THE MOLE

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” 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” How Scientists Keep Track of Atoms

Counting by weighing 1 Bean5 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. 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 1 mole = 6.02x dozen eggs = 12 eggs 1 mole eggs = 6.02x10 23 eggs 2 doz of atoms = 24 atoms 2 mols of atoms=1. 20x10 24 atoms 2 mols of atoms=1. 20x10 24 atoms

or 6.02x10 23 REPRESENTATIVE PARTICLES AVOGADRO’S #= 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: 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:

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 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 ATOMN 6.02x10 23 NITROGEN GAS MOLEC. N2N2N2N2 6.02x10 23 WATERMOLEC. H20H20H20H20 CALCIUM ION ION Ca x10 23 CALCIUM FLUORIDE FORMULA UNIT CaF x10 23

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. 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 = 6.02x x10 23 Watermelon seeds: would be found inside a melon slightly larger than the moon. 6.02x10 23 donut holes: would cover the earth and be 5 miles deep. 6.02x10 23 grains of sand: would be cover miami beach 10 ft deep 6.02x10 23 bloodcells: would be more than the total # of blood cells found in every human on earth 6.02x10 23 Watermelon seeds: would be found inside a melon slightly larger than the moon. 6.02x10 23 donut holes: would cover the earth and be 5 miles deep. 6.02x10 23 grains of sand: would be cover miami beach 10 ft deep 6.02x10 23 bloodcells: 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 1.25x10 23 ATOMS OF MAGNESIUM? OUR UNIT EQUALITY TO DO THIS CONVERSION IS 1 mol Mg = 6.02x10 23 atoms Mg OUR UNIT EQUALITY TO DO THIS CONVERSION IS 1 mol Mg = 6.02x10 23 atoms Mg

6.02x10 23 atoms Mg 1 mole Mg THE DESIRED CONVERSION IS: ATOMS  MOLES 1.25x10 23 atoms 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 (CO 2 ) IS COMPOSED OF 3 ATOMS 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 (CO 2 ) IS COMPOSED OF 3 ATOMS

1 MOLE OF CARBON DIOXIDE CONTAINS AVOGADRO’S NUMBER OF CARBON DIOXIDE MOLECULES. –THUS A MOLE OF CO 2 CONTAINS THREE TIMES AVOGADRO’S NUMBER OF ATOMS TO FIND THE # OF ATOMS IN A MOL OF A COMPND, –YOU 1 ST DETERMINE THE # OF ATOMS IN A REPRESENTATIVE PARTICLE OF THAT COMPND –AND THEN MULTIPLY THAT # OF ATOMS BY AVOGADRO’S # 1 MOLE OF CARBON DIOXIDE CONTAINS AVOGADRO’S NUMBER OF CARBON DIOXIDE MOLECULES. –THUS A MOLE OF CO 2 CONTAINS THREE TIMES AVOGADRO’S NUMBER OF ATOMS TO FIND THE # OF ATOMS IN A MOL OF A COMPND, –YOU 1 ST 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 (C 3 H 8 )? UNIT EQUALITIES ARE 1 molecule C 3 H 8 = 11 atoms C 3 H 8 UNIT EQUALITIES ARE 1 molecule C 3 H 8 = 11 atoms C 3 H 8

6.02x10 23 molecules C 3 H 8 1 mole C 3 H 8 THE DESIRED CONVERSIONS ARE: MOLES  MOLECULES  ATOMS 2.12 moles C 3 H x10 24 molecules C 3 H 8 = = 11 atoms C 3 H 8 1 molecule C 3 H 8 = = 1.40x10 25 atoms C 3 H 8

