# Mass-to-Mole Conversions

## Mass-to-mole conversions can be facilitated by employing the molar mass as a conversion ratio.

#### Key Points

• The mole is the universal measurement of quantity in chemistry. Although we cannot directly measure how many moles a substance contains, we are able to first measure its mass and then convert that amount to moles.

• A substance's molar mass is calculated by multiplying its relative atomic mass by the molar mass constant.

• The molar mass constant provides that quantitative chemical calculations are dimensionally correct; the atomic weight is a dimensionless quantity, but the molar mass has the unit g/mol.

#### Terms

• the mass of a given substance (chemical element or chemical compound) divided by its amount of substance

• In the International System of Units, the base unit of the amount of substance; the amount of substance of a system that contains as many elementary entities as there are atoms in 0.012 kg of carbon-12. Symbol: mol. The number of atoms in a mole is known as Avogadro’s number.

#### Figures

1. ##### Mass and Mole Conversions

The mass and molar quantities of a substance can be easily interconverted by using the molecular weight as a conversion factor.

2. ##### Stoichiometry, Grams to Moles

Describes how to determine the number of moles of reactants and products if you are given the number of grams of one of the substances in the chemical equation.

The mole is the universal measurement of quantity in chemistry. However, the measurements that we take every day provide answers not in moles but in more physically concrete units, such as grams or milliliters. Therefore, we need some way of comparing what we can physically measure to the amount of measurement that we are interested in: moles.

Because scientists of the early 18th and 19th centuries could not determine the exact masses of the elements due to technology limitations, they instead assigned relative weights to each element. The relative atomic mass is a dimensionless physical quantity that is the ratio of the average mass of atoms of an element to 1/12 of the mass of an atom of carbon-12. From this scale, hydrogen has an atomic weight of 1.0079 amu, and sodium has an atomic weight of 22.9997 amu. From the relative atomic mass of each element, we can determine each element's molar mass by multiplying the molar mass constant (1 g/mol) by the atomic weight of that particular element. Multiplying by the molar mass constant ensures that the calculation is dimensionally correct because atomic weights are dimensionless. The molar mass value can be used as a conversion factor to facilitate mass-to-mole and mole-to-mass conversions.

To convert from grams to moles, we need the compound's molar mass. For a single element, the molar mass is equivalent to its atomic weight multiplied by the molar mass constant. For a compound, the molar mass is the sum of the atomic weights of each element in the compound multiplied by the molar mass constant. After the molar mass is determined, then dimensional analysis is used to convert from grams to moles.

Figure 1

For example, convert 18 grams of water to moles. The molar mass of water is 18 g/mol; therefore:

$18gH_2O * \frac{1 mol}{18 g H_2O} = 1 mol H_2O$

Figure 2

#### Key Term Glossary

atom
the smallest possible amount of matter that still retains its identity as a chemical element, now known to consist of a nucleus surrounded by electrons
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atomic mass
the quantity of matter of a particle, sub-atomic particle, or molecule
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chemistry
The branch of natural science that deals with the composition and constitution of substances and the changes that they undergo as a consequence of alterations in the constitution of their molecules.
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compound
A substance made from any combination elements.
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constant
Consistently recurring over time; persistent
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conversion factor
A conversion factor changes something to a different version or form.
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dimensional analysis
The study of the dimensions of physical quantities; used to obtain information about large complex systems, and as a means of checking mathematical and physics equations.
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dimensionless
of a physical constant, lacking units.
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element
Any one of the simplest chemical substances that cannot be decomposed in a chemical reaction or by any chemical means, and are made up of atoms all having the same number of protons.
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mass
The quantity of matter that a body contains, irrespective of its bulk or volume. It is one of four fundamental properties of matter. It is measured in kilograms in the SI system of measurement.
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measurement
magnitude (or extent or amount) determined by measurement
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molar mass
the mass of a given substance (chemical element or chemical compound) divided by its amount of substance
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mole
In the International System of Units, the base unit of the amount of substance; the amount of substance of a system that contains as many elementary entities as there are atoms in 0.012 kg of carbon-12. Symbol: mol. The number of atoms in a mole is known as Avogadro’s number.
##### Appears in these related concepts:
ratio
The relative magnitudes of two quantities (usually expressed as a quotient).