The MOLE

Introduction to stoichiometry

AVOGADRO’S NUMBER

How would you find the mass of an object with too little mass to register on your balance?

AVOGADRO'S Number

If you could put a large number of the same object on the balance, you could get a measurable mass.Then, by dividing this measurable mass by the number of objects, you would get the mass of one individual object.This idea occurred to Avogadro, an Italian scientist who did not know how large the number would be, but who hypothesized

That once one “combining mass” of an element was known, it must have theSame number of atoms as one combining mass of a different element.By the end of the nineteenth century, the SIZE of that number had been determined And a word, meaning “a heap” had been invented as the unit for that number.AVOGADRO’S NUMBER: 6.02 x 1023 = 1 mole

The natural substance with the LEAST MASS is

H2, hydrogen, with a mass of2.0156 atomic mass units.Recall that each H atom has 1.0078 atomic mass units.By definition, 1 mole of H2, hydrogen, has a mass of 2.0156 g (usually rounded to 2.02 g).How many grams is 1 molecule of hydrogen gas?

Finding the Mass in grams of one molecule of H2 and 1 atom of H:

=

=

2

224

1

1034.3

moleculeH

gHx

=

..1002.6

02.2

..1

02.223

22

prx

gH

pmolr

gH

Since molecules are the representative particles of hydrogen gas

223

2

1002.6

20.2

MoleculesHx

gH atomH

gHx

1

1067.1 24

Review

What number represents a mole? Avogadro’s numberGram formula mass divided by the Avogadro number = representative particle mass in grams.A representative particle mass will have an exponent in the 10-23 g. range (possibly as big as 10-22 g)

REVIEW

KINDS OF REPRESENTATIVE PARTICLES: ions, atoms, molecules, formula units. So if we are referring to 1020 particles, or larger number of particles, we are talking about 10-3 or larger number of moles.The least number of grams of a naturally occurring substance is 2.02 grams/mole, which is H2.

Problem solving in quantitative chemical problems.

Must use common sense; troubleshoot obvious errors by making sure that inverses have not been used as conversion factors.EXPECT information to be missing from problems:

Look for missing info in the text, other problems or sample problems, previous chapters, tables in same or previous chapters, and reference tables including of course the Periodic Table.

For example in practice prob. 1

Find data about apples per bushel.Found on p 172: 1 doz apples/ .20 bushel12 apples / dozen12 apples/ .20 bushels = x apples/.50 bushels.

The question asks about the 2 mass of .50 bushel.Mass of 1 apple, found in sample prob 7.1. Number of apples -> mass of apples.2.0 kg / 12 apples12ap/.20 bu=x ap/.50 buX ap=12ap(.5bu) /.2buX =30 ap30 ap/y kb = 12 ap/2.0 kg12 ap(y kg)= 30 ap(2 kg)

Sample prob 7.2

1.25 x 10 23 atoms of Mg. How many moles is this?6.02 x 1023

rep particles (atoms)/ 1 mol.

1.25 x 1023 /x moles = 6.02 x 1023 /1 moleX moles =1.25 x 1023 / 6.02 x 1023

The correct answer MUST be converted into _____/1, the 1 then is omitted!

2.12 moles of C3H8 contains

X atoms.1 mole contains a certain number of atoms, which is 6.02 x 1023

0f the number of atoms in one individual molecule.How many atoms per 1 molecule?

• (11 atoms/ 1molecule) (6.02x 1023atoms/1mole molecules)(2.12 mole) are present) =# of atoms present = ___?_atoms

YOU MUST show the units that cancel before you cancel them!

2.12 moles of C3H8 contains

x atoms.1 mole contains a certain number of atoms, which is 6.02 x 1023

0f the number of atoms in one individual molecule.How many atoms per 1 molecule?

Gather all given & known information:

Atoms is the final quantity desired.

molecule

atomsmolecules

mole

xnemolespropa

1

11

1

1002.612.2 23

= x atoms

Cancel all possible units, checking to make sure that appropriate units cancel rather than multiply!

Evaluate the answer including the remaining unit: means give the numerical answer in decimal form!

Frequently, lab measurable quantities are given or wanted.

