Thermochemistry Energy Energy is defined as the ability to do work.

Thermochemistry Energy Energy is defined as the ability to do work. There are several forms of energy Kinetic energy – energy due to motion EK = 1/2mv2 Potential energy – the energy due to the position of a particle in a field e.g. Gravitational, electrical, magnetic etc.

Thermochemistry Energy The unit of energy is the Joule (J) and 1 J = 1 kgm2s-2 Thermochemistry is the study of chemical energy and of the conversion of chemical energy into other forms of energy. It is part of thermodynamics – the study of the flow of heat.

Thermochemistry Thermochemically, we define the system as the part of the universe under study and the surroundings as everything else. Systems come in three forms: Open The system can exchange matter and energy with the surroundings Closed The system can exchange energy only with the surroundings Isolated There is no exchange of matter or of energy with the surroundings

Thermochemistry Matter is continually in motion and has an internal energy that is composed of several different types There is Translation Rotation Vibration Potential between molecules and inside molecules. The internal energy is written as U

Thermochemistry Matter is continually in motion and has an internal energy that is composed of several different types There is Translation Rotation Vibration Potential between molecules and inside molecules. The internal energy is written as U The internal energy is directly connected to heat and the transfer of heat.

in thermal equilibrium
Thermochemistry Heat is the transfer of internal energy between the surroundings and the system or between systems. The direction of the heat flow is indicated by the temperature – heat flows along a Temperature gradient from high temperature to low temperature. When the temperature of the system and that of the surroundings are equal, the system is said to be in thermal equilibrium

Thermochemistry Energy is the capacity to do work but what is work? Work is the action of a force over a distance. To be able to do work, we must be able to exert a force over a distance. During this process, energy is expended. w = F x d where w is the work, F is the force and d is the distance. Work is measured in Joules.

Thermochemistry PV work When a gas expands against an external pressure, for example in a cylinder, against a constant weight (weight being a force.....) the work done can be written as w = F x d As P = F then F = PA A Thus w = PAd and as Ad = Vfinal – Vinitial = V Then w = PV

Thermochemistry PV work By convention, the work done when a gas expands is negative, Thus w = - PV for an expanding gas

Thermochemistry State Functions The state of a system is defined by the precise conditions of the system: The quantity and type of matter present The temperature and pressure The molecular structure of the system As 1 mole = 6.02 x 1023 particles, defining the state of a system uniquely is experimentally impossible in an absolute sense.

Thermochemistry State Functions and U The internal energy, U, of a system is a function of the state of the system. Although we cannot measure the absolute state of a system, we can measure changes in the state of the system in a relative way, by measuring the work and the heat that takes place during a chemical change. As U is a function of the state of the system, it does not depend on the way the state of the system is prepared – it is independent of the path.

Thermochemistry State Functions and U U is therefore a state function of the system. It depends only on the present state of the system and not on the previous history or the path by which the system was prepared. Because we have no measure of the state of a system, or of the internal energy, we can only measure the change in the state, through the observation of work and transfers of heat into and out of the system.

Thermochemistry Energy Energy is defined as the ability to do work. There are several forms of energy Kinetic energy – energy due to motion EK = 1/2mv2 Potential energy – the energy due to the position of a particle in a field e.g. Gravitational, electrical, magnetic etc.

Thermochemistry Energy The unit of energy is the Joule (J) and 1 J = 1 kgm2s-2 Thermochemistry is the study of chemical energy and of the conversion of chemical energy into other forms of energy. It is part of thermodynamics – the study of the flow of heat.

Thermochemistry Thermochemically, we define the system as the part of the universe under study and the surroundings as everything else. Systems come in three forms: Open The system can exchange matter and energy with the surroundings Closed The system can exchange energy only with the surroundings Isolated There is no exchange of matter or of energy with the surroundings

Thermochemistry Matter is continually in motion and has an internal energy that is composed of several different types There is Translation Rotation Vibration Potential between molecules and inside molecules. The internal energy is written as U

Thermochemistry Matter is continually in motion and has an internal energy that is composed of several different types There is Translation Rotation Vibration Potential between molecules and inside molecules. The internal energy is written as U The internal energy is directly connected to heat and the transfer of heat.

in thermal equilibrium
Thermochemistry Heat is the transfer of internal energy between the surroundings and the system or between systems. The direction of the heat flow is indicated by the temperature – heat flows along a Temperature gradient from high temperature to low temperature. When the temperature of the system and that of the surroundings are equal, the system is said to be in thermal equilibrium

Thermochemistry Energy is the capacity to do work but what is work?

