Download The Mole

1. What does this quotient represent:
gfm
1mol
Conversion factor, ratio
2. For each blank in these equations, write the conversion factor needed to
perform the calculation. Use cancel lines to indicate which units will cancel.
a. moles  _______________ = mass
b. particles  _______________ =moles
c. volume of gas, L  _____________  _____________ = representative particles
d. mass  _______________  _______________ =volume of gas
The Mole
The term mole is used to describe a certain amount of matter. That amount is 6.02*1023 of the
smallest particles that make up that form of matter. Thus, one mole of an element contains
6.02*1023 atoms; one mole of a molecular compound contains 6.02*1023 molecules; and one
mole of an ionic compound contains 6.02*1023 formula units. Chemistry Students must be able
to convert from atoms, ions, molecules and formula units to moles, and vice versa. The
following exercises will help you develop those skills.
Example A
How many molecules are there in 6.8 mol if carbon monoxide, CO, gas?
SOLUTION The beginning point in problems of this kind should be the fundamental relationship
1 mole = 6.02*1023 representative particles (in this case, molecules). In this problem, however,
you are asked to find the number of molecules in 6.8 mol. The problem should be set up so that
units will cancel to give the correct units in the answer.
GIVEN : 6.8 mol CO
6.8mol 6.02 *10 23 moleculesC O

 40.936 *10 23 moleculesC O
1molCO
Notice that the answer must have two significant figures since the original measurement (6.8mol)
contained only two. Written in standard scientific notation the answer is 4.1*1024 molecules CO.
You Try It
1. How many sodium ions are there in 0.482 mol of Sodium Sulfate?
𝟎. 𝟒𝟖𝟐 𝐦𝐨𝐥 𝐍𝐚𝟐𝐒𝐎𝟒 𝟔. 𝟎𝟐 × 𝟏𝟎𝟐𝟑 𝐟𝐨𝐫𝐦𝐮𝐥𝐚 𝐮𝐧𝐢𝐭𝐬
𝟐 𝐍𝐚 + 𝐢𝐨𝐧𝐬
|
|
𝟏 𝐦𝐨𝐥 𝐍𝐚𝟐𝐒𝐎𝟒
𝟏 𝐟𝐨𝐫𝐦𝐮𝐥𝐚 𝐮𝐧𝐢𝐭 𝐍𝐚𝟐𝐒𝐎𝟒
Example B
How many moles are there in 6.32*1024 molecules of chloroform, CHCl3?
SOLUTION Begin with the fundamental relationship
1 mol CHCl3 = 6.02*1023 molecules CHCl3
Then multiply the given number of molecules of chloroform by a conversion factor that will give
an answer expressed in moles.
1 mol CHCl 3
6.32 *10 24 molecules CHCl 3 
 1.05 *101 mol CHCl 3
23
6.02 *10 molecules CHCl 3
The answer should contain three significant figures and should probably be written in a simpler
form 10.5 mol CHCl3.
You Try it
2. A sample of silver metal contains 1.91*1021 atoms. How many moles of silver is this?
1.91 × 1021 𝑎𝑡𝑜𝑚𝑠 𝐴𝑔
1 𝑚𝑜𝑙 𝐴𝑔
|
=
6.02 × 1023 𝑎𝑡𝑜𝑚𝑠 𝐴𝑔
Problems For You To Try
3. How many moles are there in 3.04*1023 molecules of hydrogen, H2, gas?
4. How many phosphorus atoms are there in 1.75 mol of calcium phosphate, Ca3(PO4)2?
Gram Formula Mass
Atomic, molecular, and formula masses are all relative numbers. That is, they contain no units.
Saying that the atomic mass of magnesium is 24 means that its atoms are twice as heavy as those
of some other element (carbon) with an atomic mass of 12. It is possible, however, to assign
units to atomic, molecular, and formula masses. When the unit gram is used with an atomic
mass, we define the gram atomic mass of an element. The gram atomic mass is the mass of one
mole of an element. Similarly the gram molecular mass is the mass of one mole of a molecular
compound, and the gram formula mass is the mass of one mole of an ionic compound. The term
molar mass is a general expression that refers to the gram atomic, molecular, or formula mass of
any substance. The exercises below will help you improve your ability to use these concepts.
Example A
What is the gram molecular mass of phosphoric acid, H3PO4?
SOLUTION The formula for phosphoric acid, H3PO4 tells you that one mole of this compound
consists of three moles of hydrogen atoms, one mole of phosphorus atoms, and four moles of
oxygen atoms. The gram molecular mass of H3PO4 then can be found by first determining the
molar mass of the three elements that make up the compound.
