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Quantitative Chemistry
•matter
•units
•significant figures
•atomic structure, isotopes, periodic table
•basic nomenclature (ions, molecular &inorganic compounds)
•stoichiometry and balancing equations by inspection
•moles and Avogadro’s number
•empirical and molecular formulae
•limiting reagents
1
PRACTICE EXAMPLE
A nugget of gold with a mass of 521 g is added to 50.0 mL of water. The
water level rises to a volume of 77.0 mL. What is the density of the gold?
2
PRACTICE EXAMPLE
Naturally occurring Mg has three isotopes:
24Mg (78.90 %) 23.9850 u
25Mg (10.00 % )24.9858 u
26Mg (11.10 %) 25.9826 u
AAM=?
3
PRACTICE EXAMPLE
NAME:
NaCl
K2SO4
Ba(OH)2
cobalt(II) nitrate
silver sulfide
ferric chloride
4
PRACTICE EXAMPLE
Anion
Corresponding acid
ClS2ClO4ClO3ClO2ClO-
5
PRACTICE EXAMPLE
NAME:
SO2
PCl5
N2O3
NF3
P4S10
silicon tetrabromide
6
PRACTICE EXAMPLE
BALANCE:
C2H6 + O2 → CO2 + H2O
Al + HCl → AlCl3 + H2
7
PRACTICE EXAMPLE
How many oxygen atoms are in 1.50 mol of sodium carbonate?
8
PRACTICE EXAMPLE
Determine the empirical formula of a compound with 10.4% C, 27.8% S and 61.8% Cl.
9
PRACTICE EXAMPLE
Eucalyptol has an empirical formula of C10H18O. The experimentally determined
molecular mass of this substance is 152 u. What is its molecular formula?
10
PRACTICE EXAMPLE
Determine (i) which reactant is the limiting reactant and (ii) how much excess
reactant is leftover in the following reaction:
3NH4NO3 + Na3PO4 → (NH4)3PO4 + 3NaNO3
30.0 g
50.0 g
11
PRACTICE EXAMPLE
Determine the theoretical yield and the % yield of NaNO3 if 15.0 g of sodium nitrate
is formed when the reaction is carried out.
3NH4NO3 + Na3PO4 → (NH4)3PO4 + 3NaNO3
30.0 g
50.0 g
12
TYPES OF REACTIONS
•
•
•
•
•
•
•
•
Electrolytes
Acid- base reactions
Solubility rules
Precipitation reactions
Writing ionic equations
Oxidation numbers
Redox reactions
Concentration
13
PRACTICE EXAMPLE
BALANCE AND SHOW PHASES:
BaCl2 + H2SO4 → BaSO4 + HCl
14
PRACTICE EXAMPLE
BALANCE:
H2SO4(aq) + NaOH(aq) →
15
PRACTICE EXAMPLES
OXIDATION No OF BOLD:
S2O32FeO42Na2SO3
S8
NH4+
16
PRACTICE EXAMPLE
BALANCE IN ACIDIC:
Fe2+(aq) + MnO4¯  Fe3+(aq) + Mn2+(aq)
17
PRACTICE EXAMPLE
BALANCE IN BASIC:
S(s) + ClO¯(aq)  SO32- (aq) + Cl¯(aq)
18
PRACTICE EXAMPLE
Calculate the molarity of a solution made by dissolving 5.00 g of glucose,
C6H12O6 , in sufficient water to form exactly 100. mL of solution.
19
PRACTICE EXAMPLE
**How many grams of NaOH are needed to neutralise 20.0 cm3 of 0.150 M
H2SO4 solution?
20
PRACTICE EXAMPLE
How many millilitres of 5.00 M K2Cr2O7 solution must be diluted to prepare 250.
cm3 of 0.100 M solution?
21
PRACTICE EXAMPLE
What mass of Ag2CrO4 (331.8 g mol-1) will precipitate if excess K2CrO4(aq) is added to
514.6 mL of 0.1683 M AgNO3 . The unbalanced equation for the reaction is:
AgNO3(aq) + K2CrO4(aq) → Ag2CrO4(s) + KNO3(aq)
22
PRACTICE EXAMPLE
BALANCE AND SHOW PHASES:
Ba(NO3)2 (aq) + Li2SO4 (aq) →
23
GASES
• Properties of gases
• Gas Laws
• Gas equations
– General gas equation
– Ideal gas equation (density & molar mass derivation)
– Partial pressures
– Gas collected over water
– Van der Waal’s real gas equation
• Kinetic molecular theory of gases
24
PRACTICE EXAMPLES
Convert:
253 Torr → atm
326 Pa → atm
51 atm → mmHg
65 atm → bar
25
PRACTICE EXAMPLE
A gas bubble with a volume of 1.00 mm3 originates at the bottom of the lake
where the pressure is 3.00 atm and the temperature is 12.5 0 C. Calculate its
volume (in mm3) when the bubble reaches the surface of the lake where the
pressure is 695 Torr and the temperature is 15 0C.
