Download 6.1 Moles and Molar Masses

6.1
Moles and Molar Masses
A mole (mol) is a chemical unit of measurement
commonly used in equations and is equal to both...
• Avogadro's Number: 6.022e23 particles
(602,200,000,000,000,000,000,000)
• The molar mass of a substance, found by
adding the masses of each atom in that
substance's formula.
Avogadro's number is similar to a "dozen" in that it
refers to a specific number of something. A mol of a
substance is just 6.022e23 of that substance, just as
a dozen refers to 12 of something.
The atomic masses of the periodic table are also
molar masses for those elements.
Ex.
1.00 mol C = 6.022e23 atoms C = 12.011 g C
mol
Avo's #
Molar Mass
~1~
Molar masses change for each element as 6.022e23
atoms of one element would not have the same
mass as 6.022e23 atoms of another.
Ex.
1 mol carbon atoms
g
≠
1 mol iron atoms
g
The same is true for compounds. A mol of CO2
would differ in mass from a mol of NaCl.
Ex.
1 mol NaCl
(22.99 g+ 35.453 g)
58.443 g
≠
1 mol CO2
(12.011 g + 32 g)
44.011 g
Overall, a mol is just a very large quantity of very
small things (atoms, ions, formula units, molecules)
which, together, equal a measurable mass in lab.
Ex.
1 mol H
1mol Fe2O3
1 mol Cl1 mol H2O
=
=
=
=
6.022e23 atoms = 1.008 g H
6.022e23 f.units = 159.69 g Fe2O3
6.022e23 ions
= 35.453 g Cl6.022e23 molec. = 18.016 g H2O
~2~
To find the molar mass of an atom, use the atomic
mass given on the p. table. Assume ions (+/-) have
the same mass as neutral atoms. The gain/loss of
electrons has a negligible effect on mass.
Ex.1) 1 mol Fe = 6.022e23 atoms Fe = ___________
Ex.2) 1 mol Fe2+ = ________________ = ___________
Ex.3) _______
= 6.022e23 atoms Li = ___________
Ex.4) _______
= _______________ = 14.007 g N3-
For compounds, sum up the moles of each atom/ion
within the substance. The sum of these masses is
the molar mass of the entire compound, M:
Ex.5) 1 mol CO2
M(CO2)
=
=
1 mol C + 2 mol O
12.011 g + 2(16 g)
=
44.011 g CO2
~3~
Ex.6) FeCl2
Contains.... 1 mol Fe and 2 mol Cl
M(FeCl2) =
Ex.7) Cr(NO3)4
Contains...
M(Cr(NO3)4) =
Ex.8) (NH4)3N
M( (NH4)3N ) =
Ex.9) iron (III) chlorate
Ex.10) NaC2H3O2
M(NaC2H3O2) =
Ex.11) magnesium sulfate
Ex.12) Li3PO4
M(Li3PO4) =
~4~
Self-Check Problems: if you are feeling confident,
complete these problems and check them against
the posted key. Otherwise, we will do them in class.
SC.1) Na3N
Contains....
M( Na3N ) =
SC.2) HClO4
Contains....
M(HClO4 ) =
Determine the molar masses of.....
SC.3) silver chloride
SC.4) zinc phosphate:
SC.5) sulfuric acid:
~5~
6.2
Mass / Mole Conversions
When to use it: any time you need to convert
between grams and moles. Either as a single DA or
as a step within a larger problem.
Why we learn it: moles are used like "measuring
cups" in chemical reactions. This knowledge allows
you to control chemical reactions and create
specific amounts of product.
Ex.1) Give the mass of 2.40 mol pure iron, Fe(s):
Ex.2) How many mol KMnO4 are found in 4.528 g KMnO4?
~6~
Ex.3) What is the mass of 2.00 mol hydrobromic acid, in
kg?
Ex.4) A reaction calls for 0.032 mol sodium carbonate.
How many mg do you need to measure out?
Ex.5) On average, you exhale 681 g of carbon dioxide
each day. What is this is mol?
~7~
Self-Check Problems: if you are feeling confident,
complete these problems and check them against
the posted key. Otherwise, we will do them in class.
SC.1) What is the mass of 3.50 mol Li2O, in kg?
SC.2) How many moles are contained by 240 mg of silver
metal?
SC.3) What is the mass, in g, of 7.61 mol sodium chloride?
~8~
SC.4) An equation calls for 4.00 g plutonium metal. What
is this in moles?
