Download Unit 6- Math of Chemistry

Formulas, Equations And The Math Involved
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Analysis
Chemical change
Coefficient
Combustion
Decomposition
Diatomic molecule
Double replacement
Empirical Formula
Formula
Formula mass
Gram formula mass
Mole
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Molecular formula
Molecule
Percent composition
Polyatomic ion
Product
Qualitative
Quantitative
Reactant
Single replacement
Subscript
Symbol
Synthesis
Review:
• What’s the SI unit for amount?
– A mole
• What do we know about moles?
– # of atoms in 12 grams of C-12
– Avogadro’s number
– 6.022 x 1023
• What is the gram formula mass?
– Mass in grams of 1 mole of a substance
– Units are g/mol….. The formula mass is in amu
– Ex: Carbon 12g/mol
• Is the atomic masses on the Periodic Table an average?
– YES, it’s the average of the masses of each isotope
Review:
• How do you calculate average atomic mass?
• Converting grams < -- > moles < -- > molecules
Molecules
Grams
6.022x1023
g/mol
Moles
What are chemical formulas used for?
• To express composition
– KBr 1:1 ratio (in ionic compounds the ratio is of cations and anions)
– H2O 2:1 ratio (covalent)
• To give ratios of polyatomic ions
– KNO3 1:1 ratio because NO3 is a polyatomic ion
• To calculate formula masses
– ZnCl2
= 136.29g/mol
• To calculate the percent composition of each element
– Percent composition- % by mass of each element in a compound
• What is the percent composition of O in KClO3?
• 1st: Determine formula mass of element and of the compound
• 2nd: % of element = element formula mass/ total formula mass x 100
Molecular vs. Empirical Formula
• Empirical formula– Chemical formula that shows the composition of a compound in its
simplest ratios
– Ex: CH2O
• Molecular formula– Chemical formula that shows the number and kinds of atoms in a
molecule
– Multiples of the empirical formula
– Ex: C6H12O6
• You can find the molecular formula from the empirical formula
– If a compound has a mass of 180 amu and an empirical formula of CH2O,
what is the molecular formula?
• Get formula mass of empirical formula (C + H +H +O = 30amu)
• Divide molecular mass given by empirical formula mass (180amu / 30amu = 6)
• Multiply subscripts by 6 (C 1x6 H 2x6 O 1x6 = C6H12O6)
Chemical Equations and Reactions
• What is a chemical reaction?
– When 1 or more substances change into 1 or more substances whose
chemical and physical properties differ from the original substances
• Chemical formulas- use chemical symbols and #’s to show
quantitative and qualitative info about a substance
– Coefficients- written in front of a formula, tells you how many units of
the formula are present
• Ex: 2H2O
 4 H’s and 2 O’s
– Subscripts- written after an element, tells how many atoms of that
element
Describing a Chemical Reaction
Indications of a Chemical Reaction
– Evolution of heat, light, and/or sound
– Production of a gas
– Formation of a precipitate
– Color change
Signs of Chemical Reactions
There are five main signs that indicate a chemical reaction has taken place:
release
input
change in color
change in odor
production of new
gases or vapor
input or release
of energy
difficult to reverse
Chemical Equations
aluminum oxide
Depict the kind of reactants and products
and their relative amounts in a reaction.
4 Al(s) + 3 O2(g)
2 Al2O3(s)
The letters (s), (g), and (l) are the
physical states of compounds.
The numbers in the front are called
stoichiometric coefficients.
Chemical Equations and Reactions Con’t
Reactants
Products
“yields/produces”
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1st- word equation: carbon + oxygen  carbon dioxide
2nd- formula eqn: C(s) + O(g)  CO2(g)
3rd- balance:
C(s) + O2(g)  CO2(g)
What law does this follow?
– Conservation of mass
• Equations are like recipes
– Show physical states and rx conditions
Balancing Equations
• Identify reactants and products
• Count atoms
– Treat polyatomic ions like a single unit
• Insert coefficients
– Try odd-even technique
• Multiply odd by 2 gives an even
– Can’t change subscripts**
• Check results
• Practice:
Fe2O3 + H2  Fe + H2O
NH3
+ O2  NO + H2O
HgCl2 + AgNO3  Hg(NO3)2 + AgCl
CH4 + 2 O2  CO2 + 2 H2O
Reactants
1 C atom
4 H atoms
4 O atoms
Products
1 C atom
4 H atoms
4 O atoms
Write a balanced equation for the reaction between chlorine
and sodium bromide to produce bromine and sodium chloride.
1) Write a word equation for the reaction.
chlorine + sodium bromide  bromine + sodium chloride
2) Write the correct formulas for all reactants and products.
Cl2
+
NaBr

