CHEM1100 Lecture Notes PDF

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Chemistry End of Semester Revision Contents Chemistry End of Semester Revision.................................................................................................... Module 2....................................................................................................................

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Chemistry End of Semester Revision Contents Chemistry End of Semester Revision.....................................................................................................1 Module 2...........................................................................................................................................2 Lecture 13: Ideal Gases and Real Gases.........................................................................................2 Lecture 14: Intermolecular Forces.................................................................................................6 Lecture 15: Introduction to Thermodynamics.............................................................................11 Lecture 16: Energy Transfer and Chemical Change......................................................................15 Lecture 17: Spontaneity...............................................................................................................23 Lecture 18: Spontaneity and Gibbs Energy..................................................................................27 Lecture 19: Chemical Equilibrium................................................................................................32 Lecture 20: Equilibrium (K) and Spontaneity (G)..........................................................................35 Lecture 21: Predicting Equilibrium Response to Change..............................................................40 Lecture 22: Heterogenous Equilibria............................................................................................43 Lecture 23: Phase Transitions......................................................................................................45 Module 3.........................................................................................................................................50 Lecture 25: Equilibrium and Solutions.........................................................................................50 Lecture 26: Aqueous Solution Equilibria......................................................................................55 Lecture 27: Colligative Properties................................................................................................58 Lecture 28: Dissociation Equilibria...............................................................................................61 Lecture 29: Aqueous Ionic Equilibria............................................................................................64 Lecture 30: Determining Ion Solubility Common Ion Effect.........................................................66 Lecture 31: Predicting Precipitation – Selective Precipitation......................................................69 Lecture 32: Redox Reactions........................................................................................................72

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Module 2 Lecture 13: Ideal Gases and Real Gases Combined Gas Laws - Comparing between two systems (initial and a final): When n is constant:

When n and T are constant:  p1V1 = p2V2

When p and T are constant: 

 When n and p are constant:

When n and V are constant: 



Ideal Gas Law: pV = nRT  

Three of the four constituents need to be known to find an unknown Where R = Gas constant =

The gas laws are inter-related – Proportional Reasoning:   

Vgas = Constant x 1/pgas Vgas = Constant’ x Tgas Vgas= Constant’’ x ngas

The Ideal Gas Equation: pV = nRT   

One of the most important equations in physical chemistry Describes how an ideal gas behaves under give conditions of pressure, volume and temperature Assumptions for an ‘ideal gas’: o The molecules are very small compared to the distance between them  They have negligible volume o The molecules do not ‘see’ each other

o

 No intermolecular interactions The molecules move in completely random motion  Different speeds and direction

The Gas Constant, R: 

R = gas Constant = 8.314 J mol-1 K-1 = 0.0082057 L atm K-1 mol1

2

Volume of 1 mole of gas at STP:

Where at STP (standard pressure and temperature):   

R = 8.314 J mol-1 K-1 T = 273.15 K = 0oC P = 100 000 N m-2 = 1.00 atm

Dalton’s Law of Partial Pressures: 



The total pressure of a mixture of gases is the sum of the pressures that each gas would exert if its were alone in the container.’ o PT = p1 + p2 + p3 ……. pi  Where pi = partial pressures If a sample contains gases A and B, total pressure is given by:

o 

For ideal gases, the identity of the gas does not make a difference – only the amount of gas.

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Relation of partial pressure and total pressure: 

XA = the mole fraction of gas A o XA: Ranges from 0 to 1

 

pA = XA · ptotal PB = XB · ptotal

∴ pi = Xi · ptotal

Kinetic Theory: Molecular View of Gases  

The Ideal Gas Law provides a quantitative route for predicting gas behaviour based on macroscopic observations (changes in pressure and volume). Kinetic theory of gases is used to predict the same behaviour on a molecular basis

Molecular speeds:  Gas molecules are in constant random motion, they have mass (m) and velocity (u).  The energy of a molecules is related to its speed.  There is a distribution of speeds amongst a population of gas molecules.

