# Calculate the molar mass of a compound if 0.472 mole of it has a mass of 178 g.

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The molar mass of a substance is defined as the mass of the substance divided by the amount of a substance. The units for molar mass are technically kg/mole but are most commonly expressed as g/mole (read as "grams per mole") to give easier numbers to work with. It is very closely related to the molecular weight of a substance which can be gotten from the periodic table, except the molecular weight is an average weight based on the ratios of the different isotopes of each element as found in nature (different isotopes of an element will have slightly different masses).

Regardless, since molar mass is defined as grams per mole, we simply set up a fraction with the mass in grams in the numerator and the amount in moles in the denominator and then divide to get the molar mass:

`(178 g)/(0.472 mol) = 377.12 g/(mol)`

So the answer is 377.12 g/mol.

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178g / .472 = 377.11g

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Use dimensional analysis:

`178 "g" = (1"mol")/(?"g") = 0.472"mol"`

This can be simplified to:

`(178"g")/(?"g") = 0.472"mol"`

Solve for the unknown by cross multiplying.

`?"g" = 377"g"`

The compound would have a molar mass of 377 grams. Because all the values given in the problem has three sig figs, your answer should also be in three sig figs.

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178g / .472 = 377.11 but if you had to do it based on the sig fig it would be 377g per 1 mole

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Molar mass is how much the compound would weigh if we had one mole of it. (Think, how many grams per mole?)

To figure this out we take 178g and divide it by the number of moles:

`(178g)/(.472mol) = (377g)/(mol)`