Br2
+
NaCl
3) Determine the coefficients that make the equation balance.
Cl2
+
2 NaBr

Br2
+
2 NaCl
Write the balanced equation for the reaction between aluminum sulfate
and calcium chloride to form a white precipitate of calcium sulfate.
1) Write a word equation for the reaction.
?
?
aluminum sulfate + calcium chloride  calcium sulfate + aluminum chloride
2) Write the correct formulas for all reactants and products.
Al2(SO4)3
+
CaCl2

CaSO4
+
AlCl3
3) Determine the coefficients that make the equation balance.
Al2(SO4)3
+
3 CaCl2

3 CaSO4
+
2 AlCl3
Types of Chemical Reactions
• Synthesis (combination) Rx:
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–
–
2 Na
Na
Na
2 reactants form a single product
A + B  AB
Ex: CO2(g) + H2O(l)  H2CO3(aq)
*dehydration synthesis
+
Cl2

2 NaCl
Cl
Na+ Cl -
Cl
Cl - Na+
• Decomposition (analysis) Rx:
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1 reactant forms 2 or more products
AB  A + B
Ex: 2NI3(s)  N2(g) + 3I2(g)
*airbags NaN3 +spark 2Na(s) + 3N2(g)
2 H2 O
2 H2
+
H
O
H
H
O
H
+
O2
• Combustion Rx:
– Reaction of carbon based compound with oxygen to produce carbon
dioxide and water vapor
– Ex: burning of wood
– Incomplete combustion= CO, unburned carbon(soot), carbon dioxide
and water vapor
Displacement reactions
• Single and double replacement reactions
• It’s necessary to use Reference Table J to
determine if the reaction can take place
• Element can replace those listed below it
• Ex: F2 + 2NaCl  Cl2 + 2NaF
– F replaces Cl
Ca
Foiled again –
Aluminum loses to Calcium
** H2- all metals
above it will react
with acids to
release H gas and
form a salt
• Single replacement Rx:
– 1 element replaces another in a compound
– A + BX  B + AX
– Ex: Cu(s) + 2AgNO3(aq)  2Ag(s) + Cu(NO3)2(aq)
• Reverse Rx won’t happen due to the reactivity of the metals
Predict if these reactions will occur
3 Mg
+ 2 Al Cl3
2 Al
+ 3MgCl2
Can magnesium replace aluminum? YES, magnesium is more reactive than aluminum.
Activity Series
Al
+
MgCl2
No reaction
Can aluminum replace magnesium? NO, aluminum is less reactive than magnesium.
Activity Series
MgCl2
+
Al
Therefore, no reaction will occur.
No reaction
Order of reactants
DOES NOT
determine how
they react.
The question we must ask is can the single element replace its counterpart?
metal replaces metal or nonmetal replaces nonmetal.
Single-Replacement Reactions
Activity Series
Fe
+
FeCl2
CuCl2
+
Cu
Can Fe replace Cu? Yes
Zinc in nitric acid
Zn
+
2 3
HNO
Can Zn replace H?
Zn(NO3)2
+ H2
Yes
NO REACTION
MgCl2
+
MgBr2
Br2
Can Br replace Cl?
+
No
General Form
A
+
BC
AC + B
Cl2
Li
Rb
K
Ba
Ca
Na
Mg
Al
Mn
Zn
Cr
Fe
Ni
Sn
Pb
H2
Cu
Hg
Ag
Pt
Au
F2
Cl2
Br2
I2
• Double replacement Rx:
– Usually involves 2 soluble ionic compounds that react in solution to
produce a precipitate, a gas or a molecular compound such as water
– AB + CD  AD + CB
– Ex: 2KI(aq) + Pb(NO3)2(aq)  PbI2(s) + 2KNO3(aq)
Determining Unknowns
• Follow Law of Conservation of Mass
• Unknown reactant or product:
– 2Na + 2H2O  X + 2NaOH
• You must have the same amount of each element on each side of the reaction
– X = H2
• Missing mass:
– How many grams of silver nitrate are needed to react with 156.2g of
sodium sulfide to produce 595.8g of silver sulfide and 340.0g of
sodium nitrate?
2AgNO3 + Na2S  Ag2S + 2NaNO3
X
+ 156.2g = 595.8g + 340.0g
X = 595.8g + 340.0g - 156.2g = 779.6g
Stoichiometry
• Proportional relationship between 2 or more substances
during a chemical reaction
