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Chapter 10 - How does a chemist measure? How does the chemist count?
2H2(g) + O2 → 2H2O(g)
This reaction requires two molecules of hydrogen and one molecule of oxygen. To carry out this
chemical reaction a chemist must mix hydrogen and oxygen together in the correct ratio (2:1). How does
the chemist know when the correct ratio is present? These molecules are too small to see so we cannot
count them directly. The chemist must use an indirect method of counting.
Example: Your job is to put pennies into rolls. How can you do this?
1. You can physically count out fifty pennies.
2. You could find the average mass of a penny and set the balance to mass the 50 pennies.
3. You could use the plastic rolls with the set volume for fifty pennies.
For a chemist, counting directly is not an option because the particles are too small. The chemist uses
mass (grams) or volume (liters) to count particles indirectly.
Because molecules, atoms and ions are so small the chemist cannot count them directly. The chemist
counts them using the Mole, a word that represents a definite number. The mole is like another word
that represents a number, a dozen, which represent 12. The role of the mole in chemistry is that of
counting ions, atoms or molecules. The chemist can "count" ions, atoms or molecules by weighing very
large numbers of them to get a significant mass. One mole contains as many atoms as there are in 12
grams of carbon-12. There are 6.02 x 1023 atoms of carbon in 12.0 grams of carbon-12. In one mole,
there are 6.02 x 1023 particles; the mole can be treated like a very large dozen. The number 6.02 x 1023 is
called Avogadro’s number, named in honor of Amedeo Avogadro, an Italian chemist who first
suggested it use. The chemist views the Mole as a collection of 6.02 x 1023 representative particles
(symbol - N). Representative particles are the smallest pieces of a substance;
For a molecular compound the representative particle is a molecule.
For an ionic compound the representative particle is a formula unit.
For an element the representative particle is an atom (except for elements that are diatomic molecules).
Molar Mass for Elements
The u (atomic mass unit) is a very small unit of mass and is of no use in the lab, so the chemist uses the
mole, 6.02x1023 atoms. The mass of 1 mole of atoms of an element in grams is called the molar mass,
which is numerically the same as the u (atomic mass unit). The mass in grams of one mole of a
substance is called molar mass. Each element has its own unique molar mass. For example, carbon’s
molar mass is 12.011 g/mol, and hydrogen’s molar mass is 1.0079g/mol, 1 mole of Fe has a mass of
55.847g. 1 mole of carbon has the same number of atoms as 1.0079 grams of hydrogen and 55.847
grams of iron. We can write this as 12.011 g C = 1 mole C; we count by mass. The mass that describes
one mole is the molar mass:
Element
Molar Mass
C =
12.01g
mole
H =
1.0079g
mole
Fe = 55.847g
mole
To see why these elements have different molar masses, we need to remember that the atoms of different
elements contain different numbers of protons, neutrons, and electrons, so they have different masses.
The atomic masses given in the periodic table represent the different weighted average masses of the
naturally occurring atoms (isotopes) of each element. Different atomic masses lead to different molar
masses. (Compare the mass of 50 pennies, 50 nickels and 50 dimes.)
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For example, the atomic mass of hydrogen (1.0079u) shows us that the average mass of hydrogen atoms
is about one twelfth the average mass of carbon atoms (12.011u), so the mass of 6.02 x 1023 hydrogen
atoms (the number of atoms in 1 mole of hydrogen) is about one twelfth the mass of 6.02 x 1023 carbon
atoms (the number of atoms in 1 mole of carbon). Thus, the molar mass of hydrogen is 1.0079g/mol,
compared to carbon’s molar mass of 12.011g/mol.
The number of grams in the molar mass of an element is the same as the atomic mass. Translating
atomic masses into molar masses, you take the atomic mass of an element and change the unit to grams,
which is the mass of one mole of the element. The importance of the molar mass is its use as a
conversion factor. In a conversion factor the top term equals the bottom term, the value of the ratio is 1.
