How Many Atoms Are Needed To Form A Molecule

12.2: The Mole

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Learning Objectives

• To define the mole unit.

Figure \(\PageIndex{ane}\) shows that nosotros need 2 hydrogen atoms and 1 oxygen atom to make 1 water molecule. If nosotros want to make 2 h2o molecules, nosotros volition need 4 hydrogen atoms and 2 oxygen atoms. If we want to make 5 molecules of water, nosotros need ten hydrogen atoms and 5 oxygen atoms. The ratio of atoms we volition demand to make whatever number of water molecules is the same: 2 hydrogen atoms to 1 oxygen atom.

Figure \(\PageIndex{i}\) Water Molecules. The ratio of hydrogen atoms to oxygen atoms used to brand water molecules is always 2:1, no matter how many water molecules are being made.

One problem we accept, notwithstanding, is that information technology is extremely difficult, if not impossible, to organize atoms i at a time. As stated in the introduction, nosotros deal with billions of atoms at a time. How tin nosotros proceed track of then many atoms (and molecules) at a time? We do it by using mass rather than by counting individual atoms.

A hydrogen atom has a mass of approximately ane u. An oxygen atom has a mass of approximately xvi u. The ratio of the mass of an oxygen atom to the mass of a hydrogen cantlet is therefore approximately xvi:1.

If we have ii atoms of each chemical element, the ratio of their masses is approximately 32:2, which reduces to 16:i—the same ratio. If we have 12 atoms of each element, the ratio of their total masses is approximately (12 × 16):(12 × 1), or 192:12, which also reduces to 16:i. If nosotros have 100 atoms of each element, the ratio of the masses is approximately 1,600:100, which again reduces to sixteen:1. Equally long every bit we have equal numbers of hydrogen and oxygen atoms, the ratio of the masses will always be 16:1.

The same consistency is seen when ratios of the masses of other elements are compared. For instance, the ratio of the masses of silicon atoms to equal numbers of hydrogen atoms is always approximately 28:1, while the ratio of the masses of calcium atoms to equal numbers of lithium atoms is approximately 40:seven.

And so we have established that the masses of atoms are abiding with respect to each other, equally long as nosotros have the same number of each type of cantlet. Consider a more macroscopic example. If a sample contains 40 grand of Ca, this sample has the same number of atoms as at that place are in a sample of 7 thousand of Li. What we need, and then, is a number that represents a convenient quantity of atoms so nosotros can relate macroscopic quantities of substances. Conspicuously even 12 atoms are likewise few because atoms themselves are so small. Nosotros need a number that represents billions and billions of atoms.

Chemists utilize the term 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 later the 19th-century chemist Amedeo Avogadro, is the number we utilise in chemical science to represent macroscopic amounts of atoms and molecules. Thus, if we have six.022 × 10²³ O atoms, we say we have ane mol of O atoms. If we take 2 mol of Na atoms, nosotros have 2 × (half dozen.022 × 10²³) Na atoms, or 1.2044 × 10²⁴ Na atoms. Similarly, if we have 0.5 mol of benzene (C₆H_{half dozen}) molecules, we have 0.5 × (6.022 × 10²³) C_viH_half-dozen molecules, or iii.011 × 10²³ C₆H_half-dozen molecules.

A mole represents a very large number! If 1 mol of quarters were stacked in a cavalcade, it could stretch back and forth between Earth and the sun 6.8 billion times.

Notice that we are applying the mole unit to unlike types of chemic entities. In these examples, we cited moles of atoms and moles of molecules. The word mole represents a number of things—6.022 × 10²³ of them—but does not by itself specify what "they" are. They can be atoms, formula units (of ionic compounds), or molecules. That information still needs to exist specified.

Because 1 H_ii molecule contains ii H atoms, one mol of H₂ molecules (6.022 × 10²³ molecules) has 2 mol of H atoms. Using formulas to indicate how many atoms of each element we have in a substance, nosotros tin chronicle the number of moles of molecules to the number of moles of atoms. For example, in ane mol of ethanol (C₂H_{half dozen}O), we can construct the following relationships (Table \(\PageIndex{1}\)):

Table \(\PageIndex{i}\): Molecular Relationships

1 Molecule of \(C_2H_6O\) Has	ane Mol of \(C_2H_6O\) Has	Molecular Relationships
two C atoms	ii mol of C atoms	\(\mathrm{\dfrac{2\: mol\: C\: atoms}{1\: mol\: C_2H_6O\: molecules}}\) or \(\mathrm{\dfrac{ane\: mol\: C_2H_6O\: molecules}{2\: mol\: C\: atoms}}\)
6 H atoms	6 mol of H atoms	\(\mathrm{\dfrac{6\: mol\: H\: atoms}{ane\: mol\: C_2H_6O\: molecules}}\) or \(\mathrm{\dfrac{1\: mol\: C_2H_6O\: molecules}{half dozen\: mol\: H\: atoms}}\)
1 O atom	1 mol of O atoms	\(\mathrm{\dfrac{1\: mol\: O\: atoms}{ane\: mol\: C_2H_6O\: molecules}}\) or \(\mathrm{\dfrac{1\: mol\: C_2H_6O\: molecules}{1\: mol\: O\: atoms}}\)

The post-obit example illustrates how we can use these relationships every bit conversion factors.

