Chemical Calculations
Chapter 9
Outline
•
The Mole
•
Stoichemistry
Avogadro’s Number
•
When using samples in the laboratory it is impossible
to work with a single molecule or atom of a substance
•
Scientist use a derived unit to make counting atoms
more practical
•
The mole (mol) is the amount of substance contained in
6.022 x 1023 particles.
•
The number 6.022 x 1023 is named for an Italian
physicist Amedeo Avogadro and is referred to as
Avogadro’s number (Na)
Avogadro’s Number and the
Mole
•
1 mol of He atoms = 6.022 x 1023 He atoms
•
1 mol of H2O molecules = 6.022 x 1023 H2O molecules
•
1 mol of NaCl formula units = 6.022 x 1023 NaCl formula
units
•
Example: How many atoms are in a 4.5 mol sample of
helium?
Molar Mass
•
Just because you have the same quantity of
something does not mean that the masses of the
groups are the same
•
Similarly, 1 mol of one substance is not going to
contain the same mass as 1 mol of another
•
The molar mass is the mass of one mole of any pure
substance and can be found by converting the object’s
mass from atomic mass units to grams
Molar Mass
•
1 atomic mass unit is equal to 1 g
•
So in 1 mol of Carbon-12 there are 12 grams of carbon
but in 1 mol of hydrogen atoms there is 1 gram
•
Example: Calculate the mass of 0.500 mol of helium
atoms
Chemistry
×
Mass
(grams)
1 mol
molar mass
Moles
×
×
molar mass
1 mol
1 mol
NA units
×
NA units
1 mol
No. of
particles
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Molar Mass
•
Example: How many atoms are in 33.3 mg of gold?
Compounds and the Mole
•
Compounds contain two or more bonded atoms that
behave as one unit
•
The masses of a compound can be found by simply
adding the masses of the atoms that make up the
compound
•
For example, 1 mol of water has a mass of 2(1.008 u) +
1(16.00 u) = 18.02 u
•
This can also be expressed as grams/mol because 1
u=1 g
Compounds and the Mole
•
Example: Find the molar mass of Al2(SO4)3
Types of Formulas
•
Structural formula-shows the types of atoms involved,
the exact composition of each molecule, and the
arrangement of chemical bonds
•
Molecular formula-shows the types and numbers of
atoms involved as they appear in the molecule
•
Empirical formula-tell what elements are present and
give the simplest whole-number ratio of atoms in the
compound
Types of Formulas
•
Identify which type of formula is shown:
•
C6H12O6
•
CH2O
Percent Composition
•
Percent composition describes the mass composition
of a compound by showing what percentage of its
total mass comes from each element
•
Percent composition gives more weight to those
elements that make up most of the mass of the
compound. Think about water…
•
To find percent composition you divide part/whole and
multiply by 100
Percent Composition
Examples
•
A laboratory analysis of a 30.00 g sample of Al2(SO4)3
showed that it contained 4.731 g of aluminum, 8.436 g
of sulfur, and 16.833 g of oxygen. What is the percent
composition of this compound?
•
Find the percent composition of Al2(SO4)3
Calculations with Empirical
Formulas
•
To calculate the empirical formula with percent composition
data:
•
Change the percent composition to mass composition
•
Convert mass composition to the number of moles of the
sample
•
Divide each value of the number of moles by the smallest of
the values
•
Multiply each number by the same smallest while number so
the results are all whole numbers or round them up or down if
they are close to a whole number
Chart
Percent
composition
Mass
composition
(for a 100 g
sample)
Mole
composition
Mole
ratio
Empirical
formula
75.00% C
25.00% H
75.00 g C
25.00 g H
6.245 mol C
24.80 mol H
1 mol C
4 mol H
CH4
Chemistry
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Example
•
A laboratory analysis of an unknown gas has
determined that the gas is 72.55% oxygen and 27.45%
carbon by mass. What is the empirical formula of the
compound?