Thermochemistry Energy is the capacity to do work but what is work? Work is the action of a force over a distance. To be able to do work, we must be able to exert a force over a distance. During this process, energy is expended.

Thermochemistry Energy is the capacity to do work but what is work? Work is the action of a force over a distance. To be able to do work, we must be able to exert a force over a distance. During this process, energy is expended. w = F x d where w is the work, F is the force and d is the distance. Work is measured in Joules.

Thermochemistry PV work When a gas expands against an external pressure, for example in a cylinder, against a constant weight (weight being a force.....) the work done can be written as w = F x d As P = F then F = PA A Thus w = PAd and as Ad = Vfinal – Vinitial = V Then w = PV

Thermochemistry PV work By convention, the work done when a gas expands is negative, Thus w = - PV for an expanding gas

Thermochemistry State Functions The state of a system is defined by the precise conditions of the system: The quantity and type of matter present The temperature and pressure The molecular structure of the system As 1 mole = 6.02 x 1023 particles, defining the state of a system uniquely is experimentally impossible in an absolute sense.

Thermochemistry State Functions and U The internal energy, U, of a system is a function of the state of the system. Although we cannot measure the absolute state of a system, we can measure changes in the state of the system in a relative way, by measuring the work and the heat that takes place during a chemical change. As U is a function of the state of the system, it does not depend on the way the state of the system is prepared – it is independent of the path.

Thermochemistry State Functions and U U is therefore a state function of the system. It depends only on the present state of the system and not on the previous history or the path by which the system was prepared. Because we have no measure of the state of a system, or of the internal energy, we can only measure the change in the state, through the observation of work and transfers of heat into and out of the system.

Thermochemistry Internal Energy, U and State Functions Energy, and therefore the capacity to do work is present in all matter. This internal energy is stored in translational, rotational, vibrational and potential forms or modes in the material. The exact distribution of energy defines the state of the system, together with external variables such as pressure, temperature.

Thermochemistry Internal Energy, U and State Functions U is a function of the state of the material only, not of the history of the sample or the path taken to prepare the state of the sample. Heat is the transfer of energy between the surroundings and the sample - the symbol for heat is q Work is the result of a force acting over a distance - the symbol for work is w

Thermochemistry Internal Energy, U and State Functions Heat and work are the only two ways of changing the internal energy of a system. Temperature is defined by the direction of the flow of heat, which is always from high temperature to low temperature. When the the temperature of the system and the surroundings are the same, the system is at thermal equilibrium with it’s surroundings.

Thermochemistry The sign conventions of thermochemistry When the internal energy of the system rises, this energy change has a positive sign. - The energy of the system rises when heat is absorbed - The energy of the system rises when work is done on the system e.g. a gas is compressed - in these cases, q is positive w is positive

Thermochemistry The sign conventions of thermochemistry When the internal energy of the system lowers, this energy change has a negative sign. - The energy of the system lowers when heat is leaves the system - The energy of the system rises when the system does work e.g. a gas expands against an external pressure - in these cases, q is negative w is negative

Thermochemistry Internal energy rises: q > 0 w > 0 Internal energy drops: q < 0 w < 0

Thermochemistry The First Law of Thermodynamics Energy can be exchanged but cannot be created or destroyed. It is a statement of the Law of Conservation of Energy U = Ufinal – Uinitial = q + w

Thermochemistry Chemical applications of the 1st Law Any chemical change can be characterized as an Endothermic change or an Exothermic change. In an exothermic reaction, internal chemical energy is converted into heat, which leaves the system if the system is not isolated or causes the temperature to rise if the system in isolated.

Thermochemistry Chemical applications of the 1st Law In an endothermic reaction, heat is required to drive the chemical reaction and in an isolated system, the temperature will fall. In an non-isolated system, heat is absorbed from the surroundings. Exothermic T rises (isolated) q negative (non-isolated) Endothermic T falls (isolated) q positive (non-isolated)

Thermochemistry Reactions at constant pressure and constant volume At constant volume, V = 0 and so UV = qV - PV UV = qV + 0 = qV When the system can do PV work, i.e. a system at constant pressure, UP = qP - PV where w = - PV

Thermochemistry Most reactions take place at constant pressure and therefore we define a new function, which is a state function in the same way that U is a state function Rearranging UP = qP - PV UP + PV = qP We term qP the enthalpy of the reaction qP = H = UP + PV

Thermochemistry Enthalpy is an extensive property – one that depends on the quantity of the material present in the reaction. This follows directly from the fact that the enthalpy is the heat generated by a reaction – there is more energy released from 1000 kg of methane when it burns than from 1 g.

