How Many Hydrogen Atoms Are in 2 Mol of H2o

How Many Hydrogen Atoms Are in 2 Mol of H2o

6.one
The Mole

Learning Objective

  1. Ascertain the mole unit.

Figure 6.1 “Water Molecules” shows that we need two hydrogen atoms and i oxygen atom to make ane water molecule. If we want to make 2 h2o molecules, we will need 4 hydrogen atoms and two oxygen atoms. If we want to make 5 molecules of water, we demand 10 hydrogen atoms and 5 oxygen atoms. The ratio of atoms we will need to make any number of water molecules is the same: two hydrogen atoms to 1 oxygen atom.

Figure 6.1
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 beingness fabricated.

One problem we have, however, is that it is extremely difficult, if not incommunicable, to organize atoms one at a time. As stated in the introduction, we bargain with billions of atoms at a fourth dimension. How can we go on track of so 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 1 u. An oxygen atom has a mass of approximately sixteen u. The ratio of the mass of an oxygen atom to the mass of a hydrogen atom is therefore approximately 16:ane.

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

The aforementioned consistency is seen when ratios of the masses of other elements are compared. For example, 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 xl:7.

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So we accept established that the masses of atoms are abiding with respect to each other, as long equally we have the same number of each type of atom. Consider a more macroscopic example. If a sample contains twoscore g of Ca, this sample has the aforementioned number of atoms equally there are in a sample of 7 one thousand of Li. What nosotros need, then, is a number that represents a user-friendly quantity of atoms so we can relate macroscopic quantities of substances. Conspicuously even 12 atoms are as well few because atoms themselves are so small. We need a number that represents billions and billions of atoms.

Chemists use the term
moleA number of things equal to 6.022 × 1023
items.


to represent a big number of atoms or molecules. Only equally a dozen implies 12 things, a mole (mol) represents 6.022 × 1023
things. The number 6.022 × 1023, chosen
Avogadro’s numberThe value 6.022 × x23.

subsequently the 19th-century chemist Amedeo Avogadro, is the number nosotros use in chemistry to represent macroscopic amounts of atoms and molecules. Thus, if we have 6.022 × ten23
O atoms, we say we have ane mol of O atoms. If we have ii mol of Na atoms, we take two × (6.022 × 1023) Na atoms, or 1.2044 × 1024
Na atoms. Similarly, if we have 0.v mol of benzene (Chalf dozenH6) molecules, we have 0.five × (six.022 × 1023) C6Hsix
molecules, or 3.011 × 1023
C6H6
molecules.

Note

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

Notice that we are applying the mole unit of measurement 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—half dozen.022 × 1023
of them—but does not past itself specify what “they” are. They tin be atoms, formula units (of ionic compounds), or molecules. That information withal needs to exist specified.

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Because 1 H2
molecule contains 2 H atoms, ane 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 can relate the number of moles of molecules to the number of moles of atoms. For case, in 1 mol of ethanol (C2Hhalf-dozenO), we can construct the following relationships (Table half-dozen.i “Molecular Relationships”):

Table 6.1
Molecular Relationships

one Molecule of CiiHhalf-dozenO Has 1 Mol of C2H6O Has Molecular Relationships
ii C atoms 2 mol of C atoms





ii
 mol C atoms




i mol C

two


H
6

O molecules





or





ane


 mol C

2


H
6

O molecules


ii mol C atoms




6 H atoms half dozen mol of H atoms





6
 mol H atoms




1 mol C

two


H
6

O molecules





or





1


 mol C

ii


H
half dozen

O molecules


six mol H atoms




1 O atom 1 mol of O atoms





1
 mol O atoms




1 mol C

2


H
6

O molecules





or





1


 mol C

ii


H
six

O molecules


1 mol O atoms




The following example illustrates how we can use these relationships every bit conversion factors.

Example i

If a sample consists of two.5 mol of ethanol (C2H6O), how many moles of carbon atoms, hydrogen atoms, and oxygen atoms does it have?

Solution

Using the relationships in Table 6.ane “Molecular Relationships”, we employ the appropriate conversion factor for each chemical element:

Notation how the unit
mol C

2

H

6

O molecules
cancels algebraically. Like equations can exist constructed for determining the number of H and O atoms:



2
.five




 mol C

2


H
6

O molecules


×


six mol H atoms


one




 mol C

2


H
6

O molecules




=
xv mol H atoms





2
.v




 mol C

ii


H
vi

O molecules


×


1 mol O atoms


1




 mol C

2


H
half dozen

O molecules




=
2.five
 mol O atoms


Skill-Building Exercise

  1. If a sample contains half-dozen.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 × x23
items tin can also be used as a conversion factor.

Example 2

How many formula units are nowadays in 2.34 mol of NaCl? How many ions are in ii.34 mol?

Solution

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



2.34


 mol NaCl


×


6
.022
×


ten


23


 NaCl units


1


 mol NaCl




=
i.41
×


x


24


 NaCl units


Because in that location are two ions per formula unit, there are



1.41
×


x


24




 NaCl units


×


2 ions




NaCl units




=
two.82
×


10


24


 ions


in the sample.

Skill-Edifice Exercise

  1. How many molecules are present in 16.02 mol of CivHx? How many atoms are in 16.02 mol?

Concept Review Exercise

  1. What is a mole?

Answer

  1. A mole is vi.022 × 1023
    things.

Fundamental Takeaway

  • A mole is 6.022 × 1023
    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 1 mol? Express your answer in proper scientific notation.

  3. How many moles of each blazon of atom are in i.0 mol of Chalf-dozenH12Ovi?

  4. How many moles of each type of atom are in 1.0 mol of K2Cr2O7?

  5. How many moles of each type of atom are in ii.58 mol of Na2SO4?

  6. How many moles of each type of atom are in 0.683 mol of C34H32FeNivO4? (This is the formula of heme, a component of hemoglobin.)

  7. How many molecules are in xvi.viii mol of H2O?

  8. How many formula units are in 0.778 mol of iron(III) nitrate?

  9. A sample of gold contains 7.02 × 1024
    atoms. How many moles of gold 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 comprise 1.72 mol of sodium chloride (NaCl). How many sodium and chlorine atoms are nowadays in the solution?

  12. A lethal dose of arsenic is 1.00 × ten21
    atoms. How many moles of arsenic is this?

Answers

  1. 5.018 × ten22
    dozens

  2. 6.0 mol of C atoms, 12.0 mol of H atoms, and 6.0 mol of O atoms

  3. 5.16 mol of Na atoms, 2.58 mol of Due south atoms, and 10.32 mol of O atoms

  4. 1.012 × 1025
    molecules

  5. 11.7 mol

  6. 1.04 × 1024
    Na atoms and 1.04 × 1024
    Cl atoms

How Many Hydrogen Atoms Are in 2 Mol of H2o

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