Molar mass of an element = element atomic mass in grams (periodic table)
1 mole element
For example, the atomic mass of the element sodium on the periodic table is 22.98977u, giving a molar
mass of 22.98977g/mol. This molar mass provides two conversion factors for converting between grams
and moles of sodium. Conversion factors merely change the unit not the value of the number. Example:
75 cm x 1m = 0.75m
100cm
22.98977g Na or 1 mole Na Example: 11.4949g Na x 1 mole Na = 0.50000 mole Na
1 mole Na
22.98977g Na
22.9898g Na
Molar Mass for Molecular Compounds
The first step in the determination of the molar mass of a molecular compound is to determine the
molecular mass of the compound, which is the sum of the atomic masses of each atom in the molecule.
This is found by adding the atomic masses of all of the atoms in the molecule.
The chemist studies the composition of matter and knows that water is made up of hydrogen and oxygen
as shown in the formula H2O. This formula shows that one molecule of water contains two atoms of
hydrogen bonded to one oxygen atom. The mass of the water molecule consists of the mass of these
three atoms. The molecular mass of a substance is the total mass of all the atoms given in a formula. The
average atomic mass of atoms, found on the Periodic Table, is given in atomic mass units.
For hydrogen the atomic mass is 1.0079 and for oxygen it is 15.9994. To find the molecular mass of
water:
2 x H = 2 atoms x 1.0079 amu/atom = 2.0158amu
1 x O = 1 atom x 15.9994amu/atom = 15.9994amu
H2O
= 18.0152amu (molecular mass)
The number of grams in one mole of a molecular compound is the same number as its molecular mass.
The molar mass has gram as a unit instead of u (atomic mass unit) for the molecular mass.
Molar mass of a molecular compound = molecular mass in grams
1 mole
For water molar mass = 18.0152g Example: 1.50mole H2O x 18.0152g = 27.0g H2O
1 mole
1 mole
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Chemical composition
To find the number of atoms of each element in a compound use:
Subscript x coefficient = number of atoms
2H2SO4: H = 2 x 2 = 4 atoms; S = 1 x 2 = 2 atoms; O = 4 x 2 = 8 atoms (total for 2 molecules).
If there are parentheses:
Subscript (outside) x subscript (inside) x coefficient = number of atoms
Ca(NO3)2: Ca = 1 x 1 = 1Ca; 2 x 1 x 1 = 2N; O 2 x 3 x 1 = 6O (total for 1 formula unit).
Find the number of atoms or ions in each of these:
Al(NO3)3
(NH4)2CO3
3H2O2
Molar Mass for Ionic Compounds
For an ionic compound the representative particle is the formula unit Al2(SO4)3. The first step in the
determination of the molar mass of an ionic compound is to find the formula mass. To find the formula
mass multiply each element's atomic mass by how many atoms are present in the formula:
2 x Al = 2 atoms x 26.98amu/atom = 53.96amu
3 x S = 3 atoms x 32.06amu/atom =
96.18amu
12 x O = 12 atoms x 16.00amu/atom = 192.00amu
Al2(SO4)3 =
342.14amu (formula mass)
So formula mass = the sum of the atomic masses of each atom in a formula unit
The number of grams in the molar mass of any ionic compound is the same number as the formula mass.
Molar mass of an ionic formula = formula mass expressed in grams
1 mole
The molar mass for Al2(SO4)3 is 342.14 g.
mole
The formula mass of sodium chloride is equal to the sum of the atomic masses of sodium and chlorine,
which can be found on the periodic table.
Formula mass NaCl = 22.9898u + 35.4527u = 58.4425u
The molar mass for NaCl = 58.4425g
1 mole
Practice:
What is the molar mass of Fe2O3?
2 x Fe x 55.85u = 111.70u
3 x O x 16.00u = 48.00u
Total formula mass = 111.70u + 48.00u = 159.70u.
the molar mass of Fe2O3 = 159.70g
mole
Examples:
Calculate the molar mass of the following.
