Chapter 3
(Essentials of General Chemistry, 2nd Edition)
(Ebbing and Gammon)
Calculations with Chemical
Formulas and Equations
Mass and Moles of Substance
molecular weight (MW) (molecular mass)
- the sum of the atomic weights of all the atoms in a
molecule of the substance
formula weight (FW) (formula mass)
- the sum of the atomic weights of all atoms in a
formula units of the compound (whether molecule
or not)
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Mole and Molar Mass
mole (mol)
- the quantity of a given substance that contains as many
molecules or formulsa units as the number of atoms in
exactly 12 g of carbon-12
- refers to a particular number of things
- that is, contains Avogadro s number of molecules (or
formula units)
Avogadro s number (NA)
- number of atoms in a 12-g sample
- recent measurement: 6.0221367 x 1023 (6.02 x 1023)
molar mass
the mass of one mole of a substance
- by definition, carbon-12 has a molar mass of exactly 12 g/mol
Note: for all substances, the molar mass in grams per mole is
numerically equal to the formula weight in atomic mass units
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Avogadro s Number
How many molecules are there in a 0.050 g sample of
vitamin C, C6H8O6?
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Mole Conversions
Mass-to-Mole Conversions
How many moles are represented by 454 g Si, an element
used in semiconductors?
Mole-to-Mass Conversions
If you have a 35.67 g piece of chromium metal on you car,
how many atoms of chromium are in the piece?
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Mole Conversions
1.) How many moles are represented by 454 g Si, an
element used in semiconductors?
2.) Calculate the number of grams in 1.25 x 10-3 mol of
iron?
3.) If you have a 35.67 g piece of chromium metal on your
car, how many atoms of chromium are in the piece?
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Determining Chemical Formulas
percentage composition
- the amounts of the elements for a given amount of
compound expressed as percentages
Mass percentages from the formulas
mass percentage of A
- the parts of A per hundred parts of the total by
mass
Mass % A = mass of A in the whole x 100%
mass of the whole
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Mass Percentage
1.) Vinyl chloride, CH2CHCl, is the basis of many
important plastics and fibers. Calculate the mass
percent of each element in the compound.
2.) A fertilizer is advertised as containing 15.8% nitrogen
(by mass). How much nitrogen is there in 4.15 kg of
fertilizer?
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Elemental Analysis
Percentages of Carbon, Hydrogen and Oxygen
To determine formula of new compound which contains
only carbon, hydrogen and oxygen:
i.) burn sample of compound of known mass to get
CO2 and H2O
ii.) relate masses of CO2 and H2O to mass of carbon
and hydrogen
iii.) calculate mass percentage of C and H
iv.) determine mass percentage of O by difference
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Percent Composition
Coniine, a toxic substance isolated from poison hemlock,
contains only carbon, hydrogen and nitrogen. Combustion
analysis of a 5.024 mg sample yields 13.90 mg of CO2 and
6.048 mg of H2O. What is the percentage of each element
in coniine?
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Determining Formulas
empirical formula (simplest formula)
- the formula of a substance written with the smallest
integer (whole-number) subscripts
- for most ionic substances, empirical formula is the
formula of the compound (Note: not the case for
molecular substances)
- tells you the ratio of number of atoms in the
compound
Note: compounds with different molecular formulas can
have the same empirical formula (and will have the
same percentage composition)
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Molecular Formula from Empirical Formula
- molecular formula of compound is a multiple of the
empirical formula
- that is, the molecular weight is some multiple of the
empirical formula weight
To obtain molecular formula of a substance:
1.) percentage composition, from which empirical
formula can be determined
2.) the molecular weight
For any molecular compound,
molecular weight = n x empirical formula weight
where,
n = number of empirical formula units in the molecule
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- the molecular formula is obtained by multiplying the
subscripts of the empirical formula by n, where
n=
molecular weight
empirical formula weight
- after determining empirical formula for a compound,
calculate empirical formula weight
- from experimental determination of its molecular
weight, you can calculate n and then the molecular
formula
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Formulas from Composition
An analysis of nicotine, a poisonous compound found in
tobacco leaves, shows that it is 74.0% C, 8.65% H and
17.35 % N. Its molar mass is 162 g/mol. What are the
empirical and molecular formulas of nicotine?
