How many molecules of ethanol (C2H5OH) (the alcohol in alcoholic beverages) are present in 145 mL of ethanol? The density of ethanol is 0.789 g/cm3.

Video transcript

Welcome everyone. Our next question says, how many molecules of phenol V six H 50 are present in 248 mL of phenol. The density of phenol is 1.07 g per centimeters cubed. A 1.70 times 10 to the 24th molecules of phenol B 3.25 times 10 to the 24th molecules. C 7.01 times 10 to the 25th molecules or D 5.58 times 10 to the 25th molecules. So let's think about where we're starting and where we're going here. This is mainly going to be a conversion factor problem. So we're starting with milliliters of phenol and we want to end up with molecules. So we want to go from milliliters to grams. We have density to help us convert, notice that our density is in grams per centimeters cubed, but that's the same as grams per milliliter. Milliliters are the same as cubic centimeters. So we can go from milliliters, phenol phenol to grams of phenol using density then from grams of phenol to moles a phenol. And from there two molecules. So we kind of have our pathway here. We could set up our conversion factors to do that. Now note that to go from grams to moles, we need the molar mass of phenol. So we need to calculate that. So we have our formula C six H 50, so we need six time similar mass of carbon. So 12.01 g from all. And then we need, we have six hydrogens. So six times the molar mass of hydrogen, which is 1.01 g per M and for oxygen just one. So one times the molar mass of oxygen, 6.00 g per mole. So do those calculations and then we add all those together and we get 94.12 g per mole as the molar mass of beal. So now let's set up our conversion factors. Here we start with 248 g. Excuse me, milliliters, not grams, 248 mL of phenol times. And now we're going to go from milliliters to grams using density. So we have on the numerator here, 1.07 g and underneath 1 mL then multiplied by. So that's going to go. Now we're going to be at grams. Now we need to go from grams to moles. We want to cancel out grams and have them on the bottom. So we'll have put in the denominator 94.12 g and the numerator per one mole and now, we just need to go from moles to molecules. And for that, we need Avogadro's number. So 6.022 times 10 to the 23rd molecules per one mole. Let's make sure all our units cancel out correctly. So milliliters cancel out grams, cancel out moles, cancel out and we're left with molecules. So let's do all the math here. So we'll end up with 248 multiplied by 1.07 divided by 94.12 multiplied by 6.022 times 10 to the 23rd note, our big figs here, we have three S figs in our question. So we end up with 1.0 times 10 Mr to the 24th molecules of phenol. And when we look at our answer choices, we see that that matches with choice A. So in our 248 mL phenol, we use these conversion factors to get to choice a 1.70 times 10 to the 24th molecules. See you in the next video.