What if the given mass is in kilograms or milligrams?

You must convert the mass to grams first before applying the molar mass. Multiply kilograms by 1000 to get grams, or divide milligrams by 1000.

How many significant figures should I retain in my final answer?

Your final answer should have the same number of significant figures as the provided mass or mole value. Always use a molar mass that has at least one more significant figure than your given value to prevent rounding errors.

Does this calculation change for specific isotopes?

Yes. If the problem specifies a pure isotope (like Carbon-14), you must use the exact isotopic mass instead of the standard average atomic weight found on the periodic table.

How to convert grams to moles and back

Converting grams to moles requires dividing the given mass by the molar mass of the substance. To convert moles back to grams, you multiply the amount in moles by the molar mass.<br><br>This method applies whenever you need to translate bulk mass measurements into discrete particle counts for stoichiometric calculations in chemistry.

The setup

Identify the exact chemical formula of the substance. Calculate its molar mass ( $M$ ) in g/mol by summing the standard atomic weights of all atoms present in the formula.

The steps

To convert mass ( $m$ ) to moles ( $n$ ), use the formula $n = m / M$ . 2. To convert moles ( $n$ ) to mass ( $m$ ), use the formula $m = n imes M$ . 3. Keep units attached to all numbers during the calculation to ensure they cancel correctly (dimensional analysis).

Checking the result

Set up the conversion as a fraction. When converting grams to moles, the unit 'grams' must be in the denominator of the conversion factor so it cancels out. A typical mole of a laboratory chemical has a mass between 10 and 300 grams; if your answer is vastly outside this range for standard quantities, check your arithmetic.

Common errors

A frequent mistake is using the atomic mass instead of the molecular mass for diatomic elements (e.g., using 16.00 g/mol for oxygen gas instead of 32.00 g/mol for $O_2$ ). Another error is failing to distribute subscripts outside parentheses in complex formulas like $Ca(NO_3)_2$ when calculating molar mass.

Worked example

Convert 45.0 grams of water ( $H_2O$ ) to moles, then convert 0.750 moles of $H_2O$ to grams.

First, calculate the molar mass of $H_2O$ : $M = (2 imes 1.008) + 16.00 = 18.016$ g/mol. To convert 45.0 g to moles: $n = 45.0 ext{ g} imes (1 ext{ mol} / 18.016 ext{ g}) = 2.50 ext{ moles}$ . To convert 0.750 moles to grams: $m = 0.750 ext{ moles} imes (18.016 ext{ g} / 1 ext{ mol}) = 13.5 ext{ grams}$ .

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References: OpenStax Chemistry 2e, Chapter 3.1: Formula Mass and the Mole Concept · Zumdahl Chemistry, 10th Edition, Chapter 3: Stoichiometry