1. Calculations with Elements and Compounds
The Mole Concept
Calculations with Elements and Compounds
Pisgah High School
M. Jones
Rev
050212

3. Moles?

4. No. Not real moles, or Whack-a-moles, or even the moles on your back.
Chemistry moles

5. It’s a way of measuring atoms and molecules.
What is a mole?
It’s a way of measuring atoms and molecules.
The “mole concept” is a lot like the “dozen concept.”

6. A dozen is 12. A dozen is always 12.
It doesn’t make any difference what you are counting.
A dozen is 12.
A dozen is always 12.

7. A dozen is 12. A dozen is always 12.
It doesn’t make any difference what you are counting.
A dozen is 12.
A dozen is always 12.
A dozen donuts.

8. A dozen is 12. A dozen is always 12.
It doesn’t make any difference what you are counting.
A dozen is 12.
A dozen is always 12.
A dozen donuts.
A dozen pencils.

9. A dozen is 12. A dozen is always 12.
It doesn’t make any difference what you are counting.
A dozen is 12.
A dozen is always 12.
A dozen donuts.
A dozen pencils.
A dozen Volkswagons.

11. A dozen is always 12.

12. Like we can count by dozens, or multiples of 12, we can also count by multiples of a much larger number, which we call Avogadro’s number.

13. Avogadro’s number is 6.022 x 1023. Avogadro’s number is much larger…
So how did chemists come up with such a huge number?

14. It began with Amedeo Avogadro about a 150 years ago.
He said that for equal volumes of gases at constant temperature and pressure, the masses of the gases are proportional to their atomic weights.

15. Avogadro’s law
10.0 liters of CO2 weighs 19.6 grams
10.0 liters of N2 weighs 12.5 grams
10.0 liters of Xe weighs 58.6 grams
19.6 g
12.5 g =
44.0 g
28.0 g =
1.57
1.57
Ratio of the masses of equal volumes of CO2 and N2
Ratio of the molar masses of CO2 and N2

16. Avogadro’s law
10.0 liters of CO2 weighs 19.6 grams
10.0 liters of N2 weighs 12.5 grams
10.0 liters of Xe weighs 58.6 grams
19.6 g
58.6 g =
0.335
44.0 g
131.3 g =
0.335
Ratio of the masses of equal volumes of CO2 and Xe
Ratio of the molar masses of CO2 and Xe

17. See!
I told you so.
He said that for equal volumes of gases at constant temperature and pressure, the masses of the gases are proportional to their atomic weights.

18. I wish I knew what my number was.
But Avogadro never determined the value we know as Avogadro’s number.
I wish I knew what my number was.
It was called Avogadro’s number as a tribute to his pioneering work.

19. After Avogadro’s death, Stanislao Cannizzaro published an explanation of Avogadro’s law.
Equal volumes of gases at the same temperature and pressure have equal numbers of particles.

20. Cannizzaro was able to convince chemists of the value of standardized atomic weights.
Loschmidt (1865) was the first to determine the number of atoms or molecules in a fixed volume of gas.

21. Jean Perrin was the first to use the term Avogadro’s number in 1909 to describe the number of atoms in the atomic weight of an element.
He was the first to determine a value of Avogadro’s number which is close to the present-day value of x 1023.

22. Atomic Mass
We can relate Avogadro’s number to the amount of an element equal to its atomic mass measured in grams.

23. Atomic Mass
This used to be called the “gram atomic weight”. Atomic weights are now called atomic masses.
Atomic masses are given in units of “atomic mass units”, or amu. The amu is also called the dalton.

24. Atomic Mass
The “atomic mass unit” (amu) is based on the mass of the carbon-12 isotope.
It was decided that an atom of C-12 be assigned a mass of exactly amu

25. Atomic Mass
This way, hydrogen,the lightest element (H) would have a mass very close to 1.
The average atomic mass of hydrogen is amu.

26. Atomic Mass
Instead of amu of carbon-12, which is too small to even see, we consider grams of C-12.
How many atoms are in g of C-12?

27. Atomic Mass 1 C atom C atom x 12.000 g C 1.993 x 10-23 g C
How many atoms are in g of carbon-12?
A C-12 atom has a mass of x g
1 C atom
C atom x
g C
1.993 x g C
= x 1023 C atoms

28. Atomic Mass
The mole is the “official” metric unit for the “quantity of matter”.
A mole is the quantity of an element which has a mass equal to the atomic mass expressed in grams.

29. The word “mole” can be abbreviated as “mol”.

30. So, what is a mole?
It is a word that describes a very large number of atoms.
6.022 x 1023 atoms
It comes from the Latin word moles which means “quantity”
6.022 x 1023 is also called Avogadro’s Number.

31. A mole is …
6.022 x 1023 atoms, molecules, electrons or ions …
– any particle.
Can you count to a mole?
Since they are so small, we must count atoms indirectly.

32. Suppose you wanted to know the number of marbles in a large jar.
Weigh a few marbles,
weigh all the marbles,
use a conversion factor.