ONLY use 6.02 x 1023 as a factor if a representative particle is a known or wanted quantity.IF grams are wanted and moles are given, use the gram formula mass (gfm) as the conversion factor.

For example, how many moles of pentene are found in 65.0 g. of pentene, C5H10.

What is pentene? It is the compound whose formula is next to the name.What do we do next?

Solving a gram to mole problem:

1) find the gram formula mass (gfm) of the substance in question2) by definition, the mass of one mole is the gfm.3) consult the PERIODIC TABLE for average atomic masses.

Remember that the entire atomic mass is made of both protons & neutrons ; DON’T choose the atomic number!4) Find the total mass of each element; find the sum of all the masses.

For example, C5H10

Contains 5 Carbons and 10 hydrogens.The atomic number of C is 6; its average atomic mass is 12.0.The atomic number of H is 1; its average atomic mass is 1.01.The total gram mass of C in 1 mole of compound is 5 x 12.0g= 60.0 g

The total gram mass of H in the compound is 10 x 1.01 gram=10.1 g.The sum of all the elements in the compound is thus 70.1 g/mole.

g

mole

1.70

HC1HC g 65.0• 8383 =

1.70

)1(0.65 mole =0.927 moles

How many moles is 65.0 g of (NH4)3(PO4)?

Steps: gram formula mass = mass/1 mole.Total number of N in this formula? 3 x 1 = 3Total number of H in this formula?3x4 = 12Total # of P=1; of O=4

Gram atomic masses of N, H, P and O?N : 7 or 14.0?H : 1 or 1.01?P : 15 or 30 or 31.0?O : 8 or 15 or 16.0?Answers: N, 14.0g; H, 1.01g, P, 31.0g; O, 16.0 g.

The gram formula mass of ammonium phosphate is

Then we can find the number of moles of ammonium phosphate in 65.0 g.By …..

3 x 14.0g = 42.0 g.N12 x 1.01g = 12.1 g H1 x 31.0 g = 31.0 g P4 x 16.0 g = 64.0 g O

_________________Gfm=

mole 1

PO)(NH g 149.1 434

Fill in the blanks:

Grams of ammonium phosphate available = ________1mole/Molar mass (gfm) of ammonium phosphate = ______/_____

( _______) (__________)= ___ moles( )

Answer:

Grams available: 65.0 gMolar mass:

mole 1

PO)(NH g 149.1 434

Invert the molar mass so that g will cancel out!

434 )(1.149

)1(0.65

PONHg

moleg=0.436 moles (NH4)3PO4

And the answer is

)PO)(149.1g(NH

1mole) (PO)(NH0.65

434

434g

=0.436 g (NH4)3PO4

The reverse procedure gives grams when moles are given.

How many grams are there in 0.645 moles of O2?

We know the number of moles.We go to the periodic table to find the gfm of oxygen gas.Since moles must be cancelled, the g/1mol format is NOT inverted:

The only question left is , what is the CORRECT formula mass of oxygen gas.1 atom of O is 15.9994 amu; 1 mol of O is 15.9994 g and one mole of O2= 32.0 g.

To set up the problem,

•0.645 moles O2 mol

gO

1

)0.32( 2

= ____ g O2

And the answer is …………

20.64 g O2

For gases at standard temperature of 0oC and 1 atm.

1 mole of gas occupies 22.4 L.This conversion factor does not apply to liquids or solids which have definite density.The density of a gas varies with pressure and temperature.The abbreviation for 0oC and 1 atm. isS.T.P.

Here are some molar volume questions:

If you have 11.2 L of H2 at STP, how many moles and how many grams of hydrogen gas are present.

Since one mole of H2 = 2.02 g,And there are 0.500 molesThere are 1.01 g.Set this entire mathematical scenario up using the format previously used!

mol

L

xmoles

L

1

4.222.11

11.2 L = 0.500 mol

More molar volume questions

1. How many grams of oxygen gas are present in 3.54 L at STP?2. How many grams of iron are present in 3.54 L at STP?3. How many grams of C2H4 (ethene gas) at STP are present in 2.0 L?4. How many grams of CH4(natural gas or methane) are present in 4.48 L at STP?