Average and total kinetic energy:  

For a gas at a given pressure and temperature, the average energy per molecule (and hence the temperature) is independent of the amount of gas. However, the total kinetic energy is proportional to the amount of the substance o Average kinetic energy: Sum of individual molecular kinetic energies divided by the total number of molecules for any gas 

∑ Molecular Kinetic Energies n x NA

‘Real’ Gas Properties:  

Ideal gas behaviour breaks down at very high pressures and/or Very low temperatures

Correction for real gases: 

Include the repulsive interactions in Ideal Gas Eq

i)

nRT

p = V −nb

where nb is the volume of the molecules

Now include the attractive interactions in Eq. i

ii)

n 2 nRT −a( ) V V −nb

p=



attractive interactions between molecules reduce pressure

rearrange Eq. ii to obtain the van der Waals Equation:

iii)

n2 a nRT = ( p+ 2 )(V −nb) V



Attractive interactions between molecules



Repulsive interactions between molecules 5

o

Values for van der Waals parameters, a & b, available in tables

Lecture 14: Intermolecular Forces 

 

Ideal gas behaviour breaks down at low temperatures (gas molecules lose kinetic energy) or high pressures (gas molecules experience greater number of collisions). Under these conditions, intermolecular forces become important. Intermolecular forces: forces between molecules Intramolecular forces: forces within a molecule – a chemical bond

London Dispersion Forces (van der Waals interactions):  

Transient changes in the change distribution (electron cloud) in a molecule can occur. When this happens near another atom, the dipole induces a dipole in the other atom. Dispersion force = weak interaction



Relationship between physical properites and intermolecular forces: 

Halogens are diatomic and experience intermolecular interactions via dispersion forces.

Boiling point  

More electrons = more polarizable electron cloud volume = stronger intermolecular forces. Whereby, the size of the molecule influences the strength of intermolecular interactions.

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Electronegativity and bond polarity  

Electronegativity is the affinity for an atom in a molecule to attract an electron towards itself If atom A has a greater electronnegativity than atom B, the shared electron will tend to be clsoe to atom A than atom B o This cause partial negative (atom A) and partial positive charges (atom B) in the molecule.

Molecular Polarity   

Additional of a carbonyl functional group (-C=O) introduce a dipole. Electrons become more localised in one region of the molecule. Dipole-dipole interactions can occur depending on symmetry.



The molecule exhibits a dipole momemnt due to a pernament change and will align with an apllied electroic field.



There are two ways to represent a molecular dipole: o A lewis electric dipole moment shows the direction of a dipole from positive to negative charge (used in CHEM1100)

o

 The electric dipole moment is a vector that show direction that a molecule aligns with an applied field (used in text book)

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Steps to working out molecule polarity:

1. Draw the Lewis structure for the molecule 2. Consider the bonding pairs and lne pairs to decide on molecular shape by applying VSEPR a. VSEPR = Valence Shell Electron Pair Repulsion theory 3. Decide which bonds are polcar by considering relative electronegativities of atom in bonds 4. Identifyu whether there is a net molecular dipole (sum the vectors) 5. Decide what type of intermolecular interactions are most likely based on the polarity Molecular Dipole Strength: The strength of the dipole momen (μ) is measured in units od Debye and reflects the net polarity of the molcule as a result of molecular shape and any localisation of electrons 

1 Debye (D) = 3.3 × 10−30 coulomb metre.



The netdirection of the moleclar dipole moment is the summation of the vectors for individual polar bonds and is a function of the molecule shape.

Dipole-Dipole interactions: 

Polar molecules align so that negative and positive ends are in close proximity leading to an electrostaic attraction (generally important over short distances) o Electrostatic attraction: Attraction of oppositive charges

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

A molecule with a pernament dipole moment can induce a dipole in a nonpolar molecule

Hydrogen Bonding: Hydrogen bonds are very strong dipole-dipole interactions observed between either:   

Two separate like molecules Two separate unline molecules Between groups within a sginle molcules



A netwrok of H bonding can be very strong

Hydrogen bonding: Donor and Acceptor A hydrogen bond forms between a paritally positively charged hydron atom (bonded to an atom known as the donor) and the lone pair of electrons on an adjacent electronegative atom (known as the acceptor. 