26
PRACTICE EXAMPLE
Determine the molar mass and identity of a 0.134 g sample of gas with a volume 75.0 mL at
STP?
27
PRACTICE EXAMPLE
What is the density (in g dm-3) of a sample of Cl2 gas at 1124 Torr and 24 0C?
28
PRACTICE EXAMPLE
A gaseous mixture made from 6.00 g O2 and 9.00 g CH4 is placed in a 15.0 L vessel at 0 °C.
Calculate the partial pressure of each gas and the total pressure in the vessel (in Pa).
29
PRACTICE EXAMPLE
A 31.46 mL sample of gas was collected over water at 296.9 K and at a pressure of
706.4 mmHg. Consider the gas sample to be a mixture of water vapour and N2 gas.
What mass of nitrogen was collected? (Vapour pressure of water at 296.9 K is 22.3
mmHg)
30
PRACTICE EXAMPLE
Calculate the pressure of 1.00 mol Cl2(g) confined to a volume of 3.00 dm3 at 0.0 C
using the van der Waals equation.
(Note a= 3.64 kPa dm6 mol-2, b = 0.0427 dm3 mol-1, R = 8.314 kPa dm3 mol-1 K-1)
31
ELECTRONIC STRUCTURE OF ATOMS
•
•
•
•
•
Wave nature of light
Quantum theory
Line spectra (Bohr model)
Quantum numbers and atomic orbitals
Electron configuration
32
PRACTICE EXAMPLE
For radiation of wavelength 242.4 nm, what is the energy of one photon of light?
33
PRACTICE EXAMPLE
Calculate the wavelength (in nm) associated with an electronic transition in the
hydrogen atom from n=4 to n=1.
34
PRACTICE EXAMPLE
Determine E for the transition of an electron from n=5 to n=2 in a hydrogen atom.
35
PRACTICE EXAMPLES
Give the numerical values of n and l and ml corresponding to each of the
following designations:
i)
3p
ii) 2s
iii) 4f
36
PRACTICE EXAMPLE
Write the expanded and condensed electron configuration of the following:
i) N
ii) Si
iii) Cu
37
PRACTICE EXAMPLE
Draw the electron “block” diagram of carbon and aluminium
38
BASICS OF BONDING
•
•
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Octet rule
Ionic bonds and compounds
Covalent bonds and compounds
Polarity and Electronegativity
Lewis symbols and structures
Formal Charge
Resonance structures
Exceptions to Lewis Rules
39
PRACTICE EXAMPLES
Draw Lewis symbols or structures for Calcium, silicon, neon, PCl3, CH3OH, N2, NH4+, OH-
40
PRACTICE EXAMPLE
Draw three structures of CNS- with N as the central atom and decide with formal charge
which is the best structure.
41
PRACTICE EXAMPLE
Draw the resonance structures of O3 and NO3-
42
ELECTRON & MOLECULAR GEOMETRY
• VSEPR
• Electron geometries
• Molecular geometries
43
PRACTICE EXAMPLES
DETERMINE ELECTRON AND MOLECULAR GEOMETRY AND
BOND ANGLE:
PF4+ , AlCl63- , ICl3 , CH3+
44
INTERMOLECULAR FORCES
• Physical state
• Inter- vs Intra• Types of IM forces
–
–
–
–
–
Dipole-dipole forces
Hydrogen bonding
Ion-ion forces
Ion-dipole forces
Van der Waal’s forces
• Liquid properties
45
PRACTICE EXAMPLES
Why does NH3 have a higher boiling point than CH4 ?
Why does KCl have a higher melting point than I2 ?
46
PRACTICE EXAMPLE
Arrange the following in order of increasing boiling points and
identify the IM forces present in each compound:
CH3OH, CO2, RbF, CH3Br
47
PRACTICE EXAMPLES
INTERMOLECULARE FORCES PRESENT=?
i. H2O
ii. N2
iii. C6H5Cl
iv. C6H6
THERMOCHEMISTRY
• Energy
– Heat
– Heat capacity
– Calorimetry
• Enthalpy
– Heat of formation
– Heat of reaction
– Bond energies
49
PRACTICE EXAMPLES
A piece of titanium metal with a mass of 20.8 g is heated in boiling water to 99.5 °C and
then dropped into a coffee-cup calorimeter containing 75.0 g of water at 21.7 °C. When
thermal equilibrium is reached, the final temperature is 24.3 °C.
Calculate the specific heat capacity of titanium. (Specific heat of water is 4.184 J g-1 K-1)
50
PRACTICE EXAMPLES
A 50.0 g sample of water at 100 °C is poured into a 75.0 g sample of water at 25 °C.