Na2S
N2O4
Ca(NO3)2
C6H12O6
(NH4)3PO4
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Using Molar Mass
1. We can make a conversion factor using the Molar Mass to change grams of a compound to moles
of a compound.
How many moles is 5.69 g of NaOH?
5.69g NaOH x 1 mole = 0.142mole NaOH.
40.0g
How many moles is 4.56 g of CO2?
4.56g CO2 x 1 mole = 0.104 mole CO2.
44.0g
Now you try:
How many moles of H2O in 29.87g?
2. We can make a conversion factor using the Molar Mass to change moles of a compound to grams
of a compound.
Examples
What is the mass of 2.50 moles of carbon? (start with moles and want grams in the end)
2.50mole x 12.01g = 30.0gC
mole
What is the mass of 0.100 moles of magnesium?
0.100 mole Mg x 24.3g = 2.43g of Mg
1 mole
Now you try:
How many grams are in 9.87 moles of H2O?
3. Avogadro’s number can also be used as a conversion factor to change moles to number of particles.
When given the mass of an element convert to moles and then to number.
0.100 mole Mg x 6.02x1023 = 6.02x1022 atoms Mg.
1 mole
How many molecules in 6.8 g of CH4?
6.8g CH4 x 1 mole = 0.425 mole CH4 x 6.02 x 1023 molecules = 2.56 1023 molecules
16.0g
1 mole
What is the mass of 49 molecules of C6H12O6?
49 molecules x 1
mole
= 8.14 x 10 –23 mole x 180.0g = 1.47 x 10-20g
23
6.02 x 10 molecules
1 mole
Try these questions
1. How many molecules of CO2 are the in 4.56 moles of CO2?
2. How many moles of water is 5.87 x 1022 molecules?
3. How many atoms of carbon are there in 1.23 moles of C6H12O6?
4. How many moles are 7.78 x 1024 formula units of MgCl2?
5. How many atoms of lithium in 1.00 g of Li?
Gases and the Mole
Many of the chemicals we deal with are gases. Gases are difficult to mass. As with solids we need to
know how many moles of gas we have. There are three variables that affect the volume of a gas:
temperature, pressure and the number of particles. At higher temperature particles move faster, collide
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harder and spread further apart (become less dense). At lower temperature particles move slower, softer
collisions and move closer together (become more dense).
An increase in pressure squeezes the molecules closer together and a reduction in pressure allows the
particles to move further apart.
When the number of particles increases the particles will occupy a greater volume.
To make a comparison of volumes of gases fair we need to compare the volumes at the same
temperature and pressure. When we have equal volumes at the same pressure and temperature, the equal
volumes contain equal numbers of moles (particles) of gas. Because the temperature, pressure and
moles of gas affect the volume of a gas the chemist will measure the volume of a gas under controlled
conditions. The chemist has set the conditions to measure the volumes of gas to 0ºC and 101kPa, known
as standard temperature and pressure (STP). Since temperature and pressure are held constant the
volume of the gas depends on the number of particles. The chemist counts by using moles, so if 1 mole
of any gas is measured at STP it will have a volume of 22.4L. We an express this as 1 mole of gas =
22.4L at STP or molar volume = 22.4L/mole. Avogadro’s Hypothesis states that at the same temperature
and pressure equal volumes of gas have the same number of particles.
As with molar mass, molar volume can be used as a conversion factor.
22.4L or 1 mole
1 mole
22.4L
Examples:
What is the volume of 4.59 mole of CO2 gas at STP?
You must convert mole to L (volume).
4.59 mole x 22.4L = 102.816L = 103L at STP
1 mole
How many moles is 5.67 L of O2 at STP?
You must convert L (volume) to mole.
5.67L x 1 mole = 0.253125 mole = 0.253mole
22.4L
Here is one for you to try.
What is the volume of 8.8g of CH4 gas at STP?
