Download the mole

THE MOLE
How Scientists Keep Track of Atoms
• One way to measure how much substance
available is to count the # of particles in
that sample
– However, atoms & molecules are
extremely small
– Also, the # of individual particles in even a
small sample is very large
– Therefore, counting the # of particles is not
a practical measure of amount
• To solve this problem, scientists
developed the concept of the mole
– It’s the “chemical counting unit”
Counting by weighing
• 1 Bean 5 grams
• 5 beans 50 grams
• HOW?
Average Mass
• Mass out 50 beans and find the average
Multiple Stuff
• I Bean 5 grams
• 1 Mint 15 grams
• Just as a dozen eggs equals 12 eggs, a
mole = 602,000,000,000,000,000,000,000
– It is equal to that number no matter what
kind of particles you’re talking about
– It could be represent marbles, pencils, or
bikes
– usually deals with atoms and molecules
• The word “mole” was introduced about
1896 by wilhelm oswald, who derived the
term from the latin word moles meaning a
“heap” or “pile.”
• The mole, whose abbreviation is “mol”, is
the SI base unit for measuring amount of
a pure substance.
• The mole is the chemist’s six-pack or
dozen. Many objects in our everyday lives
come in similar counting units.
1 dozen = 12
23
1 mole = 6.02x10
1 dozen eggs = 12 eggs
1 mole eggs = 6.02x1023 eggs
2 doz of atoms = 24 atoms
2 mols of atoms=1.
24
20x10
atoms
• THE MOLE, AS A UNIT, IS ONLY
USED TO COUNT VERY SMALL
ITEMS
– REPRESENTS A # OF ITEMS, SO,
WE CAN KNOW EXACTLY HOW
MANY ITEMS ARE IN 1 MOLE
• THE EXPERIMENTALLY
DETERMINED NUMBER A MOLE IS
THE EQUIVALENT
OF
IS
CALLED:
AVOGADRO’S #=
23
or 6.02x10
REPRESENTATIVE
PARTICLES
• THE TERM REPRESENTATIVE
PARTICLE REFERS TO THE SPECIES
PRESENT IN A SUBSTANCE
– USUALLY ATOMS
– MOLECULES
– OR FORMULA UNITS (IONS)
• IT’S IMPORTANT TO NOTE THAT A
DOZEN CUPS OF MARBLES CONTAINS
MORE THAN A DOZEN MARBLES
– SIMILARLY, A MOLE OF MOLECULES
CONTAINS MORE THAN A MOLE OF
ATOMS
REPRESENTATIVE PARTICLES & MOLES
ATOMIC
NITROGEN
ATOM
N
6.02x1023
NITROGEN
GAS
MOLEC.
N2
6.02x1023
WATER
MOLEC.
H 20
6.02x1023
CALCIUM ION
ION
Ca2+
6.02x1023
CALCIUM
FLUORIDE
FORMULA
UNIT
CaF2
6.02x1023
HOW DO WE USE THE MOLE?
• SINCE THE MOLE IS SUCH A HUGE
NUMBER OF ITEMS, IT IS ONLY USED
TO DESCRIBE THE AMOUNT OF
THINGS THAT ARE VERY, VERY
SMALL.
• WE’D NEVER USE THE MOLE TO
DESCRIBE MACROSCOPIC OR REAL
WORLD OBJECTS.
HOW BIG A NUMBER
ARE WE TALKING?
1 mole =
23
6.02x10
• 6.02x1023 Watermelon seeds:
would be found inside a melon
slightly larger than the moon.
• 6.02x1023donut holes: would cover
the earth and be 5 miles deep.
• 6.02x1023 grains of sand: would
be cover miami beach 10 ft deep
• 6.02x1023bloodcells: would be
more than the total # of blood cells
found in every human on earth
USING THE MOLE IN
CALCULATIONS #1
HOW MANY MOLES OF MAGNESIUM
IS 1.25x1023 ATOMS OF
MAGNESIUM?