– mass relationships between substances in a chemical reaction
– based on the mole ratio
• Mole ratio
– indicated by coefficients in a balanced equation
2 Mg + O2  2 MgO
Proportional Relationships
2 1/4 c. flour
1 tsp. baking soda
1 tsp. salt
Conversion
Factor
1 c. butter
3/4 c. sugar
3/4 c. brown sugar
1 tsp vanilla extract
2 eggs
2 c. chocolate chips
Makes 5 dozen cookies.
I have 5 eggs. How many cookies can I make?
Ratio of eggs to cookies
5 eggs
5 dozen
2 eggs
150 dozen
cookiescookies
= 12.5
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Visualizing a Chemical Reaction
2 Na
10 mole Na
___
+
Cl2
5 mole Cl2
___
2 NaCl
10
? mole NaCl
___
Formation of Ammonia
Stoichiometry Steps
1. Write a balanced equation.
2. Identify known & unknown.
3. Line up conversion factors.
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–
–
–
–
Mole ratio Molarratio
mass-Mole
Molarity Molar volume -
moles  moles
molesmoles
grams
moles
moles  liters soln
moles  liters gas
Core step in all stoichiometry problems!!
4. Check answer.
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Molar Volume at STP
1 mol of a gas=22.4 L
at STP
Standard Temperature
&
0°C and 1 atm
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Pressure
Molar Volume at STP
LITERS
OF GAS
AT STP
Molar Volume
(22.4 L/mol)
MASS
IN
GRAMS
Molar Mass
(g/mol)
6.02  1023
MOLES
particles/mol
NUMBER
OF
PARTICLES
Molarity (mol/L)
LITERS
OF
SOLUTION
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Stoichiometry Problems
• How many moles of KClO3 must decompose in
order to produce 9 moles of oxygen gas?
2KClO3  2KCl + 3O2
? mol
9 mol O2
2 mol KClO3
3 mol O2
9 mol
= 6 mol KClO3
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
2
1.
5 mol
2 Sb + 3 Cl2  2 SbCl3
excess
5 mol
7.5
excess
x mol
mol
=
3
x mol
2 x = 15
x = 7. 5 mol
x mol
How many moles of chlorine gas are required to react with 5 moles of antimony?
x mol Cl2 = 5 mol Sb
3 mol Cl2
2 mol Sb
= 7.5 mol Cl2
How many moles of SbCl3 are produced from 5 moles of antimony and excess Cl2?
x mol SbCl3 = 5 mol Sb
2 mol SbCl3
2 mol Sb
= 5 mol SbCl3
How many moles of SbCl3 are produced from 7.5 moles of Cl2 and excess Sb?
x mol SbCl3 = 7.5 mol Cl2
2 mol SbCl3
3 mol Cl2
= 5 mol SbCl3
2.
2 Mg + O2  2 MgO
10 mol
xL
x mol
How many moles of magnesium oxide are produced from the burning of 10 mol of Mg?
x mol MgO = 10 mol Mg
2 mol MgO
2 mol Mg
= 10 mol MgO
How many liters of oxygen are needed to burn 10 mol of Mg? Assume 1 mol O2 = 22.4 L
x L O2 = 10 mol Mg
x L O2 = 10 mol Mg
1 mol O2
2 mol Mg
= 5 mol O2
1 mol O2
22.4 L O2
2 mol Mg
1 mol O2
22.4 L O2
1 mol O2
= 112 L O2
= 112 L O2
3.
CaCl2  Ca + Cl2
8 mol
x mol
How many moles of calcium metal and chlorine gas are produced
from the decomposition of 8 mol of calcium chloride?
x mol Ca = 8 mol CaCl2
1 mol Ca
1 mol CaCl2
= 8 mol Ca
How many moles of calcium metal and chlorine gas are produced
from the decomposition of 8 mol of calcium chloride?
x mol Cl2 = 8 mol CaCl2
1 mol Cl2
1 mol CaCl2
= 8 mol Cl2
2C2H6 + 7O2  4CO2 + 6H2O
1. How many liters of CO2 gas will be produced from the
complete combustion of 30.0L of C2H6 according to the
equation?
vol C2H6(g)= 30L
vol of CO2(g) = x
ratio C2H6(g) to CO2(g) = 2:4
30L/ 2 = X/4 X= 60L of CO2
2. How many moles of H2O will be produced from the complete
combustion of 3 mol of C2H6 according to the equation?
mol C2H6 = 3 mol
mol water = x mol
ratio ethane to water = 2:6
3mol C2H6/ 2 mol C2H6 = x/6mol water X=9mol water