H-Bond Donor: atom bonded to hydrogen that transfers a lone pair of electrons to the acceptor H-bond Acceptor: accepts lone pair of electons from donor

Requires hydrogen to be involved in a highly polar bond with a highly electronegative atom: 

Oxygen

o

 

O-H in H2O Nitrogen o N-H in NH3 Fluorine 9

o

F-H in HF

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Examples of Hydrogen bonding: 

Intermolecular (between separate molecules) or intramolecular (within a single molecule but not a covalent bond)

Overcoming attractive forces: 

An increasing amount of energy input is required to overcome increasing strength of attractive forces

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Lecture 15: Introduction to Thermodynamics Evidence of chemical change:    

Heat released (exothermic) Heat absorbed (endothermic) Chemical change (new substances) Useful for work (gas generated)

o o

2KClO3 (l)  2KCl(s) + 3O2 (g) C12H22O11 (s) + 12O2 (g)  12CO2 + 11H2O (l)  Large amount of heat is released

Chemical Reactions involve Energy Transfer: Work and heat are two fundamental ways in which energy is transferred to or from a system. 

The system is usually the chemical reacts and products. The system is our frame of reference and what we can experimentally measures.

Energy is transferred into a system by the surrounding OR energy is transferred out of a system into the surroundings. Types of systems:    

Open System: Can exchange matter and energy with the surroundings Closed System: Can exchange only energy with the surroundings Isolated System: cannot exchange matter nor energy with the surroundings. Adiabatic system: Can exchange only work with the surroundings.

Internal energy, U  





U = the sum of all energies (potential and kinetic energy) – for all particles in the system. Kinetic energy: energy due to motion o Thermochemistry involves the movement of atoms, molecules or ions (including vibration, translation and rotation). Potential energy: depends on the position of objects o Potential energy at the molecular level due to the electronic states of atoms, molecules or ions and their relative positions to each other. The change I internal energy during reaction o ΔU = UFinal – UInitial    

The absolute value is impossible to determine When ΔU is positive, the system gained energy When ΔU is negative, the system loses energy All energy must be released or gained from the surrounding ∴ ΔU system = - ΔU surroundings

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The First Law of Thermodynamics Energy is not created or destroyed, just transferred from one form to another.  

In chemical reactions, energy is exchange with the surrounding as either heat (q) or work (w). With respect to chemical reactions: the 1st Law can be expressed in terms of w and q: o ΔU = q + w 



q = heat added to the system  q > 0 = heat transferred in  q < 0 = heat transferred out w = work done on system  w > 0 = work done by surrounding on system  w < 0 = work done by system on surrounding

Energy and Chemical reactions: Heat and work are the only ways that a chemical system can exchange energy with its surroundings: 1. The capacity to do work (w) a. Work = Force x distance  E.g. lifting an object 2. The capacity to transfer heat (q) a. Heat = the process of transfer of thermal energy between two bodies or systems at different temperatures. It is considered that heat cannot do work. Example of 1st Law: Combustion of Methane 

CH4 (g) + 2O2 (g)  CO2 (g) + 2H2O (l)



In the combustion of methane, the system has lower energy at the end of the reaction – energy has been transferred to the surrounding. ∴ Exothermic reaction.

Example 2: Creation of 2NO(g) 

N2 (g) + O2 (g) + energy  2NO (g)

Reactions also may cause energy to flow from surroundings to system. ∴ Endothermic 13

Work (w) in thermodynamics:   

Different types of work: electrical, mechanical, expansion etc. CHEM1100: Most interested in work associated with contraction and expansion of a gas: “pV” work. E.g. If the temperature of a gas increase, the volume also increases. As the gas it expands, it pushes back the surroundings, thus undergoing mechanical work. w = work pext = pressure exerted ΔV = change in volume = VFinal – VInitial

Rationalisation:

Example: Calculation of work

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Heat (q) in thermodynamics Heat = the transfer of thermal energy between two bodies or system due to a temperature difference. 