Thermochemistry Enthalpies and internal energies are measured in kJ mol-1 and the stoichiometry of a reaction is directly applicable to the enthalpy – half the quantity of the reaction results in half the enthalpy change taking place.

Thermochemistry We can characterize reactions as endothermic or exothermic using the enthalpy, H. If the enthalpy change is negative, the reaction is exothermic and heat is given out by the system

Thermochemistry We can characterize reactions as endothermic or exothermic using the enthalpy, H. If the enthalpy change is negative, the reaction is endothermic and heat is absorbed by the system

Thermochemistry Using the enthalpy, we can account for the heat entering a reaction at constant pressure – in the same way that we account for the products and reactants in a reaction. In an endothermic reaction, the energy absorbed by the system can be considered as a reactant. Conversely, an exothermic reaction, one which evolves heat, has the energy as a product.

Thermochemistry Enthalpies and internal energies are measured in kJ mol-1 and the stoichiometry of a reaction is directly applicable to the enthalpy – half the quantity of the reaction results in half the enthalpy change taking place.

Thermochemistry Heat Capacities When a definite quantity of energy is absorbed by materials, the temperature rises.With different materials, the temperature rise, T, is different. The quantity of energy required to raise a quantity of material by 1 K is termed the heat capacity. Mathematically, C = q T where C is the heat capacity, q is the heat.

Thermochemistry Heat Capacities The specific heat is the heat per gram of sample and the molar heat capacity is the heat capacity per mole.

Thermochemistry Specific Heats, Molar Heats and Calorimetry The heat capacity is the quantity of heat required to raise a given quantity of a substance by 1 K The specific heat 1 gram though 1 K The molar heat 1 mole through 1 K The units of heat capacity are Jg-1K-1 (specific heat) or Jmol-1K-1 (molar heat)

Thermochemistry Specific Heats, Molar Heats and Calorimetry To calculate the heat transferred to a sample we use q = quantity x heat capacity x T For the specific heat q = mCsT where m = mass For the molar heat q = nCmT where n = no. of moles Make sure that the units of the heat capacity matches the units of quantity that is in the heat equation

Thermochemistry Specific Heats, Molar Heats and Calorimetry To measure the heat capacity, a calorimeter is used. A calorimeter measures heat transfers, heats of reaction or heats of dissolution.

Thermochemistry Specific Heats, Molar Heats and Calorimetry In principle, they consist of an insulated chamber and an accurate way of measuring temperature (a thermocouple or thermometer). Insulation ensures that the only heat involved in the temperature rise is that inside the calorimeter.

Thermochemistry Heat capacity measurements A sample with a known temperature is placed into a fluid of known heat capacity and known temperature and allowed to come to thermal equilibrium.

Thermochemistry Heat capacity measurements A sample with a known temperature is placed into a fluid of known heat capacity and known temperature and allowed to come to thermal equilibrium. At thermal equilibrium, Tsample = Tfluid and so we know T for the sample and for the fluid.

Thermochemistry Heat capacity measurements A sample with a known temperature is placed into a fluid of known heat capacity and known temperature and allowed to come to thermal equilibrium. At thermal equilibrium, Tsample = Tfluid and so we know T for the sample and for the fluid. We also know Cfluid and therefore we know qfluid, the heat transferred into the fluid - q = CfluidTfluid

Thermochemistry Heat capacity measurements A sample with a known temperature is placed into a fluid of known heat capacity and known temperature and allowed to come to thermal equilibrium. At thermal equilibrium, Tsample = Tfluid and so we know T for the sample and for the fluid. We also know Cfluid and therefore we know qfluid, the heat transferred into the fluid - q = CfluidTfluid As this is the only source of heat in the calorimeter, we know qfluid and Tsample, so we can calculate Csample

Thermochemistry Example 15.5g of alloy A has a temperature of 98.9 oC. It is placed into a calorimeter containing 25 g of water at 22.5oC. Thermal equilibrium is achieved at 25.7 oC. What is the heat capacity of A?