–THEREFORE, INSTEAD OF USING THE ACTUAL MASS OF A CARBON ATOM IN GRAMS, CHEMISTS USE RELATIVE ATOMIC MASSES WHAT IS AN ATOM’S MASS? –IF MEASURED IN GRAMS, THE MASSES OF ATOMS WOULD BE TOO SMALL TO WORK WITH WHAT IS AN ATOM’S MASS? –IF MEASURED IN GRAMS, THE MASSES OF ATOMS WOULD BE TOO SMALL TO WORK WITH 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 RELATION TO THIS STANDARD VALUE IN DETERMINING RELATIVE MASSES, ONE ATOM IS ARBITRARILY CHOSEN AS THE STANDARD THE MASS OF ALL THE OTHER ATOMS ARE THEN EXPRESSED IN RELATION TO THIS STANDARD VALUE FOR THE RELATIVE MASS OF AN ATOM CHEMISTS AGREED UPON THE CARBON-12 ATOM

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 (UNUSABLE) 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 (UNUSABLE) ATOMIC MASS UNITS

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 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 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 6.02x10 23 ATOMS OF THAT ELEMENT. –ALSO CALLED A MOLE 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 6.02x10 23 ATOMS OF THAT ELEMENT. –ALSO CALLED A MOLE

CARBON ATOMS HYDROGEN ATOMS 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 g –1 MOLE OF HYDROGEN ATOMS WEIGH g –1 MOLE OF TUNGSTEN ATOMS WEIGH 183.8; ETC. 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 g –1 MOLE OF HYDROGEN ATOMS WEIGH 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? 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. 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.ModelFormulaModelFormula

YOU CAN CALCULATE THE MASS OF A MOLECULE OF SO 3 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 SO 3 = 32.1g/mol + 48 g/mol = 80.1 g/mol YOU CAN CALCULATE THE MASS OF A MOLECULE OF SO 3 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 SO 3 = 32.1g/mol + 48 g/mol = 80.1 g/mol

MM of C 6 H 12 O 6 : (6C’S)(12g/mol)= 180 g/mol CALCULATING MOLAR MASSES USING CHEMICAL FORMULAS (12H’S)(1 g/mol)= (6O’S)(16 g/mol)= IF WE HAD 1 MOLE OF THE COMPND C 6 H 12 O 6 OR 6.02X10 23 MOLECULES OF THE COMPND – IT WOULD WEIGH 180 grams 72g/mol 12g/mol 96g/mol

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 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 (N 2 O 3 ) UNIT EQUALITY TO USE

1 mole N 2 O 3 76 grams N 2 O 3 76 grams N 2 O 3 THE DESIRED CONVERSION IS: MOLES  GRAMS 9.45 mol N 2 O mol N 2 O 3 = 718 g N 2 O 3

USING THE MOLE IN CALCULATIONS #4 FIND THE NUMBER OF MOLES OF 92.2g OF IRON (III) OXIDE (Fe 2 O 3 ) UNIT EQUALITY TO USE

1 mole Fe 2 O g Fe 2 O 3 THE DESIRED CONVERSION IS: GRAMS  MOLES 92.2 g Fe 2 O 3 = mol Fe 2 O 3

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 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 molSO 2 GAS AT STP. UNIT EQUALITY TO USE

1 mole SO L SO 2 THE DESIRED CONVERSION IS: MOLES  LITERS 0.60 moles SO moles SO 2 = 13 L SO 2

MOLEMOLE MASS (in grams) MOLAR VOLUME Volume (of gas at STP) MOLAR MASS AVOGADRO’S NUMBER

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 YOU ARE GIVEN MASS AND ASKED FOR NUMBER OF PARTICLES LET’S GET SOME STRATEGY

WE ARE GIVEN MASS

WE ARE ASKED FOR ATOMS

IT’S GOING TO TAKE US 2 STEPS, WE JUST FOLLOW THE ARROWS WE ARE GIVEN MASS WE ARE ASKED FOR ATOMS

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 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 52 g Cr 1 mole 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 WOULD HAVE 6.02X10 23 ATOMS 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 WOULD HAVE 6.02X10 23 ATOMS

.686 mole Cr 1 mole Cr 6.02x10 23 atoms Cr = 4.130x10 23 atoms Cr