HEAT IS A MEANS OF ENERGY TRANSER, NOT ENERGY ITSELF

Measure heat from the temperature change that occurs because heat flows from one body to another: q = C · ΔT Where:   

q = heat C = specific heat capacity ΔT = change in temperature

q is determined experimentally by calorimetry: measuring the temperature change of a body.

Internal Energy changes at constant volume: ΔU = q + w:  

When ΔV = 0, w = 0 ∴ ΔU = qv ΔrU = heat of reaction at constant volume. o A ‘Bomb’ calorimeter enables measurement of ΔrU.

Calorimetry: Measuring Heat Transfer   

The simplest type of calorimeter is a ‘coffee cup’ calorimeter under constant external pressure. When ΔrHθ < 0, heat released (temperature rises) qp = c · m · ΔT

Note: water has a large specific heat capacity of 4.18 J K-1 g-1 

Specific heat capacity: the heat required to raise the temperature of the unit mass of a given substance by a given amount (usually one degree).

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Lecture 16: Energy Transfer and Chemical Change Key thermodynamic terms encountered in L15: Term Kinetic energy

Potential energy

Heat (q)

Internal energy (U)

Work (w)

System + Surroundings = Universe Exothermic and endothermic processes

Definition energy due to motion  Thermochemistry involves the movement of atoms, molecules or ions (including vibration, translation and rotation). depends on the position of objects  Potential energy at the molecular level due to the electronic states of atoms, molecules or ions and their relative positions to each other. the process of transfer of thermal energy between two bodies or systems at different temperatures. It is considered that heat cannot do work. q = heat added to the system  q > 0 = heat transferred in  q < 0 = heat transferred out the sum of all energies (potential and kinetic energy) – for all particles in the system. ΔU = q + w ΔU = UFinal – UInitial Work = work done on system = Force x distance  w > 0 = work done by surrounding on system  w < 0 = work done by system on surrounding ΔU system = - ΔU surroundings Exothermic when q < 0 Endothermic when q > 0

Enthalpy:  

most reactions occur under conditions of constant pressure (typically atmospheric pressure). ΔU = q + w o ΔU = qp – p·ΔV qp = ΔU + p·ΔV

o   

Note: qp = heat at constant pressure

Convenient to define a new thermodynamic property that is equivalent to the heat of reaction a constant pressure: Enthalpy (H) ∴ Enthalpy (H) = the heat of reaction a constant pressure o H = U + pV Enthalpy chance (e.g. during a chemical reaction) at constant pressure: o ΔH = ΔU + p·ΔV

Enthalpy (gases): 

From the definition of ΔH: ΔH = qp o ΔH = heat transferred in a reaction at constant pressure

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Enthalpy change of a reaction: Example of enthalpy change in a reaction: 

CH4 (g) + 202 (g)  CO2 (g) + 2H2O (g) ΔrH = -802 kJ o Negative ΔrH value implies exothermic reaction

o

The difference arises from the energy released or absorbed in the breaking and making of bonds.

‘Breaking and Making’ bonds: 

A change in enthalpy is the net change in energy in the system which is the total of the individuals changes in bond energies o Energy must be absorbed to break a bond and energy is released when a new bond is formed.

Important Enthalpy Point: 

Enthalpy is an extensive property (depends on the amount of substance). o If the amount of reactants doubles, the enthalpy doubles

o

o 



It is implicit that a quoted applies to a balanced equation.  CH4 (g) + 202 (g)  CO2 (g) + 2H2O (g) ΔrH = -802 kJ  2CH4 (g) + 402 (g)  2CO2 (g) + 4H2O (g) ΔrH = -1604 kJ This is a ‘thermodynamically balanced’ equations

 Includes the enthalpy of the reaction. Enthalpy change of the reverse reaction is of the same magnitude but opposite sign  CH4 (g) + 202 (g)  CO2 (g) + 2H2O (g) ΔrH = -802 kJ (exo)  CO2 (g) + 2H2O (g) CH4 (g) + 202 (g) ΔrH = -8...