OUR UNIT EQUALITY TO DO THIS
CONVERSION IS
1 mol Mg = 6.02x1023 atoms Mg
THE DESIRED CONVERSION IS:
ATOMS MOLES
1.25x1023
atoms Mg
1 mole Mg
6.02x1023atoms Mg
= .208 mol Mg
• NOW SUPPOSE YOU WANT TO
DETERMINE HOW MANY ATOMS ARE
IN A MOLE OF A COMPOUND
– TO DO THIS YOU MUST KNOW HOW
MANY ATOMS ARE IN A
REPRESENTATIVE PARTICLE OF THE
COMPOUND.
• TO DETERMINE THE NUMBER OF
ATOMS IN A PARTICLE REQUIRES
KNOWING THE CHEMICAL FORMULA
– FOR EXAMPLE, EACH MOLECULE OF
CARBON DIOXIDE (CO2) IS COMPOSED
OF 3 ATOMS
• 1 MOLE OF CARBON DIOXIDE
CONTAINS AVOGADRO’S NUMBER OF
CARBON DIOXIDE MOLECULES.
– THUS A MOLE OF CO2 CONTAINS
THREE TIMES AVOGADRO’S NUMBER
OF ATOMS
• TO FIND THE # OF ATOMS IN A MOL
OF A COMPND,
– YOU 1ST DETERMINE THE # OF ATOMS
IN A REPRESENTATIVE PARTICLE OF
THAT COMPND
– AND THEN MULTIPLY THAT # OF
ATOMS BY AVOGADRO’S #
USING THE MOLE IN
CALCULATIONS #2
HOW MANY ATOMS ARE IN 2.12 mols
OF PROPANE (C3H8)?
UNIT EQUALITIES ARE
1 molecule C3H8 = 11 atoms C3H8
THE DESIRED CONVERSIONS ARE:
MOLES  MOLECULES  ATOMS
23 molecules
6.02x10
2.12 moles
C3 H8
C3 H8
=
1 mole C3H8
1.276x1024
11 atoms C3H8
molecules
C3 H8
1 molecule C3H8
25
1.40x10 atoms
C 3 H8
=
ATOMIC MASSES
• WHAT IS AN ATOM’S MASS?
– IF MEASURED IN GRAMS, THE
MASSES OF ATOMS WOULD BE
TOO SMALL TO WORK WITH
– THEREFORE, INSTEAD OF USING
THE ACTUAL MASS OF A CARBON
ATOM IN GRAMS, CHEMISTS USE
RELATIVE ATOMIC MASSES
ATOMIC MASS UNITS
• IN DETERMINING RELATIVE
MASSES, ONE ATOM IS
ARBITRARILY CHOSEN AS THE
STANDARD
• THE MASS OF ALL THE OTHER
ATOMS ARE THEN EXPRESSED IN
TO THIS STANDARD
• RELATION
FOR THE RELATIVE
VALUE
MASS OF AN ATOM
CHEMISTS AGREED
UPON THE CARBON-12
ATOM
ATOMIC MASS UNITS
• A SINGLE CARBON-12 ATOM WAS
ASSIGNED THE VALUE OF 12
ATOMIC MASS UNITS (AMU).