Thermochemistry Example 15.5g of alloy A has a temperature of 98.9 oC. It is placed into a calorimeter containing 25 g of water at 22.5 oC. Thermal equilibrium is achieved at 25.7 oC. What is the heat capacity of A? Cwater = 4.18 Jg-1K-1 1. Calculate qwater 2. qwater = - qA from conservation of energy 3. Calculate CA from qA

Thermochemistry Example 15.5g of alloy A has a temperature of 98.9 oC. It is placed into a calorimeter containing 25 g of water at 22.5 oC. Thermal equilibrium is achieved at 25.7 oC. What is the heat capacity of A? Cwater = 4.18 Jg-1K-1 1. Calculate qwater: Twater = Tfinal – Tinitial = (25.7 – 22.5) oC = 3.2 oC qwater= 25 x 4.18 x 3.2 = 334 J Note: qwater is positive as heat is entering the water

Thermochemistry Example 15.5g of alloy A has a temperature of 98.9 oC. It is placed into a calorimeter containing 25 g of water at 22.5 oC. Thermal equilibrium is achieved at 25.7 oC. What is the heat capacity of A? Cwater = 4.18 Jg-1K-1 1. qwater = 334 J 2. qwater = - qA thus qA = J

Thermochemistry Example 15.5g of alloy A has a temperature of 98.9 oC. It is placed into a calorimeter containing 25 g of water at 22.5 oC. Thermal equilibrium is achieved at 25.7 oC. What is the heat capacity of A? Cwater = 4.18 Jg-1K-1 1. qwater = 334 J 2. qwater = - qA thus qA = J 3. qA = mCATA TA = Tfinal – Tinitial = (25.7 – 98.9) oC = oC

Thermochemistry Example 15.5g of alloy A has a temperature of 98.9 oC. It is placed into a calorimeter containing 25 g of water at 22.5 oC. Thermal equilibrium is achieved at 25.7 oC. What is the heat capacity of A? Cwater = 4.18 Jg-1K-1 1. qwater = 334 J 2. qwater = - qA thus qA = J 3. qA = mCATA; TA = oC CA = qA/mTA = -334/(15.5 x –73.2) = 0.29 Jg-1K-1

Thermochemistry Bomb Calorimetry For reactions which generate gas, the PV work makes a significant contribution and the quanitiy we will measure in an open calorimeter is the enthalpy. We cannot easily measure the PV work in this case. We can measure U in a bomb calorimeter – one where the volume change is zero and therefore V = 0. The calorimeter is calibrated using a known sample.

Thermochemistry Hess’ Law of Summation If we wish to determine the heat of reaction or formation of a compound which is not stable, cannot be isolated or cannot be measured for some reason, we use Hess’ Law to determine this quantity. Hess’ law states that the the heat of reaction is constant and is not determined by the path of the reaction. We know this as U (and H) is a state function

Thermochemistry Hess’ Law of Summation Practically, if we can find a cycle of reactions that is measureable, then we can derive the unmeasurable quantity as we know the total sum of all the energy changes in the cycle.

Thermochemistry Hess’ Law of Summation Example The combustion of C results in the formation of CO2 in a bomb calorimeter. The heat of formation of CO is therefore hard to measure. We can measure the heat of combustion of CO and that of C both to give CO2.

Thermochemistry Hess’ Law of Summation

Thermochemistry Hess’ Law of Summation Of the reactions in this cycle, the heats of combustion of CO and C are known, but the heat of formation of CO from C is not.

Thermochemistry Hess’ Law of Summation

Thermochemistry Hess’ Law of Summation Using the lower equation and the values for the heats of combustion of CO and C, we can calculate the unknown heat in the cycle

Thermochemistry Hess’ Law of Summation Using the lower equation and the values for the heats of combustion of CO and C, we can calculate the unknown heat in the cycle DHf(CO2) = kJ DHcombustion(CO) = kJ DHf(CO2) = DHf(CO2) - DHcombustion(CO)

Thermochemistry Hess’ Law of Summation Using the lower equation and the values for the heats of combustion of CO and C, we can calculate the unknown heat in the cycle DHf(CO2) = kJ DHcombustion(CO) = kJ DHf(CO2) = ( ) – ( ) = kJ

Thermochemistry Standard enthalpies of formation and reaction Just as we cannot determine the absolute value for the internal energy of a system and so concentrate on the change in internal energy, so we cannot fix an absolute zero-point for reaction and formation enthalpies. We chose the Standard state of a material as that at 1 bar pressure (1 bar = 1 x 105 Pa) and the temperature of interest.

