Summary (CAIE) Cambridge A Level Chemistry (9701) - Stoichiometry
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Course
Chemistry
Institution
Book
Chemistry
A complete, broad and sufficiently detailed explanation of the theory of stoichiometry, including: definition of the mole, molar mass of molecule, converting the mass of a molecular substance to moles, number of particles or volume of gas at standard temperature and pressure, writing balanced equat...
Cambridge International AS and A Level Chemistry (9701)
UI CHEM 006
Study Notes & Examples with Solutions
Stoichiometry
,1. Atomic Mass
The mass of an atom depends on the number of electrons, protons, and neutrons it
contains. By international agreement, atomic mass is the mass of the atom in atomic
mass unit (amu). One atomic mass unit is defined as a mass exactly equal to one-
twelfth the mass of one carbon-12 atom. Carbon-12 is the carbon isotope that has six
protons and six neutrons. Setting the atomic mass of carbon-12 at 12 amu provides the
standard for measuring the atomic mass of the other elements. For example, on average,
a hydrogen atom is only 8.400 percent as massive as the carbon-12 atom. Thus, if the
mass of onecarbon-12 atom is exactly 12 amu, the atomic mass of hydrogen must be
0.084 x 12.00 amu or 1.008 amu. Similar calculations show that the atomic mass of iron
is 55.85 amu. Thus, although we do not know just how much an average iron atom’s mass
is, we know that it is approximately 56 times as massive as a hydrogen atom.
Average Atomic Mass
Most naturally occurring elements (including carbon) have more than one isotope. This
means that when we measure the atomic mass of an element, we must generally settle
for the average mass of the naturally occurring mixture of isotopes. For example, the
natural abundance of carbon-12 and carbon-13 are 98.90 percent and 1.10 percent,
respectively. The atomic mass of carbon-13 has been determined to be 13.00335 amu.
Thus, the average atomic mass of carbon can be calculated as follows:
When we say that the atomic mass of carbon is 12.01 amu, we are referring to the
average value.
Example
Naturally occurring chlorine is a mixture of two isotope. In every sample of this element,
75.77% of the atoms are 35Cl and 24.23% are atoms of 37Cl. The accurately measured
atomic mass of 35Cl is 34.9689 amu and that of 37Cl is 36.9659 amu. From these data,
calculate the average atomic mass of chlorine.
Solution
In a sample of chlorine, 75.77% of the mass is contributed by atoms of 35Cl and 24.23%
are atoms of 37Cl. Thus, when we calculate the mass of the “average atom” we have to
take into account both of the masses of the isotopes and their relative abundances.
Mass contribution of 35Cl = 34.9689 amu x 75.77% 35Cl = 26.496 amu
, Mass contribution of 37Cl = 36.9659 amu x 24.23% 37Cl = 8.9568 amu
Now we add these contributions to give the total mass of the “average atom.”
The amount of substance does not refer to the mass or volume of the sample but it does
refer to the number of atoms, molecules, or formula units, etc. in the sample. Exactly one
mole (mol) is defined as a number equal to the number of atoms in exactly 12 grams of
12C atoms. Based on this definition and the fact that the average atomic masses in the
periodic table are relative values, we can deduce that we will have a mole of atoms of
any element if weigh an amount equal to the atomic mass in gram units (this often called
the gram atomic mass).
1 mole of element X = gram atomic mass of X
For example, the atomic mass of sulfur is 32.06 amu and one mole of sulfur will weigh
32.06 g and it will have as many atoms as exactly 12 g of carbon-12.
The Mole Concept Applied to Compounds
The gram molecular mass of a molecular substance (the mass in grams equal to the
molecular mass) is also equal to one mole of those molecules.
1 mole of molecule X = gram molecular mass of X
For example, the molecular mass of water is 18.02 amu, the sum of the atomic masses
of two H atoms and one O atom. Similarly, the gram formula mass of an ionic compound
is the sum of the atomic masses of all the atoms in the formula of an ionic compound
expressed with units in grams.
1 mole of ionic compound X = gram formula mass of X
The ionic compound Al2O3 has two aluminum atoms with an atomic mass of 26.98 amu
each and three oxygen atoms with a mass of 16.00 amu each. This adds up to 101.96
amu, and one mole of Al2O3 has a gram formula mass of 101.96 g.
To simplify, we will often use the following relationship between moles and mass unless
one of the other, equivalent, definitions provides more clarity.
, 1 mole of X = gram molar of X
Example
1. In an experiment to prepare TiO2, we start with a 23.5 g sample of titanium. How
many moles of Ti do we have?
Solution
We have a tool for converting the mass into moles that states 1 mol X is equal to the
atomic mass of X with gram units. Now we make it specific for Titanium by replacing
X with the symbol for titanium and entering the atomic mass of Ti to get
1 mol Ti = 47.867 g Ti
Start by setting up the problem in the form of an equation showing the number and
its units that we start with and the units we want when we are finished.
23.5 g Ti = ? mol Ti
Now use the quality between mass and moles to set up the ratio that will cancel the
grams of titanium as shown below
1 𝑚𝑜𝑙 𝑇𝑖
23.5 g Ti x ( ) = 0.491 mol Ti
47.867 𝑔 𝑇𝑖
2. We need 0.254 moles of FeCl3 for a certain experiment. How many grams do we
need to weigh?
Solution
We need the tool for calculating the molar mass of FeCl3. That is the sum of masses
of one mole of iron atoms and three moles of chlorine atoms.
Molar mass FeCl3 = 55.845 g/mol + (3 x 35.453 g/mol) = 162.204 g/mol
Now the tool that represents the quality between mass and moles can be written:
1 mol FeCl3 = 162.204 g FeCl3
Then we construct the conversion factor from the quality between mass and moles
to perform the conversion:
𝟏𝟔𝟐.𝟐𝟎𝟒 𝒈 𝑭𝒆𝑪𝒍𝟑
0.254 mol FeCl3 x ( ) = 41.2 g FeCl3
𝟏 𝒎𝒐𝒍 𝑭𝒆𝑪𝒍𝟑
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