We have learned how to change:
moles to grams; moles to numbers;
moles to liters
Stoichiometry
Stoichiometry is Greek for “measuring elements” and involves the calculations of quantities in chemical
reactions based on a balanced equation. We can interpret balanced chemical equations several ways.
In terms of Particles
Element - atoms
Molecular compound (nonmetals)- molecules
Ionic Compounds (Metal and nonmetal) - formula units
2H2(g) + O2(g) → 2H2O(l)
Two molecules of hydrogen and one molecule of oxygen form two molecules of water.
2Al2O3(s) → 4Al(s) + 3O2(g)
2 formula units of Al2O3 decompose to yield 4 atoms of solid aluminium metal and 3 molecules of
oxygen gas.
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2Na(s) + 2H2O(l) → 2NaOH(aq) + H2(g)
2 atoms of solid sodium metal react with 2 molecules of liquid water to yield 2 formula units of aqueous
sodium hydroxide and one molecule of hydrogen gas.
We can look at the equation differently
2H2(g) + O2(g) → 2H2O(g)
2 dozen molecules of hydrogen and 1 dozen molecules of oxygen form 2 dozen molecules of water. The
balanced equation shows a count of how many of each we need to have the chemical reaction. The
chemist counts using moles (6.02x1023 particles.
2H2(g) + O2(g) → 2H2O(g)
2 moles x (6.02 x 1023) molecules/mole of hydrogen and 1mole x (6.02 x 1023) molecules/mole of
oxygen react to form 2 mole x (6.02 x 1023) molecules/mole of water.
2 moles of hydrogen gas and 1 mole of oxygen gas react to form 2 moles of water vapour.
In terms of Moles
2Al2O3(s) → 4Al(s) + 3O2(g)
2Na(s) + 2H2O(l) → 2NaOH(aq) + H2(g)
The coefficients tell us how many moles of each reactant and product present in the chemical reaction.
In terms of mass
The law of conservation of mass applies to a balanced chemical equation. The number of atoms of each
element must be the same on each side of the equation; therefore the number of moles of atoms for each
element must be the same on each side of the equation. The particles are too small to count so the
chemist uses mass to indirectly count the particles. One mole of a substance has a definite mass known
as the molar mass. Molar mass can be used as a conversion factor to change moles to grams; the inverse
of molar mass can be used to change grams to moles of substance.
We can check the Law of Conservation of Mass using moles
2H2(g) + O2(g)→ 2H2O(g)
Reactants
Products
2 mole H2 x 2.02g = 4.04g H2
mole
2 mole H2O x 18.02g = 36.04g
1 mole O2 x 32.00g = 32.00g O2
mole
mole
Total mass = 36.04g
Total mass = 36.04g
2H2(g) + O2(g)→ 2H2O(g)
36.04g = 36.04g
Example:
Show that the following equation follows the Law of conservation of mass.
2Al2O3(s) → 4Al(s) + 3O2(g)
Reactants
Products
Al2O3 = 2 x 26.98 + 3 x 16.00 = 101.96g/mole
4 moles Al x 26.98g = 107.92g
2 moles x 101.96g = 203.92g
mole
mole
3 moles O2 x 32.00g = 96.00g
mole
Total mass = 203.92g
Total mass =
203.92g
The balanced chemical equation tells us that 2 moles of Al2O3 will yield 3 moles of O2. When we
compare these numbers we form a mole ratio
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Al2O3 = 2 the ratio could be written as
O2 = 3
O2
3
Al2O3 2
Every time we use 2 moles of Al2O3 we make 3 moles of O2.
How many moles of O2 are produced when 4.0 moles of Al2O3 decompose?
From the balanced chemical equation:
2Al2O3(s) → 4Al(s) + 3O2(g)
The unknown is O2 so the ratio is set up with the unknown as the top term and the known as the bottom
term. Use x as the unknown and the known value as the bottom term to set up a proportion:
O2 = 3 = x mole
Al2O3 2
4.0 mole
Solve for x.
x = 6.0 mole O2.will be produced when 4.0 moles of Al2O3 decompose.
