Chemistry conversions

Question

Mouthwash is 21.0% ethanol by mass. If each bottle of mouthwash has 1.60 pt of mouthwash with a density of .876g/mL, how many kg of ethanol are in 170 bottles of mouthwash? Express your answer in 3 significant figures and appropriate units.

Answer 1

One of the biggest ways to reduce errors in problems like this is to keep your units in your calculations and cancel them out as you work through the problem. I prefer to get all of my equations/conversions set up, cancel out all of the units to make sure I didn't miss anything, and then do the final calculations. I typically find that when I'm doing problems or when my students are doing problems cancelling your units shows you quickly if you've made a mistake.

170 bottles * (1.60 pt/1 bottle) * (473.176 mL/1 pt) * (0.876 g mouthwash/1 mL) * (21 g ethanol/100 g mouthwash)* (1 kg ethanol/1000 g ethanol)

Now that everything is together I would go through and cross out the units on my paper (note that usually on paper I would write the numerator over the denominator to make it easier to follow the units):

170 bottles * (1.60 pt/1 bottle) * (473.176 mL/1 pt) * (0.876 g mouthwash/1 mL) * (21 g ethanol/100 g mouthwash)* (1 kg ethanol/1000 g ethanol)

OK now that we see that all units are cancelled and we have the units we want on the answer I would go ahead and do the calculations. When I perform the calculation I get 23.67636 kg of ethanol. Finally we need to round to 3 significant figures and report the result:

23.7 kg of ethanol

A couple of areas where students have trouble getting started are:

1) Where do I start in dimensional analysis? A lot of times it helps to distinguish between amounts and conversion factors. I started with 170 bottles because it is not a conversion factor it's how many bottles you have total.

2) Mixing up mass of mouthwash and mass of ethanol. This happens all of the time, and you really have to be careful about specifying solute (ethanol) and solution (mouthwash).

3) What do I do with the percentage? Or, how do I make percentage a conversion factor? Here you have to know how percentages are calculated. Percentages are ratios of two measurements, typically in the same unit so that the units cancel out. Also, it's always useful to put 100 as the denominator in percentages because then you do not have to convert the percentage in your head or even move the decimal point in the percentage.

Please let me know if you need clarification on the above, and/or if you'd like to set up tutoring sessions to go over these concepts.