• THEREFORE, 1 ATOMIC MASS
UNIT IS EXACTLY 1/12 OF THE
MASS OF A CARBON-12 ATOM
– HYDROGEN THEN WEIGHS 1 AMU
– HELIUM WEIGHS 4 AMUS
• AMU’S GAVE SCIENTISTS A UNIT
TO WORK WITH, BUT IT STILL
DESCRIBED THE MASS IN
TERMS OF INDIVIDUAL ATOMS
• SCIENTISTS MUST FIGURE OUT A
WAY TO WORK WITH A COLLECTION
OF PARTICLES THAT AREN’T
HANDLED INDIVIDUALLY
• AND THAT CAN STILL BE THOUGHT OF
IN TERMS OF A RELATIVE (OR
COMPARED) MASS
– AN AVERAGE C ATOM WITH AN
ATOMIC MASS OF 12.0 amu IS 12 TIMES
HEAVIER THAN AN AVERAGE H ATOM
WITH AN ATOMIC MASS OF 1.0 amu
– THEREFORE, 100 C ATOMS ARE 12
TIMES HEAVIER THAN 100 H ATOMS
• ANY NUMBER OF C ATOMS IS 12
TIMES HEAVIER THAN THE SAME #
OF H ATOMS
– SO, IF WE HAD IF WE HAD A PILE
OF CARBON ATOMS THAT
WEIGHED 12g AND A PILE OF
HYDROGEN ATOMS THAT
WEIGHED 1g,
– BOTH PILES SHOULD CONTAIN
THE SAME NUMBER OF ATOMS
• THE GRAM ATOMIC MASSES OF
ANY 2 ELEMENTS (SINCE THEY
ARE RELATIVE TO CARBON) MUST
CONTAIN THE SAME NUMBER OF
ATOMS
• A PILE OF ANY ATOM THAT
CORRESPONDS TO ITS AVERAGE
ATOMIC MASS FROM THE PT
CONTAINS EXACTLY 6.02x1023
ATOMS OF THAT ELEMENT.
– ALSO CALLED A MOLE
CARBON ATOMS
12
HYDROGEN
ATOMS
1
MASS RATIO
• WHAT THIS ALLOWS US TO DO IS
TO USE THE MASS OFF OF THE
PERIODIC TABLE TO REPRESENT
HOW MUCH
1 MOLE OF THAT
ELEMENT WEIGHS
– 1 MOLE OF CARBON ATOMS
WEIGH 12.01 g
– 1 MOLE OF HYDROGEN ATOMS
WEIGH 1.008 g
– 1 MOLE OF TUNGSTEN ATOMS
WEIGH 183.8; ETC.
• THIS NEW VERSION OF MASS FROM
THE PERIODIC TABLE IS CALLED THE
GRAM MOLAR MASS, OR MOLAR
MASS.
– MOLAR MASS = MASS OF 1 MOLE OF
ATOMS/MOLECULES/OR FORMULA
UNITS IN GRAMS
– SYMBOL = MM
– UNITS = GRAMS/MOLE
• SO HOW DO WE FIGURE OUT THE
MASS OF A MOLE OF A COMPOUND
RATHER THAN JUST 1 ELEMENT?
• TO ANSWER THAT QUESTION YOU
MUST HAVE THE FORMULA OF
THE COMPOUND.
– THE FORMULA OF A COMPND TELLS
YOU HOW MANY ATOMS OF EACH
ELEMENT COMBINE TO MAKE THE
REPRESENTATIVE PARTICLE OF
THAT COMPND.
Formula
Model
Formula
Model
• YOU CAN CALCULATE THE MASS OF A
MOLECULE OF SO3 BY ADDING THE
MOLAR MASSES OF THE ATOMS THAT
MAKE UP THE MOLECULE
– FROM THE PERIODIC TABLE,
THE MASS OF SULFUR IS 32.1g/mol.
– THE MASS OF THREE ATOMS OF
OXYGEN IS 3 TIMES THE MOLAR MASS
OF A SINGLE OXYGEN ATOMS, WHICH
IS (3)(16g/mol) OR 48g/mol
• THE TOTAL MASS OF EACH OF THE
ATOMS IN 1 MOLECULE OF SO3 =
32.1g/mol + 48 g/mol = 80.1 g/mol
CALCULATING MOLAR MASSES
USING CHEMICAL FORMULAS
MM of C6H12O6:
(6C’S)(12g/mol)=
(12H’S)(1 g/mol)=
(6O’S)(16 g/mol)=
72g/mol
12g/mol
96g/mol
180g/mol
IF WE HAD 1 MOLE OF THE COMPND C6H12O6
OR 6.02X1023 MOLECULES OF THE COMPND
– IT WOULD WEIGH 180 grams
• WE CAN USE THE MOLAR MASS
OF AN ELEMENT OR COMPOUND
AS A CONVERSION FACTOR TO
CONVERT BETWEEN GRAMS AND
MOLES OF A SUBSTANCE.