Your turn #1
2C2H2(g) + 5O2(g) → 4CO2(g) + 2H2O(g)
If 3.84 moles of C2H2 are burned, how many moles of O2 are needed?
How many moles of C2H2 are needed to produce 8.95 mole of H2O?
If 2.50 moles of C2H2 are burned, how many moles of CO2 are formed?
Answer to your turn #1
O2 = 5
x mole
C2H2 2
3.84 mole
9.6 mole O2 needed to burn 3.84 mole C2H2.
C2H2 = 2
x mole
H2O
2
8.95 mole
8.95 mole C2H2 needed to produce 8.95 moles of H2O.
CO2 = 4
x mole
C2H2
2
2.50 mole
5.00 mole CO2 produced when 2.50 moles of C2H2. react
In the laboratory the chemist uses mass to obtain the correct amount (number) of reactants for a
chemical reaction. The questions that the chemist asks are:
How much do you make? or How much do you need?
The balanced chemical equation gives us the number of moles of each substance in the reaction but we
can’t measure moles. What does the chemist do? Since we use mass the chemist converts grams to
moles, then does the math with the mole ratio from the balanced equation and then converts the moles
back to grams.
Example:
If 10.1 g of Fe are added to a solution of copper(II) sulphate, how much solid copper would form?
Fe(s) + CuSO4(aq) → Fe2(SO4)3(aq) + Cu(s) (need to balance)
2Fe(s) + 3CuSO4(aq) → Fe2(SO4)3(aq) + 3Cu(s) (now balanced)
10.1 g Fe x
Cu = 3 = x mole
Fe 2
0.181mole
1 mole Fe
55.85 g Fe
=
0.181 mole Fe
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x = 0.272 mole Cu(s)
0.272 mole Cu(s) x 63.5g Cu = 17.3g Cu(s)
1 mole
10.1 g of Fe are added to a solution of copper(II) sulphate will produce 17.3g Cu(s)
Your turn #2
1. To make silicon for computer chips chemist use this reaction
SiCl4(aq) + 2Mg(s) → 2MgCl2(aq) + Si(s)
(a) How many grams of Mg are needed to make 9.3 g of Si?
(b) How many grams of SiCl4 are needed to make 9.3 g of Si?
(c) How many grams of MgCl2 are produced along with 9.3 g of silicon?
2. The U.S. Space Shuttle boosters use this reaction
3Al(s) + 3NH4ClO4(s) → Al2O3(s) + AlCl3(s) + 3NO(g) + 6H2O(g)
(a) How much Al must be used to react with 652 g of NH4ClO4 ?
(b) How much water is produced?
(c) How much AlCl3?
Answer to your turn #2
1. (a)
9.3g Si x 1 mole = 0.33mole Si
28.09g
Mg = 2 = x mole
Si
1
0.33 mole
x = 0.66 mole x 24.3g = 16.0g Mg
1 mole
(b)
SiCl4 = 1 = x mole
Si
1
0.33 mole
x = 0.33 mole SiCl4 x 170.1g = 56.1g SiCl4
1 mole
(c)
MgCl2 = 2 = x mole
Si
1 0.33 mole
x = 0.66 mole MgCl2 x 95.3g = 62.9g MgCl2
1 mole
2. 5.55 mole NH4ClO4
a. 149.7g Al
b. 200.g H2O
c. 247g AlCl3
Some chemical reactions involve gases so we can change litres of a gas to moles at STP because 1 mole
of any gas = 22.4 L of a gas at STP (0ºC 101kPa)
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If 6.45 grams of water are decomposed, how many litres of oxygen will be produced at STP?