Example
•
A 5.00 g sample of an unknown compound contains
1.844 g of nitrogen and 3.156 g of oxygen. Find the
empirical formula
Example
•
Caffeine, in coffee and some carbonated beverages, is
5.170% hydrogen, 16.49% oxygen, 28.86% nitrogen,
and 49.98% carbon by mass. The molar mass of a
caffeine molecule is 194.20 g/mol. Find its molecular
formula
Stoichiometry
•
Stoichiometry is about the mathematical relationships between
the amounts of reactants and products in a chemical reaction
•
When given a formula you can scale the rest of the substances
involved based on what you start with
•
In order to scale a formula you have to have the balanced
coefficients which give a relationship between the substances
involved by letting you know the ratio that the substances
occur in.
•
This ratio is called the mole ratio and are used as a
conversion factor to solve problems
9-6 Mole-to-Mole Conversion Flow Chart
Given
Desired
Moles
Moles
coefficient bridge
from balanced equation
Chemistry
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Example
•
If 25.0 mol of diphosphorus pentoxide reacts with
water to form phosphoric acid, how many moles of
water are required?
Mass-to-Mole Conversions
9-7 Mass-to-Mole Conversion Flow Chart
•
Whenever converting between substances in a
reaction you have to do the conversions in moles
•
Balanced equations are based on molar ratios and
not by mass
Mass
(grams)
Given
1 mole
× molar mass
Desired
Moles
Moles
coefficient bridge
from balanced equation
Example
•
How many moles of phosphoric acid can be formed
from 3550 g of diphosphorus pentoxide?
Mass-to-Mass Conversions
9-8 Mass-to-Mass Conversion Flow Chart
•
When the mass of one substance in a reaction is
known, the mass of a second substance can be
calculated by following the road map shown below
Mass
(grams)
Given
1 mole
× molar
mass
Moles
Moles
coefficient bridge
from balanced equation
Desired
mass
× molar
1 mole
Mass
(grams)
Example
•
What mass of water will react with 3550 g of
diphosphorus pentoxide?
9-9 Flow Chart of All Conversions
THE FLOW CHART OF ALL
FLOW CHARTS
Mass
(grams)
Given
1 mole
s molar mass
Desired
molar mass
s 1 mole
Moles
Moles
coefficient bridge
from balanced equation
1 mole
s N units
A
No. of
particles
N units
s 1 Amole
No. of
particles
Mass
(grams)
Mass-to-Mass Conversions
•
How many grams of sodium chloride decompose to
yield 27 g of chlorine gas?
•
2 NaCl → 2 Na + Cl2
Limiting Reactants
•
During a reaction one of the reactants is always used
up before the other which limits the amount of
products that are formed.
•
This reactant is called the limiting reactant and then
the reactant that is left over is the excess reactant
•
Example: Using the formula of 2 pieces of bread, 3
pieces of meat, and 1 piece of cheese how many
sandwiches could you make when given 8 pieces of
bread, 9 pieces of meat, and 5 pieces of cheese?
Example
•
Lithium hydroxide canisters used on the space
shuttles capture exhaled carbon dioxide gas and
convert it to lithium carbonate and water. If a set of
canisters contains 5750 g of LiOH and each of the six
crew members exhales 21 mol of CO2 daily, will the
lithium hydroxide canisters be a limiting reactant for
that day?
Example
•
In the previous example, how many grams of excess
reactant are there?
Percent Yield
•
The theoretical yield is the maximum amount of
product that could be created from a given amount
•
The actual yield is the measured amount of product at
the end of a reaction
•
To find the percent yield of an experiment you have to
dived the actual yield by the theoretical yield and
multiply by 100
Percent Yield Example
•
If 15.00 g of aluminum hydroxide is found in a single
tablet, determine the theoretical yield of aluminum
chloride that would form if you assume there was an
excess amount of hydrochloric acid
•
If 23.00 g aluminum chloride were measured in the
products, calculate the percent yield