The Mole
Student Expectations
The student is expected to define and use the concept of a mole AND use the mole concept to calculate the number of atoms, ions, or molecules in a sample of material AND calculate percent composition and empirical and molecular formulas.
Key Concepts
The mole is an SI unit used to describe an amount of a substance. The mole is equal to 6.02 × 1023 atoms, molecules, ions, or formula units of a substance. One mole is the amount of any substance that contains the same number of particles as the number of atoms in exactly 12 grams of carbon-12.
Mole ratios are used as conversion factors in chemical calculations. The number of atoms, molecules, ions, or formula units in any amount of a substance may be calculated using Avogadro’s number.
Moles can be used to convert from the mass of a substance to the number of atoms, ions, or molecules contained in a substance, and vice versa. This can be done using Avogadro’s number and the molar mass of a substance (g/mol), which can be found by adding the atomic masses of the atoms in the chemical formula from the Periodic Table.
The percent composition of a compound represents the percentage of each element in a compound by mass. Percent composition is calculated by dividing the mass of a single element in one mole of a compound by the molar mass of the compound and multiplying by 100 to make a percentage.
An empirical formula is a chemical formula with the lowest whole-number ratio of elements in a compound. It can be calculated by finding the representative masses of each element in the compound, then converting the masses into mole ratios, and then writing these in the smallest whole number ratios.
A molecular formula is the actual chemical formula of a compound, and it may be determined based on the molar mass and the empirical formula of the compound. The molar mass of the empirical formula is calculated, and then the molar mass of the compound is divided by the molar mass of the empirical formula to find an integer. The empirical formula is then multiplied by this integer to calculate the molecular formula.
THE MOLE
MOLE: INTERNATIONAL SYSTEM (SI) UNIT
The Système International d'Unitès (International System of Units), abbreviated as SI, contains 7 base units. The unit that is used to describe an amount of a substance is called a mole. The mole is equal to 6.02 x 1023 atoms, molecules, ions, or formula units of a substance. One mole is the amount of any substance that contains the same number of particles as the number of atoms in exactly twelve grams of carbon-12.
The unit symbol is mol. Since the number of moles is proportional to the number of particles in a sample, moles are often used in chemistry to represent quantitative interactions among particles. Moles can be used to convert from the mass of a substance to the amount of a substance, and vice versa.
FINDING MOLAR MASS
This can be done using the molar mass of a substance. The molar mass of an element is equal to the atomic mass of the element. For example, the atomic mass of carbon is 12.01 atomic mass units, or amu. The molar mass of carbon is 12.01 grams per mole, or g/mol. As you can see, the mass is the same, but the units are different. The molar masses of compounds may be found by adding the molar masses of the atoms contained within the chemical formula.
For example, the molar mass of one hydrogen atom is the same as the atomic mass of one hydrogen atom:
1 hydrogen atom = 1.008 amu = 1.008 g/mol
If we want to know the mass of 5.2 moles of H atoms, we may use the process of dimensional analysis and use molar mass as a conversion factor:
Notice how the units cancel, leaving only the desired unit.
Using another example, the molar mass of one chlorine atom is the same as the atomic mass of one chlorine atom:
1 chlorine atom = 35.45 amu = 35.45 g/mol
If we want to know the mass of 5.2 moles of Cl atoms, we may use molar mass as a conversion factor:
MOLE RATIOS
Mole ratios are used as conversion factors in chemical calculations. The number of atoms, molecules, ions, or formula units in any amount of a substance may be calculated by multiplying the number of moles of the substance by Avogadro’s number. For instance, if hydrogen gas reacts with oxygen gas in a chemical reaction, how can we calculate the molar ratio between water and hydrogen gas? First, write the balanced chemical equation for the reaction.
2 H2 + O2 → 2 H2O
The coefficients used in the correctly balanced chemical equation provide the mole ratios for the compounds found in that equation. For this reaction, two moles of hydrogen gas react with one mole of oxygen gas to produce two moles of water. These ratios can then be used as a conversion factor. For example, the number of hydrogen atoms can be calculated using the mole ratios and Avogadro’s number. If one mole of hydrogen gas reacts with oxygen gas, the total number of water molecules produced would be:
The number of oxygen atoms used in the reaction may also be calculated using the molar mass ratio. How many oxygen atoms react with 1 mole of hydrogen gas?
PERCENT COMPOSITION
The percent composition of a compound represents the percentage of each element in a compound by mass. Percent composition is calculated by dividing the mass of a single element found in one mole of a compound by the molar mass of the compound, and multiplying it by 100%.
For example, what is the percent composition of oxygen in carbon dioxide?
First, find the ratios of each element found within the compound:
1 molecule of CO2 contains 1 C atom and 2 O atoms
Next, find the molar mass of each component:
1 carbon atom = 12.01 g/mol C
2 oxygen atoms = 16.00 g/mol x 2 = 32.00 g/mol O
Then, find the total mass of the compound:
12.01 g/mol C + 32.00 g/mol O = 44.01 g/mol CO2
Finally, divide the total amount of oxygen in the compound by the total mass of the compound, and multiply by 100%.
(32.00 g/mol O / 44.01 g/mol CO2) x 100% = 72.71% O
The same process may be used to find the percent composition of carbon in CO2.
(12.01 g/mol C / 44.01 g/mol CO2) x 100% = 27.29% C
You can double check your work quite easily. Simply add the calculated percentages of each element within the compound. If they total 100%, then you have done your calculations correctly.
EMPIRICAL AND MOLECULAR FORMULAS
Empirical Formula: An empirical formula is a chemical formula with the lowest whole-number ratio of elements in a compound. It can be calculated by finding the representative masses of each element in the compound, converting the masses into mole ratios, and writing these in the smallest whole number ratios.
A hydrocarbon is composed of 85.6% carbon and 14.4% hydrogen.
Find the empirical formula of the compound. Assume that you are starting with 100 g of the compound. Therefore, 85.6 % C = 85.6 parts C per 100 = 85.6 g C.
Start by dividing the amount of each element found within the compound by the molar mass of that element to find the number of moles of that element. This converts the percentage of each element (by mass) to moles of each element.
Next, divide each of the number of moles by the smaller number of moles to find the number of moles of each element.
Molecular Formula: There are times when the actual chemical formula of a compound is a multiple of the empirical formula. To find the molecular formula, divide the molar mass of the given compound by the molar mass obtained from the empirical formula to get a whole number. Then, simply multiply the subscripts of the empirical formula by this number.
The actual molar mass of an unknown hydrocarbon is 28.05 g/mol. Find the molecular formula of this compound.
Empirical formula = CH2
Empirical formula molar mass = 14.02 g/mol
Molar mass of the unknown hydrocarbon = 28.05 g/mol
Divide the empirical mass by the actual molar mass to get a whole number.
(28.05 g/mol) / (14.02 g/mol) = 1.99 ≈ 2
Multiply all subscripts of the empirical formula by 2
2 (CH2) = molecular formula = C2H4
The molecular formula gives an exact number of atoms of each element within a compound. It is important to note that, in some cases, the empirical formula of a molecule is the same as the molecular formula of a molecule. People can master and understand potential chemical properties using molecular formulas.