Did you notice the “trick” question?

Which one is it?At 0oC, one of those substances is NOT A GAS. The solid substance does not follow the molar volume law. You would have to know its density in order to solve problem 2.The other problems simply rely on

ofmoles

L

moleofLgiven #

4.22

)1(#

and

Gfm of O2 x # of moles

And similar action with problems 3 & 4.You are REQUIRED to have solutions to ALL these problems IN YOUR NOTES, including #2, (which requires looking up and using the density of Fe!)

% composition and moles

Refer to earlier notes about the % composition of water http://www.newmex.com/lpchemistry: Dalton & atoms88.9% of water is oxygen by mass, while 11.1% of water is hydrogen by mass.This means that out of every 100 g, ___ g is oxygen. How many moles of oxygen would there be in 100 g of water?

Using percent composition.

molO

gO

molOgO 55.5

0.16

18.88

molH

gH

molHgH 1.11

01.1

12.11

What is the ratio of moles of H to moles of O?

Note: O, not O2!

Finding empirical formulas

H11.1O5.5 reduces to H2O1 or our familiar

H2OThe same process can be used with any compound for

which the % composition has been determined by experiment.

For example, a compound exists which is 75% C and 25% H by mass. It is NOT an acid, meaning that __

comes ____.

What is the formula for this compound?

Check out the flowchart for naming of compounds. Your text gives PxQy as a “template” for a binary compound. If the compound is an acid, P is H, hydrogen. Since this compound is NOT an acid, P must be __C.Change 75% into 75 g C and determine the number of moles present.

Fill in the blanks in each step for finding the formula.The first element in the formula is C.

molC

g

moleCgC ___

__

)1(75

•The second element in the formula is H, by default.

molH

gH

molHgH ___

___

)1(25

Insert the number of moles you have found in the subscript variables.C---H----

Divide the smaller subscript into the larger subscript. In this case, the rounded integers will be even.C6.25H24.75

24.75/6.25 ~ 4C1H4 or CH4

The substance is methane.

A more interesting compound is composed of

69.9% of a compound is iron. The remainder is oxygen.What % of this compound is oxygen?Change 69.9% into ___g/100g iron, and find the # of moles of iron.Since iron is a ____, it appears __ in the formula.Find the # of moles of oxygen.

1.25 moles of Fe are present for every 1.88 moles of O.Dividing 1.88/1.25 yields a ratio of 1.5/1 of O.Fe1O1.5 is the result.

But subscripts must be integers.Multiplying each subscript by 2 yields the correct empirical formula, Fe2O3.

3:4 or 4:3 ratios are also possible.

If there are 3 or more elements, a polyatomic ion may be involved. N2O6 must be “reduced” to (NO3)2 and N3H12 would “reduce” to ?

(NH4)3.

Obviously, the more adequately you have memorized your polyatomic ions, the easier this part will be for you!

The situation with molecules

Molecular compounds are often made up of apparently repeating units. For example, there are many many molecular compounds with the empirical formula CnH2n. Examples would include C2H4 and C30H60. Clearly, the molar mass of the first compound would be 28g/mol, while the molar mass of the second would be 420 g/mol. Note that instead of being “reduced”, these molecular formulas are

Expanded.

If you found that the EMPIRICAL FORMULA for a molecule was CnH2n, you would have to know its molecular mass in order to provide its molecular formula.If the molar mass were 420 g/mol, and you divided the unit mass of 14 g/mol (for C1H2) into 420, you would find that there were in fact 30C : 60 H. Thus, a molecular formula can be determined from an empirical formula IFF the molar mass can be determined.

Have we already learned a way to determine molar mass …

at least for one set of compounds????The answer isYes, for gases at S.T.P.Remember, at S.T.P. (__atm pressure and __oC), _____ L of ANY gas contain 1 mole of molecules.This number of liters can be massed.A fractional number of liters represents the same fraction of the number of moles and

thus the same fraction of the molar mass.If the % composition of a compound HAS BEEN PREVIOUSLY DETERMINEDANDThis substance can be obtained in the gaseous state at standard conditions,Then its molecular formula can be determined.This was the work of chemists following the acceptance of Dalton’s theory.

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