We just did a lab experiment converting t-amyl alcohol to t-amyl chloride via SN1. We were asked to calculate the percent yield. I figured okay, I started with 10.00 mL, so I multiply that by the density of t-amyl alcohol (0.827 g/mL) divide by its molar mass (88.148 g/mol) and multiply by the molar mass of t-amyl chloride (106.59 g/mol) to get the theoretical total yield of the reaction. It ends up as 10.00 g. Now, I don't know if I made a mistake somewhere (I don't think I did), but doesn't that seem odd? Is it pure chance that density1 / MM1 * MM2 is almost exactly equal to 1 (to 5 significant figures by wolfram|Alpha's numbers), or is it some property that I'm not aware of?
"I think nature's imagination is so much greater than man's, she's never gonna let us relax."
Mavrisa wrote:Well I wasn't suggesting that it was, I just found it curious that it was so close.. and then I thought maybe something was causing this to happen which I didn't know about. Guess not.
You can tell that it's probably not special because it's unit-dependent rather than unitless, so the number "1" is only special if the units it's measured in are special - and they're not, in the case of density.
Some people tell me I laugh too much. To them I say, "ha ha ha!"
How often have you done calculations (of theoretical yield and everything else) where your result isn't a neat number like 10.00 g? I think that thanks to Benford's Law, 1.000 * 10n, (i.e., 10.00, 1.000, 0.1000, etc) is actually (slightly) more likely to be encountered in measurements of natural or social phenomena than any other number with four significant figures, but even without that, hey, sometimes you'll get a surprisingly clean-looking number from an empirical calculations.
You didn't do anything wrong. If you think about it, it makes sense. Multiplying the volume by the density gives you the mass, which is 8.27 g in this case. T-amyl chloride is somewhat heavier than t-amyl alcohol. Your theoretical yield (10.00 g) is somewhat heavier than your starting material (8.27 g). To me, at least, looking at the starting material in mL and comparing it to the product in grams isn't as significant as comparing them in the same units. ^-^
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