Example \(\PageIndex{1}\)

If a sample consists of 2.5 mol of ethanol (C₂H_viO), how many moles of carbon atoms, hydrogen atoms, and oxygen atoms does it have?

SOLUTION

Using the relationships in Tabular array \(\PageIndex{1}\), we utilise the appropriate conversion gene for each element:

Notation how the unit of measurement mol C ₂ H ₆ O molecules cancels algebraically. Like equations tin can exist synthetic for determining the number of H and O atoms:

\(\mathrm{ii.five\: mol\: C_2H_6O\: molecules\times\dfrac{6\: mol\: H\: atoms}{1\: mol\: C_2H_6O\: molecules}=15\: mol\: H\: atoms}\)

\(\mathrm{2.5\: mol\: C_2H_6O\: molecules\times\dfrac{one\: mol\: O\: atoms}{1\: mol\: C_2H_6O\: molecules}=2.5\: mol\: O\: atoms}\)

Exercise \(\PageIndex{ane}\)

If a sample contains six.75 mol of Na₂So₄, how many moles of sodium atoms, sulfur atoms, and oxygen atoms does it accept?

The fact that 1 mol equals 6.022 × 10²³ items tin can likewise exist used every bit a conversion cistron.

Case \(\PageIndex{2}\)

How many formula units are nowadays in 2.34 mol of NaCl? How many ions are in 2.34 mol?

SOLUTION

Typically in a problem like this, we showtime with what nosotros are given and apply the appropriate conversion factor. Here, nosotros are given a quantity of 2.34 mol of NaCl, to which we can apply the definition of a mole equally a conversion factor:

\(\mathrm{two.34\: mol\: NaCl\times\dfrac{half-dozen.022\times10^{23}\: NaCl\: units}{ane\: mol\: NaCl}=1.41\times10^{24}\: NaCl\: units}\)

Because there are 2 ions per formula unit, there are

\(\mathrm{1.41\times10^{24}\: NaCl\: units\times\dfrac{ii\: ions}{NaCl\: units}=2.82\times10^{24}\: ions}\)

in the sample.

Exercise \(\PageIndex{two}\)

How many molecules are nowadays in 16.02 mol of C₄H_ten? How many atoms are in sixteen.02 mol?

Concept Review Exercise

1. What is a mole?

Answer

1. A mole is 6.022 × 10²³ things.

Key Takeaway

• A mole is 6.022 × x²³ things.

Exercises

1. How many dozens are in 1 mol? Express your answer in proper scientific notation.

2. A gross is a dozen dozen, or 144 things. How many gross are in one mol? Express your answer in proper scientific notation.

3. How many moles of each blazon of cantlet are in 1.0 mol of C_viH₁₂O₆?

4. How many moles of each blazon of cantlet are in i.0 mol of Grand_twoCr₂O_vii?

5. How many moles of each type of atom are in 2.58 mol of Na_twoSo₄?

6. How many moles of each type of atom are in 0.683 mol of C₃₄H₃₂FeN₄O₄? (This is the formula of heme, a component of hemoglobin.)

7. How many molecules are in sixteen.eight mol of H₂O?

8. How many formula units are in 0.778 mol of atomic number 26(3) nitrate?

9. A sample of gold contains 7.02 × 10²⁴ atoms. How many moles of aureate is this?

10. A flask of mercury contains 3.77 × 10²² atoms. How many moles of mercury are in the flask?

11. An intravenous solution of normal saline may contain i.72 mol of sodium chloride (NaCl). How many sodium and chlorine atoms are present in the solution?

12. A lethal dose of arsenic is one.00 × 10²¹ atoms. How many moles of arsenic is this?

Answers

1. v.018 × ten²² dozens

3. half dozen.0 mol of C atoms, 12.0 mol of H atoms, and six.0 mol of O atoms

5. five.16 mol of Na atoms, 2.58 mol of South atoms, and 10.32 mol of O atoms

7. 1.012 × 10²⁵ molecules

9. 11.7 mol

11. 1.04 × 10²⁴ Na atoms and 1.04 × ten²⁴ Cl atoms

Source: https://chem.libretexts.org/Courses/Modesto_Junior_College/Chemistry_150_-_Bunag/Textbook_for_Chemistry_150/12%3A_Quantities_in_Chemical_Reactions/12.02%3A_The_Mole

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