# 9: Going backwards

Let’s say I tell you that a sugar cube weighs 5 grams. Given the formula C6H12O6, how many mols would that be?

If this kind of problem is unfamiliar to you, start by thinking about what you do know how to do. For example, you do know how to calculate the molar weight of sugar. So, given the formula above, what’s the molecular weight of sugar?

 1 H 1.01 2 He 4.00 3 Li 6.94 4 Be 9.01 5 B 10.81 6 C 12.01 7 N 14.01 8 O 16.00 9 F 19.00 10 Ne 20.18 11 Na 22.99 12 Mg 24.30 13 Al 26.98 14 Si 28.09 15 P 30.97 16 S 32.07 17 Cl 35.47 18 Ar 39.98 19 K 39.10 20 Ca 40.09 21 Sc 44.96 22 Ti 47.88 23 V 50.94 24 Cr 51.94 25 Mn 54.94 26 Fe 55.85 27 Co 58.93 28 Ni 58.69 29 Cu 63.55 30 Zn 65.39 31 Ga 69.72 32 Ge 72.61 33 As 74.92 34 Se 78.96 35 Br 79.90 36 Kr 83.80 So the molar weight of sugar is 180 grams: in other words

180 grams / 1 mol.

But what we want to know is how many moles per gram, not grams per mole … therefore we need to flip the fraction “upside down”:

1 mol / 180 grams = 0.0055 mol/g

and we have 5 grams, so that’s

1 cube = 5 g x 0.0055 mol/g= 0.028 moles.