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Stoichiometry
Stoichiometry
the calculation of the quantities of reactants and
products involved in a chemical reaction
- based on chemical equation and the relationship
between mass and moles
Molar Interpretation of a Chemical Equation
Haber Process
- used to produce ammonia, NH3
- nitrogen (from atmosphere) reacts with hydrogen at
high temp. and pressure
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N2 (g)
1 molecule
N2
+
3 H2 (g)
+ 3 molecules
H2
1 mol N2
+
28.0 g N2
+
3 mol H2
3 x 2.02g H2
2 NH3 (g)
2 molecules (molecular
NH3
interpretation)
2 mol NH3
(molar
interpretation)
2 x 17.0 g NH3 (mass
interpretation)
Note: The number of moles involved in a reaction is
proportional to the coefficients in a balanced chemical
equation
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Stoichiometry in a Chemical Reaction
- balanced chemical equation relates anounts of substances
in a reaction
- coefficients in equation can be given molar interpretation
and can be used to calculate moles of product obtained
from any given moles of reactant
- this type of calculation can also be used to answer
questions about masses of reactant and products
N2 (g)
+
3 H2 (g)
2 NH3 (g)
Note: used coefficients within chemical equation to set up
conversion factor that is needed to solve problem
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Stoichiometry
Conversions within a Balanced Chemical Reaction
Phosphine gas reacts with oxygen according to the
following equation
4 PH3 (g) + 8 O2 (g)
P4O10 (s) + 6 H2O (l)
a.) Calculate the mass of tetraphosphorus decoxide
(P4O10) produced from 7.88 mol of phosphine (PH3).
b.) Calculate the mass of phosphine gas (PH3) that
yields 4.69 g of water?
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6
Limiting Reactant
- often reactants are added to a reaction vessel in amounts
different from the molar proportions given by the
chemical equation
- as a result, only one of the reactants may be completely
consumed at the end of the reaction, whereas some
amounts of other reactants will remain unreacted
limiting reactant ( or limiting reagent)
- the reactant that is entirely consumed when a reaction
goes to completion
excess reactant
- a reactant that is not completely consumed
*once one reactant is used up, the reaction stops
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Steps of a limiting-reactant problem:
Given the amounts of reactants added to a vessel,
calculate the amount of product obtained when the
reaction is complete.
1.) you must first identify the limiting reactant
2.) you then calculate the amount of product from the
amount of limiting reactant
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Limiting Reactants
Methanol, CH3OH, an excellent fuel, can be made by the
reaction of carbon monoxide and hydrogen.
CO (g) + 2 H2 (g)
CH3OH (l)
Suppose 365 g of CO are mixed with 65.0 g of H2. Which is
the limiting reactant? What is the maximum mass of
methanol that can be formed? What mass of the excess
reactant remains after the limiting reactant has been
consumed?
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Yields of Reactions
theoretical yield (of product)
- maximum amount of product that can be ontained by a
reaction from given amounts of reactants
- it is the amount calculated from the stoichiometry
based on the limiting reactant
actual yield
- amount of product obtained upon the completion of a
reaction
- may be much less than the theoretical yield
percentage yield (of product)
-the actual yield (experimentally determined) expressed
as a percentage of the theoretical yield
percentage yield = actual yield
x 100%
theoretical yield
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Product Yields
1.) Suppose you made aspirin in the laboratory by the
following reaction.
2 C7H6O3 (l)
+
C4H6O3 (l)
2 C9H8O4 (s)
+
CH3CO2H (l)
You began with 14.4 g of salicylic acid and an excess of
acetic anhydride. If you obtain 6.26 g of aspirin, what
was the percent yield of this product?
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Product Yields
2.) Aspirin, C9H8O4, is prepared by reacting salicylic acid,
C7H6O3, with acetic anhydride, C4H6O3, in the reaction.
2 C7H6O3 (l) + C4H6O3 (l)
2 C9H8O4 (s) + H2O (l)
A student is told to prepare 25.0 g of aspirin. He is also
told that he should use a 50.0% excess of acetic
anhydride and expect to get a 65.0% yield in the
reaction. How many grams of each reactant should be
used?
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