33. Suppose … Like this: 10 marbles = 86.45 grams
Avg. marble = grams
All the marbles = g
This is a conversion factor
1 marble
g x =
286 marbles
8.645 g

34. We can count a large number of particles by weighing them.

35. We can count atoms if we know the mass of an Avogadro's number of atoms.

36. An Avogadro's number of atoms has a mass equal to the molar mass.
6.022 x 1023 atoms of sodium
have a mass of 23.0 g
6.022 x 1023 atoms of iron
have a mass of 55.8 g
6.022 x 1023 atoms of aluminum
have a mass of 27.0 g

37. Q. How many atoms are in 50.0 grams of potassium?
We know that 1 mole of K has a mass of 39.1 grams; and
1 mole is 6.02 x 1023 atoms.
6.02 x 1023 atoms K
50.0 g K
x =
39.1 g K
7.70 x 1023 atoms K

38. The molar mass of an element is the mass of 6
The molar mass of an element is the mass of x 1023 atoms or 1 mole of that element.

39. FYI: We now use
“molar mass” instead of..
gram atomic weight,
gram molecular weight,
gram formula weight.

40. sodium (Na) 23.0 g/mol iron (Fe) 55.8 g/mol chlorine (Cl) 35.5 g/mol
The molar mass of an element is usually rounded to one decimal place:
sodium (Na)
23.0 g/mol
iron (Fe)
55.8 g/mol
chlorine (Cl)
35.5 g/mol
phosphorous (P)
31.0 g/mol

41. What do the subscripts in a formula tell us?
The subscripts give the number of moles of each element in one mole of the compound.
1 mole of Fe2O3 contains …
2 moles of iron (Fe), and …
3 moles of oxygen (O)

42. How many moles of each kind of element are in one mole of …
CaCl2
1 mole Ca and 2 moles Cl
C12H22O11
12 moles C, 22 moles H, 11 moles O
Fe3(PO4)2
3 moles Fe, 2 moles P, 8 moles O

43. Calculating molar masses of compounds …
Sum of the
molar masses of the elements
Molar mass of the compound =
The molar mass of an element its atomic mass

44. Calculate the molar mass of water:
Molar mass of H2O =
(2 x 1.0) + (1 x 16.0) =
18.0 g/mol
2 hydrogen atoms
1 oxygen atom

45. General Equation for Molar Mass
S (atomic masses)
For each element, multiply it’s atomic mass by its subscript, then add them all together.

46. What is the molar mass of calcium chlorate?
Start with the formula:
Ca(ClO3)2
1 mol Ca, 2 mol Cl, 6 mol O
(1 x 40.1) + (2 x 35.5) + (6 x 16.0)
= g/mol

47. What are the molar masses of each of the following?
1. HCl
2. Fe2O3
3. H2SO4
4. Ca3(PO4)2
5. (NH4)2CO3
36.5 g/mol
159.6 g/mol
98.1 g/mol
310.3 g/mol
96.0 g/mol

48. Molar Conversions 1 mol = 1 molar mass 1 mol = 6.022 x 1023 particles
Use conversion factors to convert between moles, grams, molecules and the volumes of gases at STP.
1 mol = 1 molar mass
1 mol = x 1023 particles
1 mol = 22.4 L of any gas at STP

49. Convert the following:
grams of iron metal to moles.
0.314 moles Fe
moles of CaCl2 to grams.
4.02 g CaCl2
x 1024 molecules of SO3 to moles.
9.05 moles SO3

50. Detailed solutions:

51. 1 mole equals 22.4 L of any gas at STP
Why 22.4 L?
What is STP?
What has this all got to do with a mole?

52. Standard temperature and pressure
STP stands for
Standard temperature and pressure

53. Standard temperature Standard pressure STP … 0 C or 273 K
…the freezing point of water
0 C or K
Standard pressure
… atmospheric pressure at sea level
1.00 atmosphere, kPa,
760. mm Hg, 760. Torr
or lbs/in2

54. 1 mole of any gas at STP has a volume of 22.4 L
Consider a box with a volume of 22.4L O2
1 atm C
1.00 mol
22.4 L
If the box contains 1.00 mole of oxygen gas, at a temperature of 0 C, the pressure will be atm.

55. More molar conversions …
1. Convert 3.00 liters of N2 gas at STP to moles.
0.134 mol N2
2. Convert moles of HCl(g) to liters at STP.
10.2 L HCl
3. How many molecules are in mL of NH3 at STP?
6.72 x 1021 molecules NH3
Click for solutions

56. Detailed solutions:
Click to return

57. Calculations with density…
Recall that density is the mass per unit volume …
D = m V
We can find the density of a gas at STP if we know the molar mass.

58. Sample density calculation:
What is the density of carbon dioxide at STP?
We know that the molar mass of CO2 is 44.0 g/mol and the volume of 1 mole of gas is 22.4L at STP

59. Sample density calculation:
What is the density of carbon dioxide at STP?
Mass of 1 mole of CO2
Volume of 1 mole of CO2

60. Additional problems:
1. Find the density of nitrogen gas (N2) at STP.

61. 2. Find the mass of 200.0 mL of propane (C3H8) at STP.
m = V D
Hint: What is the density of propane?
This is the density of propane

62. D = ----------------------- mass of one mole volume of one mole
m = V D
This is the density of propane

63. This concludes the presentation on moles and molar mass.