1. Mass Relationships in Chemical Reactions
Chapter 3
Mass Relationships in Chemical Reactions
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2. Chapter 3 (80-107) 3.1 Atomic mass. 3.2 Avogadro’s number
and the molar mass of
an element.
3.3 Molecular mass.
3.5 Percent composition
of compounds.
3.6 Experimental
determination of
empirical and molecular
formulas.
3.7 Chemical reactions.
and chemical equations.
3.8 Amounts of reactants and
products.
3.9 Limiting reagents.
3.10 Reaction yield.

3. Atomic mass is the mass of an atom in atomic mass units (amu)
Micro World
atoms & molecules
Macro World
grams
Atomic mass is the mass of an atom in atomic mass units (amu)
One atomic mass unit is defined as a mass exactly equal to one –twelfth the mass of one carbon-12 atom.
By definition:
1 atom 12C “weighs” 12 amu
On this scale
1H = amu
16O = amu
3.1

4. Each atom have more than one isotope with different abundance
Average atomic Mass: the average mass of all of the isotopes of an element, each one weighted by its proportionate abundance
Science each atom have more than one isotope with different abundance

5. Average atomic mass of lithium:
Natural lithium is:
7.42% 6Li (6.015 amu)
92.58% 7Li (7.016 amu)
Average atomic mass of lithium:
7.42 x x 7.016
100
= amu
3.1

6. Average atomic mass (6.941)

7. PRACTIES EXERICISE 3.1 EXAMPLE 3.1 10B (19.78 percent)
Atomic mass
11B (80.78percent)
Atomic mass
65Cu (30.91percent)
Atomic mass
63Cu (69.091percent)
Atomic mass 62.93
(19.78 % x ) % )
100
(30.91% x ) % x 62.93)
100
= amu
=10.81amu

8. equal abundance MEAN each atom has abundance 50% .
Iodine has two isotopes 126I and 127I, with the equal abundance.
Calculate the average atomic mass of Iodine (53I).
(a)
126.5 amu
(b)
35.45 amu
(c)
1.265 amu
(d)
71.92 amu
equal abundance MEAN each atom
has abundance 50% .

9. PROBLEM 3.6
The atomic masses of 6Li and 7Li are amu and amu , respectively. Calculate the natural abundances of these two isotopes. The average atomic mass of Li is 6.941
The sum of natural abundances of isotopes should equal = 1
If the natural abundance of isotope 1 = x1
then the natural abundance of isotope 2 = x2
So x1 + x2 = 1 → x2 = 1- x1
Average atomic mass =(natural abundance × atomic mass) isotope 1+ (natural abundance × atomic mass) isotope 2
6.941 = × x × (1- x1 ) = x x1
= (6.0151x x1) = 0.1 = x
→ x1 = → x2 = 1- x1
X2 = 92.5
The natural abundances of 6Li and 7Li are 7.55 and 92.5 respectively

10. 3.2 Avogadro’s number and molar mass of an element
Avogadro's Number , Is the number of atoms in exactly 12 grams of carbon-12 (NA = x 1023)
The mole (mol) is the amount of a substance that contains as many elementary entities as there are atoms in exactly grams of 12C
One mole of a substance contains an Avogadro's Number of units

11. Dozen = 12 Pair = 2 The mole (mol) is the amount of a substance that
contains as many elementary entities as there
are atoms in exactly grams of 12C isotope
1 mol = NA = x 1023
Avogadro’s number (NA)
3.2

12. Molar mass M is the mass of 1 mole of in grams marbles atoms
eggs
shoes
Molar mass M is the mass of 1 mole of in grams
marbles
atoms
1 mole 12C atoms = x 1023 atoms = g
1 12C atom = amu
1 mole 12C atoms = g 12C
1 mole lithium atoms = g of Li
For any element
atomic mass (amu) = molar mass (grams)
3.2

13. One mole of H2 molecules has 6.022 x 1023 molecules
THUS:
one mole of H atoms has
6.022 x 1023 atoms
&
One mole of H2 molecules has x molecules

14. C S C Hg Cu Fe
One mole of these substances contain = x 1023 atoms
but is not equal because they have different molar masses

15. 1 12C atom 12.00 amu 12.00 g 6.022 x 1023 12C atoms = 1.66 x 10-24 g
1 amu = 1.66 x g or 1 g = x 1023 amu M
= molar mass in g/mol
NA = Avogadro’s number
3.2

16. Do You Understand Molar Mass?
How many atoms are in g of potassium (K) ?
1 mol K = g K
1 mol K = x 1023 atoms K
1 mol K
39.10 g K x x
6.022 x 1023 atoms K
1 mol K =
0.551 g K
8.49 x 1021 atoms K
3.2

19. Worked Example 3.4

20. molecular mass (amu) = molar mass (grams)
Molecular mass (or molecular weight) is the sum of
the atomic masses (in amu) in a molecule.
SO2 1S
32.07 amu 2O
+ 2 x amu
SO2
64.07 amu
For any molecule
molecular mass (amu) = molar mass (grams)
1 molecule SO2 = amu
1 mole SO2 = g SO2
3.3