– THE UNIT EQUALITY IS 1 MOLE =
__ MM OF THE SUBSTANCE
USING THE MOLE IN
CALCULATIONS #3
HOW MANY GRAMS ARE IN 9.45 mol
OF DINITROGEN TRIOXIDE (N2O3)
UNIT EQUALITY TO USE
THE DESIRED CONVERSION IS:
MOLES  GRAMS
9.45 mol
N 2O 3
76 grams N2O3
1 mole N2O3
= 718 g N2O3
USING THE MOLE IN
CALCULATIONS #4
FIND THE NUMBER OF MOLES
OF 92.2g OF IRON (III) OXIDE
(Fe2O3)
UNIT EQUALITY TO USE
THE DESIRED CONVERSION IS:
GRAMS  MOLES
92.2 g
Fe2O3
1 mole Fe2O3
159.6 g Fe2O3
= 0.578 mol Fe2O3
VOLUME AND THE MOLE
• UNDER THE SAME CONDITIONS,
EQUAL VOLUMES OF GASES
CONTAIN THE SAME NUMBERS OF
PARTICLES.
– OR 1 MOLE OF A GAS WILL
OCCUPY THE SAME VOLUME AS 1
MOLE OF ANY OTHER GAS UNDER
THE SAME CONDITIONS.
• IT’S KNOWN AS THE MOLAR
VOLUME OF A GAS
MOLAR VOLUME
1 MOLE OF ANY GAS AT STP
(0°C and 1 atm) HAS A
VOLUME OF:
1 mole = 22.4 L
USING THE MOLE IN
CALCULATIONS #5
DETERMINE THE VOLUME, IN LITERS,
OF 0.60 molSO2 GAS AT STP.
UNIT EQUALITY TO USE
THE DESIRED CONVERSION IS:
MOLES  LITERS
0.60
moles SO2
22.4 L SO2
1 mole SO2
= 13 L SO2
AVOGADRO’S NUMBER
MASS
(in grams)
Volume
(of gas at STP)
MOLAR MASS
MOLE
MOLAR VOLUME
GOOD EXAMPLE PROBLEM!
IF YOU HAVE A 35.67g PIECE OF
CHROMIUM METAL ON YOUR CAR,
HOW MANY ATOMS OF CHROMIUM
DO YOU HAVE?
• YOU ARE GIVEN MASS AND
ASKED FOR NUMBER OF
PARTICLES
• LET’S GET SOME STRATEGY
WE ARE
GIVEN MASS
WE ARE
ASKED FOR
ATOMS
WE ARE
GIVEN MASS
WE ARE
ASKED FOR
ATOMS
WE ARE
GIVEN MASS
•IT’S GOING TO TAKE
US 2 STEPS, WE JUST
FOLLOW THE ARROWS
• THE FIRST STEP IS TO CONVERT
OUR GIVEN GRAMS INTO MOLES
• TO DO THIS WE USE THE MOLAR
MASS (MM) OF CHROMIUM WHICH
ON THE PT IS 52g/mol
35.67g Cr
1 mole Cr
52 g Cr
= .686 mole
Cr
• THE SECOND STEP WE ARE
GOING TO TAKE OUR NEWLY
CALCULATED MOLES OF Cr AND
CONVERT IT TO THE NUMBER OF
ATOMS OF Cr
• WE HAVE TO REMEMBER THAT IF
WE HAD 1 MOLE OF Cr ATOMS WE
23
.686
mole Cr
6.02x1023 atoms Cr
1 mole Cr
= 4.130x1023 atoms Cr