange coloration is most likely due to Br2, which is obviously not going to be helpful. It looks like you used an excess of NaBr, which is a good idea considering that H2SO4 oxidizes HBr to Br2. It's probably best to only let it go for a few minutes, as with time, you may see more of this oxidation.

Are you using pure safrole? It's actually desirable to use the crude sassafras oil, as the phenolic compounds are radical inhibitors. HBr can add anti-Markovnikov in the presence of trace amounts of peroxides, or when exposed to UV light, meaning you would get the wrong product.

Did you check the density of your safrole beforehand? 1.11g/mL isn't far from the reported value, and seems to suggest that your yield may have been low. Definitely plan on recovering unreacted safrole. Assyl would prepare that HBr solution as you did, except cold, and filter out the solids so that stirring with the safrole is possible (though many procedures say not to stir, is this just a mechanical issue regarding the salts?). It wouldn't hurt to wrap it up in aluminum foil to suppress any radical chemistry that may be going on.

If you want clean HBr, Assyl would suggest something along the lines of a typical HCl generator, except bubbling the gas through a trap with cold TCE or DCM (or even petroleum ether perhaps) to catch Br2. Anything that passes through should be relatively clean, dry HBr.

The crystals that crashed out during the addition of the bromosafrole (or whatever it is) may have dropped out just because they aren't soluble in that oil. It went from a saturated solution in acetone to a 30% solution of a relatively non-polar oil, so it wouldn't be surprising. Did you filter and weigh the solids, or characterize them in any way? You could check the density of them by adding to a graduated cylinder of petroleum ether (so you can calculate the volume). Pull solvent off them first with your vacuum pump (hope you have a trap by the way, as some of the things you may be pulling off aren't so nice to pumps). The density would offer some clue just how far the reaction went towards completion.

MgSO4 will dry your oil very quickly, 24 hours is unnecessary. Once the solution is clear, and the MgSO4 added no longer clumpy, it's dry. If it remains cloudy and the MgSO4 isn't clumping, it's probably dry and you're just seeing suspended solids - pull it through celite (diatomaceous earth) and it'll clear up.

As for drying alcohol, a bit of lithium from a battery will do in a pinch. Distillation is of course necessary. Other drying agents such as MgSO4 will dissolve in the alcohol, so distillation is necessary with those, too - they really aren't ideal anyway. How are you planning on generating your methylamine?

Use a stirbar and a warm water (30C) bath for pulling off those solvents! You'd be amazed how well solvents will stick in oils. You can get a lot more out by adding and pulling off a low boiling solvent several times, such as diethyl ether, it'll carry solvents like acetone out that may otherwise stubbornly stay behind. Probably unnecessary here, but if you're concerned, it's the way to do it.

Do you have access to TLC plates, or any other way to analyze your products? Safrole should run faster on silica than bromosafrole, and would probably visualize better with UV.

Some advice from jon:

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to test it get some sulfuric acid freezing cold then add a drop of the extracted bromosafrole to it.
it should sit on top if it has any alkene the acid will turn purple.

Good advice -- I've tried keeping it cold in the past but kept having issues with the acetic acid freezing up on me.  But that was with an ice bath.  Maybe I could just submerge in water with a temperature slightly lower than GAAs melting point.

Yes it's pretty much pure, and unfortunately I'm not in the market to be getting any more safrole in the forseeable future.  I'll look into some phenolic compound-containing OTC oil that I can possibly add in.  I'll watch out for the UV light too.  It was kept in a dark freezer sealed with saran wrap most of the time, but definitely exposed to bright light a few times.

I've tried and tried to generate HBr gas an always have issues with Br2 like you say.  I've tried bubbling through cold naptha before the GAA and I think it ended up trapping a lot (or most) of the HBr gas.  After dripping a lot of H2SO4 over a lot of NaBr the naptha was fuming heavily and the GAA weighed in at a density much less than the 33% I was shooting for.  Tried heating H3PO4/NaBr as well -- barely got any gas out of that one.  I suspect that DCM and TCE would hold even more gas than naptha.  I mean, you can't get much more non-polar than naptha.

I've read that Na2CO3 would work for drying IPA, but the lithium thing is intriguing.  Could you give me any more information on that?  Would I just, say, go pick up some lithium AAs from the drug store, break them open, and scoop out the goop (or whatever it is) inside?  How much would I need to dry, say, a gallon of 99% IPA?

I have methylamine HCl.  I'll put it in a cooled flask and drip saturated NaOH solution onto it.  Don't plan on drying the gas as jon has repeatedly said it's not necessary if things are kept cool.  My IPA will be cooled with dry-ice chilled acetone.  I have a stone bubbler to increase surface area for maximum absorption.

I've also heard that NaOH can be used to dry 91% IPA.  I wonder if it would do anything for my 99%?

I might do that next time round.  Seems like a good way to test for the bromo compound, but I can see it being really imprecise.  I don't think it would give much of an indication of purity or ratio of safrole to bromo since we don't have a set standard of color/time to compare to.

Thanks a ton for the advice this has been very very helpful.  A question -- I'm assuming that since my oil is full of safrole that I don't need to use the standard 8:1 ration of methylamine to iodo.  I'm considering cutting that to 4:1 in order to save methylamine.  Or should I stick with 8:1 because the CH2NH3 will be crowding the safrole molecules as well?  Thoughts on that?