SC.5) Calculate the mass of gold (IV) nitrate, in grams,
necessary for an equation if 2.50 mol are required.
~9~
6.3
Mole and Particle Conversions
When to use it: any time you need to convert
between moles and particles. Particles = atoms,
ions, formula units, or molecules.
Why we learn it: particles are part of the abstract
"idea" of chemistry. Through moles, we can link the
ideas of chemistry to the real-world.
Conversions between moles and particles of the
same substance are easy, one-step problems which
require you to use Avogadro's number: 6.022e23.
Ex.1) How many atoms of gold are in 0.30 mol Au?
~ 10 ~
Ex.2) Convert 2.00e5 molecules of OF2 into moles:
Ex.3) How many formula units of Fe2O3 are in 0.9 mol?
Some problems are more complex and involve
atoms/ions within larger compounds. These are
typically two-step problems involving Avo's number
and a whole number conversion:
Ex.4) How many ions of Na+ are found in 3.4 mol Na2S ?
~ 11 ~
Ex.5) How many H+ ions are in 7 mol H3PO4?
Ex.6) How many molecules of carbon dioxide could be
assembled from 280 atoms of oxygen?
Ex.7) Calculate the number of moles of rust, Fe3O4 , which
could be formed from 8.25e25 oxygen ions:
~ 12 ~
Self-Check Problems: if you are feeling confident,
complete these problems and check them against
the posted key. Otherwise, we will do them in class.
SC.1) How many molecules of oxygen gas, O2, would be
contained by 54.0 mol O2?
SC.2) How many oxygen atoms are contained by 0.200
mol O2 gas?
~ 13 ~
SC.3) Calculate the number of moles of iron metal found
in 7.2e20 iron atoms:
SC.4) Determine the number of oxygen ions contained
by 120 formula units of iron (III) nitrate:
SC.5) Given 0.400 mol carbonic acid, how many atoms of
carbon do you have?
~ 14 ~
6.4
Multi-Step Conversions
When to use it: any time you are attempting to
convert between mass and particles. You'll have to
use moles as the "bridge" between these
measurements. Your Conversion Cheat Sheet is an
excellent tool for this chapter.
Why we learn it: you can now connect the theory
(particles) of chemistry to the real world (mass).
Ex.1) What is the mass of a single atom of gold?
Ex.2) How many atoms of fluorine are found in 34 g ArF2?
~ 15 ~
Ex.3) After walking through the desert, you find you've
lost 172 g of mass. Assuming this is completely
water, how many molecules of water have you lost?
Ex.4) Calculate the mass of a single oxygen molecule, O2:
Ex.5) A gallon of water is equal to 3.78 L and water has a
density of 1.00 g = 1.00 mL. Knowing this, how
many water molecules are found in a gallon of
water?
~ 16 ~
Self-Check Problems: if you are feeling confident,
complete these problems and check them against
the posted key. Otherwise, we will do them in class.
SC.1) A pure copper penny (before 1982) has a mass of
3.1 g. Calculate the number of copper atoms used
to make a single pure copper penny.
SC.2) How many oxygen atoms are found in 1.600 kg of
sodium oxalate, Na2C2O4?
~ 17 ~
SC.3) Determine the mass, in mg, of 1.05e19 formula
units of silver oxide:
SC.4) My skeleton has a dry mass of 20.45 kg and is
composed of calcium phosphate. How many
calcium ions are contained by my skeleton?
SC.5) How many mg of sulfuric acid could be
manufactured from 1.6e22 atoms of sulfur?
~ 18 ~
6.5
Percent Composition
Percent composition is a way of breaking down a
compound to show the percentage of each atom,
ion, or (for hydrates) molecule by mass.
% Composition =
Total Mass of Substance
x 100%
Molar Mass of Compound
Calculate the % composition of sugar, C12H22O11
Carbon:
12 x 12.011 g x 100%
342.31 g
% Carbon = 42.1%
Hydrogen:
22 x 1.008 g
342.31 g
x 100%
% Hydrogen = 6.5 %
Oxygen:
11 x 16 g
342.31 g
x 100%
% Oxygen = 51.4 %
~ 19 ~
The most common use of percent composition is to
determine the percent, by mass, of individual
elements within the compound:
Ex.1) Give the % composition (both Na and Cl) for table
salt, NaCl:
Ex.2) What is the percent composition of carbon within
sodium carbonate?