Start with the balanced chemical equation
2H2O(l) → 2H2(g) + O2(g)
6.45g x 1 mole = 0.358 mole H2O
18.02g
O2 = 1 = x mole
H2O
2
0.358 mole
x = 0.179 mole O2(g) x 22.4L at STP = 4.01L O2(g) at STP
1 mole
Your Turn #3
(a) How many litres of CO2 at STP are produced from the complete combustion of 23.2g C4H10?
(b) What volume of oxygen will be required?
Answer your turn # 3
(a)
2C4H10(g) + 13O2(g) → 8CO2(g) + 10H2O(g)
23.2g C4H10 x 1 mole = 0.399mole C4H10
58.1g
CO2 = 8 = x mole
C4H10 2
0.399 mole
x = 1.60 mole CO2 x 22.4L at STP = 35.8L CO2 at STP
1 mole
(b)
O2 = 13 = x mole
C4H10 2
0.399 mole
x = 2.59mole O2 x 22.4L at STP = 58.0L O2 at STP
1 mole
Gases and Reactions
Balanced chemical equations give mole ratio of reactants and products. Avogadro told us equal volumes of gas, at
the same temperature and pressure contain the same number of particles. Moles are numbers of particles. You can
treat mole ratio as volume ratio if the substances are gases, as long as you keep the temperature and pressure the
same. Equal volumes have equal number of moles.
Example
2H2O(l) → 2H2(g) + O2(g) When gas volumes are measured under the same conditions - mole ratio
can also be used as volume ratio.
H2 = 2 = 44.8L
O2 1
22.4L
at STP
Your turn #4
1. How many litres of CH4 at STP are required to completely react with 17.5 L of O2?
CH4(g) + 2O2(g) → CO2(g) + 2H2O(g)
2. How many litres of CO2 at STP are produced by completely burning 18.8 L of CH4?
Answer your turn #4
1. CH4(g) + 2O2(g) → CO2(g) + 2H2O(g)
CH4 = 1 = x litre
at STP
O2
2 17.5L
x = 8.75L at STP
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CH4(g) + 2O2(g) → CO2(g) + 2H2O(g)
2.
CO2 = 1 = x litre
CH4 1 18.8L
x = 18.8L at STP
at STP
Show how you arrive at your answer.
1.
How many hydrogen are indicated: (NH4)2CO3
2.
How many oxygen are indicated: 3Ca(NO3)2
3.
a)
b)
c)
d)
Give the molar masses of the following compounds:
sodium fluoride (NaF)
potassium hydroxide (KOH)
manganese (IV) oxide (MnO2)
magnesium phosphate (Mg3(PO4)2)
4.
Write the formula for oxygen gas.
a) How many atoms are represented by the formula for oxygen gas?
e) What is the mass of Avogadro number of oxygen molecules?
5.
Determine the mass in grams of Avogadro number of C12H22O11 (sucrose) molecules.
6.
You need 0.0100 mole of lead (II) carbonate. How much should you mass on the scale?
7.
Alanine, C3H7NO2, is a compound, which is one of the building blocks of protein. What is
the molar mass of Alanine?
8.
The average glass of water has a capacity of 500.mL. Water has a density of 1.00 g/mL.
What mass of water is present in the full glass?
How many moles of water are in the glass?
How many water molecules are in the full glass?
a.
b.
c.
9.
How many ammonium ions are in 0.500 mol ammonium phosphate, (NH4)3PO4?
10.
a.
b.
c.
Give the molar mass for each of the following:
Iron
Carbon tetrachloride
Sodium carbonate
11.
Find the mass of each of the following:
a.
4.0 mole sulphur
b.
2.25 mole sulphuric acid
c.
0.0015 mole ammonium carbonate
12.
Find the number of moles for each of the following:
a. 72.0g of oxygen gas
b. 125g aluminium
c. 1.45 x 102g ammonium nitrate
13.
Calculate the following:
The volume at STP for 1.75 mole of oxygen gas
The volume at STP for 25.0g of methane gas (CH4)
The number of moles in 18.5L of HCL at STP
The mass of 15.6L of propane (C3H8) at STP
a.
b.
c.
d.