Thermochemistry Standard enthalpies of formation and reaction The standard enthalpy of formation of an element in the standard state is defined as zero. Using these two facts, we can calculate the heats of formation and, through Hess’ cycles, the heats of reaction for all substances.

Thermochemistry Standard enthalpies of formation and reaction When we combine different reactions, we must take account of the stoichiometry of the reaction. Remember that H can be thought of as a product of reaction and must be combine with the correct stoichiometry.

Thermochemistry Standard enthalpies of formation and reaction For the reaction We can construct a Hess’ cycle:

Thermochemistry Standard enthalpies of formation and reaction For the reaction We can construct a Hess’ cycle. Note that we must include the stoichiometry in the calculation.

Atomic Structure Introduction to Quantum Mechanics Quantum mechanics is the most important scientific and philosphical development in the last 100 years, possibly since Galileo and Newton. If you are not confused by Quantum Physics then you haven't really understood it. Niels Bohr

Introduction to Quantum Mechanics
Atomic Structure Introduction to Quantum Mechanics Web sources: COURSE CONTENT

Atomic Structure Introduction to Quantum Mechanics The Players Planck Sommerfeld Pauli Heisenberg Dirac Schrödinger Bohr

Some forms of matter I Matter comes in many different forms

Some forms of matter II Matter comes in many different forms

Some forms of matter III
Impurities in the surface of copper metal   Defects on the surface of copper metal

Chemical Basics Distance to the Horizon 1026 m Distance to M31 1022 m
Distance to the center of the galaxy m Distance to the Nearest Star m Distance of Earth to Sun m Radius of Sun m Radius of Earth m

Chemical Basics Chemical Basics Radius of Knoxville TN 104 m
A small cow m Unraveled human DNA strand m Typical size of dust m Typical size of a cell m (1 micron, 1m) Chemical Basics The Planck Length m Radius of the proton: m Radius of Electron "orbit" about an atomic nucleus m Wavelength of 1 MeV gamma-ray : m Spacing of atoms in solid copper : m (1 Ångstrom, 1Å)

? Length Smallest sensible length: The Planck Length
How big the Universe is when gravity was no longer a quantum thing: m Radius of the proton: m Radius of Electron "orbit" about an atomic nucleus m Wavelength of 1 MeV gamma-ray : m Spacing of atoms in solid copper : m (1 Ångstrom, 1Å) Typical size of a cell m (1 micron, 1m) Typical size of dust m Unraveled human DNA strand m A small cow m Radius of Eugene Oregon m Radius of Earth m Radius of Sun m Distance of Earth to Sun m Distance to the Nearest Star m Distance to the center of the galaxy m Distance to M m Distance to the Horizon m Chemical Basics The Planck Length m Radius of the proton: m Radius of Electron "orbit" about an atomic nucleus m Wavelength of 1 MeV gamma-ray : m Spacing of atoms in solid copper : m (1 Ångstrom, 1Å) ?

Atomic Structure Introduction to Quantum Mechanics Classical Mechanics: All objects move and interact through two forces Electromagnetic force Gravity and the forces obey Newton’s laws of motion. Electromagnetism obeys Clark Maxwell’s equations

Atomic Structure Introduction to Quantum Mechanics Classical Mechanics: Objects have definite trajectories in space. We understand the position of the object and it’s velocity or momentum. Energies are continuous and unrestricted. These objects are large and are in our common experience

Atomic Structure Introduction to Quantum Mechanics In order to observe a physical event, we must make a measurement of some description For large objects, this is not a problem but

Atomic Structure Introduction to Quantum Mechanics What happens when how we measure a property of a microscopic object affects the object and changes it? We can define a large object in an absolute sense as one which is perceptibly unaffected by the measurement. A small object is one where the measurement chages the object that we measure. Elephants are large – atoms are small.

Atomic Structure Introduction to Quantum Mechanics In general, Newton’s laws of motion are applicable to large objects whereas molecules and atoms and objects smaller than these are not. This fact, combined with the inherent nature of matter and energy on the microscopic scale, that make the quantum world very different from the world of our common experience.

