Figure 6.1 “Water Molecules” mirrors that we need 2 hydrogen atoms and 1 oxygen atom to make 1 water molecule. If we desire to make 2 water molecules, us will need 4 hydrogen atoms and 2 oxygen atoms. If we desire to make 5 molecule of water, we need 10 hydrogen atoms and 5 oxygen atoms. The ratio of atoms we will must make any number of water molecule is the same: 2 hydrogen atoms to 1 oxygen atom.

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Figure 6.1 Water Molecules. The proportion of hydrogen atoms to oxygen atoms provided to make water molecules is constantly 2:1, no issue how numerous water molecules room being made.


One problem we have, however, is that it is very difficult, if no impossible, to organize atoms one at a time. As declared in the introduction, we deal with billions of atoms at a time. How deserve to we keep track that so numerous atoms (and molecules) in ~ a time? We carry out it by making use of mass fairly than through counting individual atoms.

A hydrogen atom has actually a mass of around 1 u. One oxygen atom has actually a mass of roughly 16 u. The ratio of the mass of an oxygen atom come the fixed of a hydrogen atom is therefore about 16:1.

If we have actually 2 atoms of each element, the proportion of their masses is about 32:2, which reduces to 16:1—the same ratio. If we have actually 12 atoms of each element, the ratio of their total masses is around (12 × 16):(12 × 1), or 192:12, which likewise reduces come 16:1. If we have 100 atom of each element, the ratio of the masses is approximately 1,600:100, i beg your pardon again reduces come 16:1. As long as we have equal number of hydrogen and also oxygen atoms, the ratio of the masses will constantly be 16:1.

The very same consistency is seen when ratios that the masses that other facets are compared. Because that example, the proportion of the masses of silicon atom to same numbers of hydrogen atoms is always approximately 28:1, when the ratio of the masses of calcium atom to equal numbers of lithium atoms is around 40:7.

So us have developed that the masses of atom are consistent with respect to each other, as lengthy as we have actually the same variety of each kind of atom. Consider a more macroscopic example. If a sample includes 40 g that Ca, this sample has actually the same variety of atoms together there space in a sample the 7 g that Li. What we need, then, is a number the represents a convenient quantity of atom so we can relate macroscopic quantities of substances. Clearly even 12 atoms are too couple of because atom themselves space so small. We need a number the represents billions and billions that atoms.

Chemists usage the hatchet mole to represent a large number of atoms or molecules. Just as a dozen implies 12 things, a mole (mol) represents 6.022 × 1023 things. The number 6.022 × 1023, called Avogadro’s number after the 19th-century chemist Amedeo Avogadro, is the number we use in chemistry to represent macroscopic quantities of atoms and also molecules. Thus, if we have actually 6.022 × 1023 O atoms, us say we have actually 1 mol that O atoms. If we have 2 mol of Na atoms, we have actually 2 × (6.022 × 1023) Na atoms, or 1.2044 × 1024 Na atoms. Similarly, if we have actually 0.5 mol that benzene (C6H6) molecules, we have 0.5 × (6.022 × 1023) C6H6 molecules, or 3.011 × 1023 C6H6 molecules.


Note

A mole to represent a very large number! If 1 mol of soldier were stack in a column, it can stretch back and forth in between Earth and also the sunlight 6.8 billion times.

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Notice that us are applying the mole unit to different varieties of chemistry entities. In this examples, we cited moles of atom and moles of molecules. Words mole represents a number of things—6.022 × 1023 that them—but does no by itself specify what “they” are. They can be atoms, formula devices (of ionic compounds), or molecules. That information still demands to be specified.

Because 1 H2 molecule includes 2 H atoms, 1 mol the H2 molecule (6.022 × 1023 molecules) has actually 2 mol of H atoms. Using formulas to suggest how many atoms that each element we have actually in a substance, we deserve to relate the variety of moles of molecules to the variety of moles of atoms. For example, in 1 mol the ethanol (C2H6O), we deserve to construct the adhering to relationships (Table 6.1 “Molecular Relationships”):


Table 6.1 molecular Relationships1 Molecule of C2H6O Has1 Mol of C2H6O HasMolecular Relationships
2 C atoms2 mol the C atoms frac2,mol,C,atoms1,mol,C_2H_6O,molecules or frac1,mol,C_2H_6O,molecules2,mol,C,atoms
6 H atoms6 mol that H atoms frac6,mol,H,atoms1,mol,C_2H_6O,molecules or frac1,mol,C_2H_6O,molecules6,mol,H,atoms
1 O atom1 mol of O atoms frac1,mol,O,atoms1,mol,C_2H_6O,molecules or frac1,mol,C_2H_6O,molecules1,mol,O,atoms

Example 1

If a sample is composed of 2.5 mol that ethanol (C2H6O), how countless moles that carbon atoms, hydrogen atoms, and oxygen atom does that have?

Solution


Using the relationship in Table 6.1 “Molecular Relationships”, we use the ideal conversion variable for each element:



Note just how the unit mol C2H6O molecules cancels algebraically. Comparable equations have the right to be constructed for identify the number of H and also O atoms:

2.5, lap————————mol,C_2H_6O,molecules,×,frac6,mol,H,atoms1, lap—————————mol,C_2H_6O,molecules,=,15,mol,H,atoms

2.5, lap————————mol,C_2H_6O,molecules,×,frac1,mol,O,atoms1, lap—————————mol,C_2H_6O,molecules,=2.5,mol,O,atoms


Example 2

How plenty of formula units are present in 2.34 mol that NaCl? How countless ions room in 2.34 mol?

Solution

Typically in a trouble like this, we start with what we room given and apply the proper conversion factor. Here, we are provided a amount of 2.34 mol the NaCl, to which us can apply the an interpretation of a mole as a counter factor:

2.34, lap———-mol,NaCl,×,frac6.022,×,10^23,NaCl,units1, lap————-mol,NaCl,=,1.41,×,10^24,NaCl,units

Because there are two ion per formula unit, over there are

1.41×10^24, lap————-NaCl,units,×,frac2,ions lap————-NaCl,units,=,2.82,×,10^24,ions