1.0 g
3molH 
 3.0 gH
1molH
31.0 gP
1molP 
 31.0 gP
1molP
16.0 gO
4molO 
 64.0 gO
1molO
molar mass H3PO4 = 3.0g H + 31.0g P + 64.0g O = 98.0g
Therefore the gram molecular mass of H3PO4 is 98.0g.
You Try It
5. What is the gram molecular mass of aluminum hydroxide, Al(OH)3?
Example B
Find the molar mass of iron (III) sulfate, Fe2(SO4)3.
SOLUTION Each mole of Fe2(SO4)3 contains two moles of iron atoms, three moles of sulfur
atoms, and 12 moles of oxygen atoms. You can find the molar mass of Fe2(SO4)3 by adding the
molar masses of each of the three atoms that make up the compound.
55.8 g
 111.6 gFe
1molFe
32.1gS
3molS 
 96.3gs
1molS
16.0 gO
12molO 
 192.0 gO
1molO
The molar mass of Fe2(SO4)3 = 11.6g Fe + 96.3g S + 192.0g O = 399.9g
2molFe 
You Try It
6. What is the molar mass of sucrose, C12H22O11?
12C = 12(12.01g) = 144.12g
22H = 22 (1.01g ) = 22.22g
11O = 11(16.00 g) =176.00g
342.34g/mol
Problems For You To Try
7. Find the gram molecular mass of p-dichlorobenzene, C6H4Cl2.
8. What is the molar mass of calcium bisulfate, Ca(HSO4)2?
Converting With Moles
Chemists often need to know about the quantitative relationships among the elements and
compounds involved in a chemical reaction. These relationships may involve masses and or
volumes. For Example, a chemist might want to know what volume of gas is produced when a
certain mass of a compound is heated. The concept of mole is the key idea that makes it possible
for chemists to deal easily and efficiently with all mass and volume relationships in chemical
reactions. At standard temperature and pressure, one mole of a gas has a volume of 22.4L. The
following exercise illustrates methods of converting among moles, mass, and volume.
Example A
What is the mass in grams of 4.52 mol of barium chloride, BaCl2?
SOLUTION The problem involves the relationship between the number of grams and the
number of moles of a compound. Begin by expressing the conversion factor between these two
quantities.
1mol BaCl2 = 208.3g BaCl2 Determine the molar mass first! This is your conversion
factor
Then write this relationship in such a way as to convert the amount of BaCl2 in moles to its
equivalent in grams.
208.3g BaCl 2
4.52mol BaCl 2 
 941.52g BaCl 2
1 mol BaCl 2
The correct answer, expressed to three significant figures is 942g BaCl2.
You Try It
9. In a chemical reaction, 0.397 mol of ethyl chloride (C2H5Cl) is produced. What is the mass in
grams of this amount of C2H5Cl?
Example B
A chemist plans to use 435g of ammonium nitrate (NH4NO3) in a reaction. How many moles of
NH4NO3 is this?
SOLUTION 1 mol of NH4NO3 = 80.0 g NH4NO3
Use this conversion factor to convert a mass to moles. The problem is as follows.
1 mol NH 4 NO3
435 g NH 4 NO3 
 5.44 mol NH 4 NO3
80.0 g NH 4 NO3
You Try It
10. A small bottle in the chemistry stockroom contains 43.25g of nickel (II) carbonate, NiCO3.
How many moles of NiCO3 is this?
Example C
What is the volume at STP of 2.66 mol of methane(CH4) gas?
SOLUTIN
Remember that for any gas at STP the following is true
1 mol = 22.4L
To convert the volume of the gas in moles to its equivalent in liters, multiply as shown below.
22.4 L CH 4
2.66 mol CH 4 
 59.6 L CH 4
1 mol CH 4
Notice that you would obtain the same answer to this problem no matter what gas the problem
mentioned.
You Try It
11. What is the equivalent in moles of 135L of ammonia (NH3) gas?
Problems For You To Try
12. A nurse has been asked to get 0.0465 mole of quinine (C20H24N2O2). What mass of quinine
should the nurse obtain?
13. During an electroplating process, 5.8625g of silver is deposited in a steel bar. How many
moles of silver is this?
14. A helium filled balloon has a total volume of 136500L at STP. How many moles of helium
are in the balloon?
15. A chemist is studying one of five oxides of Nitrogen: N2O, NO, N2O3, NO2 or N2O5. He
learns that 250 mL of the gas has a mass of 0.335g. Which oxide is he working with?