How do units work in dimensional analysis?

Answer 1

in dimensional analysis (for chemistry) your usually converting substances to moles or grams to figure out whatever you need for the problem. For units, you always want the units to cancel out as 1/7 * 7 cancels out to 1/1 or 1.

for example, if i want to find the molar mass of 3.00 moles of Carbon (C), this is your set up:

(3.00 moles Carbon)(36.03 grams Carbon/1mole Carbon)=108.09/1 grams Carbon=108 grams Carbon(using sig. figs)

in the problem above, since moles are the numerator, and you want to find how many grams are in 3 moles of carbon, you want to set up a ratio of moles per grams. Ratios can be flip flopped based on which units you need. So i look at the Periodic Table and see there are 12.01 grams per 1 mole, setting the ratio up so that when it multiplies 3 moles of carbon, the moles cancel and im left with grams of carbon, the units i want. It seems complicated but gets easier with practice.