What will be the final temperature of the water?
Specific heat capacity of water = 4.184 J g-1 °C-1
51
PRACTICE EXAMPLES
A 0.1375 g piece of magnesium was burned in a bomb-calorimeter containing 300 .g of
water. The temperature increased by 1.126 C. The heat capacity of the calorimeter is
1769 J C-1 and the specific heat capacity of water is 4.184 J g-1 C-1. Calculate the heat
given off by the magnesium in J g-1.
52
PRACTICE EXAMPLES
When 50.0 mL of 1.00 M NaOH is added to 100.0 mL of 0.500 M HCl in a coffee cup calorimeter
at 25.8 C, the temperature rises to 34.8 C. Assume that the density of the solution is 1.00 g
mL-1 and that its specific heat capacity is 4.184 J g-1 C-1. The equation for the reaction is:
NaOH(aq) + HCl(aq) → NaCl(aq) + H2O(l)
Calculate the enthalpy of the reaction in kJ mol-1 .
53
PRACTICE EXAMPLES
Calculate Hrxn for the combustion of 1 mol of benzene (C6H6(l)) given that Hf for
C6H6(l) ,CO2(g) and H2O(l) are 49.0 kJ/mol, -393.5 kJ/mol and -285.8 kJ/mol respectively.
54
PRACTICE EXAMPLES
Find Hrxn for ½ N2(g) + O2(g)  NO2(g) given that:
½N2(g) + ½O2(g)  NO(g)
H = 90.25 kJ
2NO2(g)  2NO(g) + O2(g)
H= 114.14 kJ
55
PRACTICE EXAMPLES
Use the table of bond energies shown below to calculate Hrxn for:
C2H4(g) + HCl(g)  C2H5Cl(g)
Bond
CC
C=C
CH
HCl
CCl
Bond energy/kJ mol-1
348
614
413
431
328
56
REACTION KINETICS
•
•
•
•
•
•
•
Reaction rates
Reaction order
Reaction mechanisms
Collision frequency
Energy profile diagrams
Arrhenius equation
Catalysts
57
PRACTICE EXAMPLES
(a)N2 + 3H2  2NH3
Rate =
(b) H2O2 + 2H+ + 3I¯  I3¯ + 2H2O
Rate =
58
PRACTICE EXAMPLE
A + B  products
rate = k[A]m[B]n
initial conc/mol dm–3
[A]
[B]
0.10
0.10
0.20
0.10
0.30
0.10
0.30
0.20
0.30
0.30
initial rate/mol dm–3 s–1
0.20
0.40
0.60
2.40
5.40
1
2
3
4
5
CALCULATE m, n and k
59
PRACTICE EXAMPLE
For the reaction:
NO2(g) + CO(g)  NO(g) + CO2(g)
the variation of the initial rate with the initial concentration of
NO2 (the initial concentration of CO kept constant), was found
to be as follows:
Experiment
[NO2]/mol dm-3
Initial rate/mol dm-3 s-1
1
0.150
0.010
2
0.300
0.040
3
0.600
0.160
4
0.900
0.360
Deduce the order of the reaction with respect to NO2
60
PRACTICE EXAMPLE
For the alkaline hydrolysis of ethyl nitrobenzoate (A)
the following data were obtained at 25 C.
Time/s
0
500
800
1500
2000
[A]/mol dm-3
0.0500
0.0167
0.0119
0.0071
0.0056
Evaluate the order of the reaction and calculate k
t
[A]
t
ln[A]
t
1/[A]
0
0.05
0
-2.99573
0
20
500
0.0167
500
-4.09235
500
59.88024
800
0.0119
800
-4.43122
800
84.03361
1500
0.0071
1500
-4.94766
1500
140.8451
2000
0.0056
2000
-5.18499
2000
178.5714
61
SOLUTION
0.06
0
0
0.05
500
1000
1500
2000
2500
-1
-2
ln[A]
0.03
0.02
-3
-4
0.01
-5
0
0
500
1000
1500
2000
2500
-6
t/s
t/s
1/[A]
[A]
0.04
200
180
160
140
120
100
80
60
40
20
0
0
500
1000
1500
2000
2500
t/s
62
PRACTICE EXAMPLE
For the reaction A  products, the following
data is given in the table below:
[A]/M
0.600
0.497
0.413
0.344
0.285
0.198
0.094
Time/s
0
100
200
300
400
600
1000
A) Show that the reaction is first order by plotting the
appropriate graph for first order reactions.
B) What is the value of the rate constant, k?
C) What is [A] at t = 750 s?