~ 20 ~
You can also determine the percent water within
larger compounds, such as hydrates. Instead of
single elements, compare the mass of the dry
compound (anhydrate) against the mass of water.
Ex.3) What is the mass percentage of water in calcium
chloride dihydrate?
Ex.4) Determine the % by mass of the anhydrate in cobalt
(II) chloride tetrahydrate:
~ 21 ~
Self-Check Problems: if you are feeling confident,
complete these problems and check them against
the posted key. Otherwise, we will do them in class.
SC.1) What is the % composition of perchloric acid?
SC.2) What is the % water within magnesium sulfate
pentahydrate?
~ 22 ~
6.6
Empirical and Molecular Formulas
When to use it: as a method to predict the formula
of an unknown compound in lab.
Why we learn it: you can use your lab data to
determine chemical formulas. Historically, much of
what we know about chemical bonding and
compounds was developed using empirical
formulas.
An empirical formula represents the simplest whole
number ratios between elements within a
compound. Essentially, it's a simplified version of a
molecular (full, covalent) formula:
Glucose:
Ex.1) Octane:
Oxalic Acid:
Fructose:
C6H12O6
(Molecular)
→
C8H18
H 2 C2 O 4
C5H10O5
→
→
→
~ 23 ~
CH2O
(Empirical)
Ionic compounds are already simplified. Their
normal formulas ARE their empirical formulas:
Ex.2) Table Salt:
NaCl
Iron (III) oxide: Fe2O3
Zinc phosphate: Zn3(PO4)2
→
→
→
You can convert between molecular and empirical
formulas if you have the molar mass of the original
compound:
Ex.3) A compound's empirical formula is C2H5 and the
molar mass is experimentally determined to be
approximately 58 g. Give the molecular formula for
this compound:
Ex.4)
Empirical:
N2O
CH4
CH2O
M:
176 g
16 g
180 g
~ 24 ~
Molecular:
Empirical formulas can be calculated from lab data,
allowing us to identify unknown compounds:
STEP 1: Assume mass percentages represent masses, in g:
STEP 2: Divide each element's mass by their respective
molar masses, turning them into moles.
STEP 3: Divide all moles by the lowest number of moles in
the formula thus far. These numbers will give you
the ratios in the empirical formula. You may have
to multiply to get whole numbers.
Ex.5) Determine the empirical formula for a compound
known to be 75% carbon and 25% hydrogen:
~ 25 ~
Ex.6) A compound contains 13.5 g Ca, 10.8 g O, and 0.675
g hydrogen. What is its empirical formula?
Occasionally, your mole ratios (after step 3) will be
fractional instead of whole numbers. Ends in 0.25 multiply by 4. Ends in 0.50, multiply by 2. Ends in
0.33 or 0.67, multiply by 3.
Ex.7) Give the empirical formula for a compound which is
71.98% carbon, 6.71% hydrogen, and 21.3% oxygen.
~ 26 ~
Ex.8) Analysis of an aspirin tablet gives 60.00% C, 4.48%
H, and 35.52% O. Give the empirical formula for
aspirin:
You can combine empirical formula calculations
with molar masses to "scale up" and determine the
original molecular formulas for a substance:
Ex.9) Determine the molecular formula for a compound if
it contains 50.05% sulfur and 49.95% oxygen by
mass and has a molar mass of 192 g/mol.
~ 27 ~
These calculations can also be applied to determine
the number of water molecules within a hydrate.
Instead of individual elements, compare the ratio of
the compound to that of water.
Ex.10) Copper (II) sulfate exists as a hydrate. In lab, a
2.60 g sample of the hydrate is heated in a crucible
for several minutes, allowing the water to be
vaporized from the sample. When cooled, the mass
of the sample is now 1.66 g. Calculate the empirical
formula of this hydrate and name it:
~ 28 ~
Self-Check Problems: if you are feeling confident,
complete these problems and check them against
the posted key. Otherwise, we will do them in class.
SC.1) Calculate the empirical formula for a compound
which is 13.6% phosphorus and 86.4% selenium:
SC.2) Determine the empirical and molecular formulae for
a compound which is 39.14% carbon and 60.86%
nitrogen if it has a molar mass of 460 g/mol:
~ 29 ~
SC.3) A 5.00 g sample of a sodium sulfate hydrate is
placed in a crucible and heated to drive off the
water. If the dry (anhydrous) compound has a mass
of 2.20 g, give the formula and name of this
hydrate:
~ 30 ~
~ 31 ~