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

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Figure 6.1 Water Molecules. The proportion of hydrogen atom to oxygen atoms provided to do water molecule is always 2:1, no issue how numerous water molecules are being made.


One difficulty we have, however, is that it is exceptionally difficult, if no impossible, come organize atoms one at a time. As declared in the introduction, we attend to billions of atom at a time. How deserve to we store track the so plenty of atoms (and molecules) at a time? We execute it by using mass rather than by counting individual atoms.

A hydrogen atom has actually a massive of roughly 1 u. An oxygen atom has actually a fixed of approximately 16 u. The ratio of the massive of an oxygen atom to the mass of a hydrogen atom is therefore approximately 16:1.

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

The exact same consistency is seen once ratios that the masses the other facets are compared. For example, the proportion of the masses of silicon atom to equal numbers of hydrogen atom is constantly approximately 28:1, if the ratio of the masses of calcium atom to same numbers of lithium atoms is roughly 40:7.

So we have developed that the masses of atom are continuous with respect to every other, as long as we have actually the same number of each form of atom. Take into consideration a much more macroscopic example. If a sample contains 40 g the Ca, this sample has actually the same number of atoms together there are in a sample that 7 g that Li. What we need, then, is a number the represents a convenient quantity of atoms so we can relate macroscopic amounts of substances. Clearly even 12 atoms are too few because atoms themselves are so small. We need a number that represents billions and also billions that atoms.

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


Note

A mole represents a very big number! If 1 mol of quarters were stacked in a column, it could stretch ago and forth between Earth and also the sunlight 6.8 billion times.

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Notice that us are applying the mole unit come different species of chemical entities. In these examples, us cited mole of atoms and moles of molecules. The word mole to represent a variety of things—6.022 × 1023 that them—but does no by chin specify what “they” are. They have the right to be atoms, formula systems (of ionic compounds), or molecules. That information still needs to be specified.

Because 1 H2 molecule has 2 H atoms, 1 mol that H2 molecule (6.022 × 1023 molecules) has 2 mol of H atoms. Using formulas to suggest how many atoms of each aspect we have in a substance, we deserve to relate the variety of moles of molecule to the number of moles of atoms. Because that example, in 1 mol of 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 the C2H6O HasMolecular Relationships
2 C atoms2 mol that 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 of 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 the 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 many moles the carbon atoms, hydrogen atoms, and also oxygen atoms does that have?

Solution


Using the relationships in Table 6.1 “Molecular Relationships”, we apply the proper conversion aspect for each element:



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

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

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


Example 2

How numerous formula devices are existing in 2.34 mol the NaCl? How plenty of ions room in 2.34 mol?

Solution

Typically in a problem like this, we begin with what we room given and apply the proper conversion factor. Here, we are given a quantity of 2.34 mol the NaCl, come which we can use the an interpretation of a mole together a conversion factor:

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

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

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