21. (2 x atomic mass of H) + (1x atomic mass of O)
Molecular Mass
Molecular Mass: multiply the atomic mass of each element by the number of atoms of that element present in the molecule and sum over all the elements.
e.g. Molecular Mass of H2O is:
(2 x atomic mass of H) + (1x atomic mass of O)
(2 x amu) + (1x amu) = amu
الكتلة المولاريةmolar mass هي كمية مهمة جدا و نحسبها عن طريق ضرب عدد الذرات بعدد الكتلة و باستخدام الجدول الدوري و معرفتنا لصيغة و في كثير من الاحيان تحتاجي الى حساب الكتلة المولارية بالرغم أنها تكون غير مطلوبةو لكن حسابها مهم لحساب كمية أخرى مثل المولات و هذا ما سنراه لاحقا

22. Example What is the molar mass of the following compound ?
NH3 , CH3COOH , Na2SO4 , C6H12O6
NH3 = (1×14)+(3×1) = 17 g/mol
C2H4O2 = (2×12)+(4×1) )+(2×16) = 60 g/mol
Na2SO4 = (2×23)+(1×32) )+(4×16) = 142 g/mol
C6H12O6 = (6×12)+(12×1) )+(6×16) = 180 g/mol

23. Sulfur dioxide SO2 = 32.07+2 (16) = 64.07 amu Caffeine C8H10 N4O2
EXAMPLE 3.5
Calculate the molecular masses ( in amu) of the following compounds ?
Sulfur dioxide SO2 = (16) = amu
Caffeine C8H10 N4O2
= 8(12.01)+ 10 (1.008) + 4(14.01)+ 2(16) = amu
Practice exercise3.5
Calculate the molecular masses of methanol?
methanol C H4O
= 1(12.01)+ 4 (1.008) + 1(16) = 32.4 amu

24. m = mass (atom or molecule)
n = number of moles
m = mass (atom or molecule)
M = molar mass (atomic mass or molecular mass)
What is the relation between them?
n = number of moles
N = number of atoms or molecules
NA = Avogadro's number (atoms (or molecules)/mol)
What is the relation between them?
تذكري ان عدد المولات تساوي الكتلة على الكتلة المولارية فممكن من ان يعطيك كتلة الماده و صيغتها و يطلب المولات ببساطة من القانون و من صيغة المركب نحسب الكتلة المولارية
اذا طلب كتلة المركب و أعطاكي صيغة المركب و عدد المولات هل تستطيعين حساب الكتلة؟؟؟

25. EXAMPLE 3.2 How many moles of He atoms are in 6.46 g of He ?
How many grams of Zn are in mole of Zn?
Since one mol equal g so logically mol weight less

26. Example 3.6
Methane is the principle component of natural gas . How many CH4 are in 6.07 g of CH4?

27. Example 3.4 p84:
How many S atoms are in 16.3 g of S?
Strategy:
How many moles in 16.3 g of S = X mol
1 mole → x1023 S atoms
X moles → ? atoms

28. From the periodic Table: The atomic mass of S = 32.07 amu
Solution:
From the periodic Table: The atomic mass of S = amu
The molar mass of S = g/mol
Thus: g → 1 mole of S
16.3 g of S → ? mole
We know: 1 mol of S → x1023 S atoms
0.508 mole → ? S atoms
There is 3.06 x1023 atoms of S in 16.3 g of S
H.W. Solve the Practice Exercise p85

29. حل مختصر
How many S atoms are in 16.3 g of S?

30. How many molecules of ethane (C2H6) are present in 0.334 g of C2H6?
(a)
2.01 x 1023
(b)
6.69 x 1021
(c)
4.96 x 1022
(d)
8.89 x 1020
1 mole of C2H6 → x 1023 molecules of C2H6
0.011 mole of C2H6 → ? molecules of C2H6

31. Example 3.7 p87:
How many hydrogen atoms are present in 25.6 g of urea [(NH2)2CO]. The molar mass of urea is g/mol.

32. H.W. What is the mass, in grams, of one copper atom?
(a)  g
(b) g
(c) 1 amu
(d)  g
(e)  1021 g
Atomic mass of Cu = amu
Molar mass of Cu = g/mol
63.55 g of Cu → 1 mol of Cu
1 mol of Cu → x 1023 Cu atoms
63.55g of Cu → 6.022x1023 Cu atoms
?g of Cu → 1 Cu atom

34. Worked Example 3.6

35. Worked Example 3.7

36. Do You Understand Molecular Mass?
How many H atoms are in 72.5 g of C3H8O ?
1 mol C3H8O = (3 x 12) + (8 x 1) + 16 = 60 g C3H8O
1 mol C3H8O molecules = 8 mol H atoms
1 mol H = x 1023 atoms H
1 mol C3H8O
60 g C3H8O x
8 mol H atoms
1 mol C3H8O x
6.022 x 1023 H atoms
1 mol H atoms x =
72.5 g C3H8O
5.82 x 1024 atoms H
3.3