63
SOLUTION
time/s
time/s ln[A]
0
0
200
400
600
800
1000
-0.5
-1
ln[A]
-1.5
-2
-2.5
y/x = (-2.36-(-0.51))/(1000-0) s= -1.85 x 10-3 s-1
1200
0
-0.51
100
-0.699
200
-0.884
300
-1.07
400
-1.26
600
-1.62
1000
-2.36
PRACTICE EXAMPLE
A single step reversible reaction has an activation energy for the forward
reaction (Ea,f) of 28.9 kJ and 41.8 kJ for the reverse reaction (Ea,r)
Draw a potential energy level diagram and indicate H
PRACTICE EXAMPLE
The rate constant for the reaction:
H2(g) + I2(g)  2HI(g)
has been determined at the following temperatures:
k/M-1 s-1
T/K
5.4 x 10-4
599
2.8 x 10-2
683
Calculate the activation energy, Ea, for the reaction in J mol-1.
CHEMICAL EQUILIBRIUM
• Dynamic Equilibrium
• Equilibrium constant expression
–Kc
–Kp
–Qc
• Le Chatelier’s principle
PRACTICE EXAMPLES
EXPRESS KC
a) 2 H2S(g) ⇌ 2 H2(g) + S2(g)
b) PCl3(g) + 3 NH3(g) ⇌ P(NH2)3(g) + 3 HCl(g)
c) Na2CO3(s) + SO2(g) + ½ O2(g) ⇌ Na2SO4(s) + CO2(g)
PRACTICE EXAMPLE
N2O(g) + ½ O2(g) ⇌ 2 NO(g)
Kc = ?
N2(g) + ½ O2(g) ⇌ N2O(g)
Kc = 2.7 x 10-18
N2(g) + O2(g) ⇌ 2NO(g)
Kc = 4.7 x 10-31
PRACTICE EXAMPLE
A 5.00 L flask is filled with 1.86 mol NOBr. At equilibrium there is 0.082 mol Br2
present. Determine Kc for the reaction at 25 C.
2 NOBr(g) ⇌ 2 NO(g) + Br2(g)
PRACTICE EXAMPLE
A 0.0240 mol sample of N2O4(g) is allowed to come to equilibrium with NO2(g) in a 0.372
L flask at 25 C.
Calculate the amount of N2O4(g) at equilibrium.
N2O4(g) ⇌ 2 NO2(g) Kc = 4.61 x 10 -3 at 25 C
PRACTICE EXAMPLE
2 NH3(g) ⇌ N2(g) + 3 H2(g)
Kp = ?
Kc = 2.8 x 10-9 at 298K
PRACTICE EXAMPLE
Is a mixture of 0.0205 mol NO2(g) and 0.750 mol N2O4(g) in a 5.25 L flask at 25 C at
equilibrium? If not, in which direction will the reaction proceed?
N2O4(g) ⇌ 2 NO2(g) Kc = 4.61 x 10-3 at 25 C
PRACTICE EXAMPLE
A mixture consisting of 0.150 mol H2 and 0.150 mol I2 is brought to equilibrium at 445 C in a
3.25 L flask. What are the equilibrium amounts of H2, I2 and HI? The equilibrium reaction is
given below.
H2(g) + I2(g) ⇌ 2HI(g)
Kc = 50.2 at 445 C
PRACTICE EXAMPLE
(a)
4 HCl(g) + O2(g) ⇌ 2 H2O(g) + 2 Cl2(g)
Effect on equilibrium and Kc?
Addition of oxygen gas
(b)
An increase in temperature
(c)
Reduction of the volume of the reaction container
(d)
Addition of a catalyst
(e)
Removal of HCl(g) from the reaction vessel.
ΔH = 28 kJ
ACID-BASE EQUILIBRIA
• Definition of acids and bases
–Arrhenius
–Brønsted-Lowry
• Strong vs weak acids and bases
• Self-ionization of water (Kw)
• Ionisation constants (Ka, Kb)
• pH, pOH
PRACTICE EXAMPLES
LABEL CONJUGATE ACID-BASE PAIRS:
(a) HPO42- + NH4+ ⇌ NH3 + H2PO4¯
(b) SO42- + H2O ⇌ HSO4¯ + OH¯
PRACTICE EXAMPLE
Calculate the pH of a 0.050 M nitrous acid (HNO2) solution. Ka = 4.5 x 10-4
PRACTICE EXAMPLE
What is the pH of a 0.10 M solution of NH3? What is the % ionisation for this solution?
Kb = 1.8 x 105
PRACTICE EXAMPLE
Quinine is a naturally occurring base used to treat malaria. A 0.0015 mol dm-3 solution
of quinine has a pH of 9.84. The basicity of quinine is due to the nitrogen atom
that picks up a proton from water in the same manner as ammonia.
a) Calculate Kb for quinine.
b) Determine the degree of ionisation.