37. formula mass (amu) = molar mass (grams)
Formula mass is the sum of the atomic masses
(in amu) in a formula unit of an ionic compound.
NaCl
1Na
22.99 amu
1Cl
amu
NaCl
58.44 amu
For any ionic compound
formula mass (amu) = molar mass (grams)
1 formula unit NaCl = amu
1 mole NaCl = g NaCl
3.3

38. Do You Understand Formula Mass?
What is the formula mass of Ca3(PO4)2 ?
1 formula unit of Ca3(PO4)2
3 Ca
3 x 40.08
2 P
2 x 30.97
8 O
+ 8 x 16.00
amu
3.3

39. n x molar mass of element molar mass of compound x 100%
Percent composition of an element in a compound = is the percent by mass of each element in a compound
n x molar mass of element
molar mass of compound
x 100%
n is the number of moles of the element in 1 mole of the compound
%C =
2 x (12.01 g)
46.07 g
x 100% = 52.14%
C2H6O
%H =
6 x (1.008 g)
46.07 g
x 100% = 13.13%
%O =
1 x (16.00 g)
46.07 g
x 100% = 34.73%
52.14% % % = 100.0%
3.5

40. Example 3.8 PRACTIES EXERICISE 3.8 %H = 2(1.008) 98.72
Calculate the percent composition by mass of H , P, and O in H2SO4 acid ?
Molar mass of H2SO4
= 2(1.008)+ 1 (32.7) + 4(16)
= amu
Calculate the percent composition by mass of H , P, and O in H3PO4 acid ?
Molar mass of H3PO4
= 3(1.008)+ 1 (30.97) + 4(16)
= amu
%H =
2(1.008)
98.72
x 100% = %
%H =
3(1.008)
97.99
x 100% = %
%S =
1(32.07)
98.72
x 100% = %
%P =
1(30.97)
97.99
x 100% = %
%O=
4(16)
98.72
x 100% = 64.83%
%O=
4(16)
97.99
x 100% = 65.31%

41. H.W. Calculate the percent of nitrogen in Ca(NO3)2:
12.01%.
17.10%.
18%
16%.
H.W. All of the substances listed below are fertilizers that contribute nitrogen to the soil.
Which of these is the richest source of nitrogen on a mass percentage basis?
(a)
Urea, (NH2)2CO
(b)
Ammonium nitrate, NH4NO3
(c)
Guanidine, HNC(NH2)2
(d)
Ammonia, NH3
%N = 46.6%
%N = 58%
%N = 71.1%
%N = 82.2%
ايا من هذه المواد هواغنى مصدر للنيتروجين على اساس احتوائه على اكبر نسبه وزنيه من النيتروجين؟

43. 2.
What information would you need to calculate the average atomic mass of an element? A)
The number of neutrons in the element. B)
The atomic number of the element. C)
The mass and abundance of each isotope of the element. D)
The position in the periodic table of the element. 3.
The atomic masses of Cl (75.53 percent) and Cl (24.47 percent) are amu and amu, respectively. Calculate the average atomic mass of chlorine. The percentages in parentheses denote the relative abundances. A)
35.96 amu B)
35.45 amu C)
36.47 amu D)
71.92 amu 6.
How many amu are there in 8.4 g? A)
8.4 x1023 amu B)
1.4 x amu C)
8.4 amu D)
5.1 x 1024 amu 9.
How many atoms are there in 5.10 moles of sulfur (S)? A)
3.07 x 1024 B)
9.59 x 1022 C)
6.02 x 1023 D)
9.82 x 1025

44. 14.
What is the mass in grams of a single atom of As? A)
1.244 x g B)
2.217 x g C)
8.039 x 1021 g D)
4.510 x1025 g
16.
How many atoms are present in 3.14 g of copper (Cu)? A)
2.98 x 1022 B)
1.92 x 1023 C)
1.89 x 1024 D)
6.02 x 1023
19.
Calculate the molar mass of Li2CO3. A)
73.89 g B)
66.95 g C)
41.89 g D)
96.02 g
22.
How many molecules of ethane (C2H6) are present in g of C2H6? A)
2.01 x 1023 B)
6.69 x 1021 C)
4.96 x 1022 D)
8.89 x 1020

45. 33.
Allicin is the compound responsible for the characteristic smell of garlic. An analysis of the compound gives the following percent composition by mass: C: 44.4 percent; H: 6.21 percent; S: 39.5 percent; O: 9.86 percent. What is its molecular formula given that its molar mass is about 162 g? A)
C12H20S4O2 B)
C7H14SO C)
C6H10S2O D)
C5H12S2O2
35.
The formula for rust can be represented by Fe2O3. How many moles of Fe are present in 24.6 g of the compound? A)
2.13 mol B)
0.456 mol C)
0.154 mol D)
0.308 mol

46. Heavy
Light
KE = 1/2 x m x v2
v = (2 x KE/m)1/2
F = q x v x B
3.4