Atomic Structure Introduction to Quantum Mechanics Continuum energy states are those where there is no restriction on values for the energy of a body. The color of light is related to the wavelength and therefore the energy – in a continuous spectrum all energies are present

Atomic Structure Introduction to Quantum Mechanics When atoms are excited, the classically expected continuum spectrum does not appear

Atomic Structure Introduction to Quantum Mechanics

Atomic Structure Introduction to Quantum Mechanics When a magnetic field or electric field is applied to the gas, the lines split into two, three or more components. In a magnetic field, this splitting is known as the Zeeman effect

Atomic Structure Introduction to Quantum Mechanics In an electric field, this splitting is known as the Stark effect Increasing electric field

Atomic Structure Introduction to Quantum Mechanics These effects and the discontinuous nature of the spectra are entirely inexplicable using classical mechanics. A new dynamical and structural description of matter and the interaction of matter with energy was required. The first model was the Bohr model

Atomic Structure Quantum Mechanics: The Bohr Model The Bohr model is incorrect but is still shown as the model of the atom today. It is the model in which electrons orbit the nucleus in a similar way that planets orbit the sun. The strong central and radial force is provided by the electric force between the nucleus and the electron

Atomic Structure Quantum Mechanics: The Bohr Model It is the model in which electrons orbit the nucleus in a similar way that planets orbit the sun.

Atomic Structure Quantum Mechanics: The Schrödinger Atom Erwin Schrödinger improved on the Bohr description and succeeded in explaining the internal dynamics of the atom, revealed by the Stark and Zeeman effects. The Schrödinger description is based on the wave properties of matter, detailed by Louis de Broglie

Atomic Structure The de Broglie relationship Louis de Broglie formulated that a particle of momentum p has an associated wavelength  = h p Where p = mv

Atomic Structure The modern quantum atom By considering the electron in an atom as a wave, the energy of the electron becomes quantized and gives the correct energy relation that Bohr described empirically by E= -B n2 and we term n as the principle quantum number

Atomic Structure The modern quantum atom Classically a particle on a sphere can also move over the surface and this motion is circular. In a similar way, the electron in an atom has properties that we can associate with circular or angular motion. Electrons in an atom have angular momentum – the momentum that is associated with angular motion

Atomic Structure The modern quantum atom The angular motion is described by two quantum numbers – l and ml termed the angular quantum number and the magnetic quantum number respectively. The electron also has its own angular momentum, called spin s and these four quantum numbers, n, l, ml and s define the properties of the electron in an atom. They all follow from the wave description of the electron in an atom

Atomic Structure The modern quantum atom The principle quantum number defines the energy of the electron. The angular quantum numbers define the shape of the region of space in which the electron is confined – these are termed the orbitals of the atom and they have definite shapes:

Atomic Structure Quantum Mechanics: The Details The solutions of the Schrödinger wave equations are called wavefunctions and have discrete energies. The solutions are complicated – the Schrödinger equation is

Atomic Structure Quantum Mechanics: The Details The solutions of the Schrödinger wave equations are called wavefunctions and have discrete energies. The solutions are complicated – the Schrödinger equation is H = E

} { Atomic Structure Quantum Mechanics: The Details
The solutions of the Schrödinger wave equations are called wavefunctions and have discrete energies. The solutions are complicated – the Schrödinger equation is H = E -ħ2 2 + 2 + 2 + V(x, y, z)  = E 2m x2 y2 z2 } {

Atomic Structure Quantum Mechanics: The Details The solutions of the Schrödinger wave equations are called wavefunctions and have discrete energies. The equations are only soluble for the hydrogen atom and give the shapes of the orbitals – the space in which the electron can be found as well as the energies.

Atomic Structure Quantum Mechanics: The Details The wavefunctions are characterized and labeled by three quantum numbers, n the principal quantum number l the orbital quantum number ml the magnetic quantum number The electron also has a quantum number to define its behavior – s the spin quantum number

Atomic Structure Quantum Mechanics: The Details The three atomic quantum numbers are connected in terms to the values they can take: n any integer, except 0 In quantum number n l is confined to |n –1| e.g n = 3, l = -2, -1, 0, 1, 2, There are (2l +1) values for ml e.g l = 3, ml = -3, -2, -1, 0, 1, 2, 3

Atomic Structure Quantum Mechanics: The Details These rules give a maximum number of electrons that can take a value of n n = 1 2 electrons 2 in l = 0 n = 2 8 electrons 2 in l = 0, 6 in l = 1 n = electrons 2 in l = 0, 6 in l = 1 10 in l = 2 n = electrons 2 in l = 0, 6 in l = 1 10 in l = 2, 14 in l = 3

Atomic Structure Quantum Mechanics: The Details The orbitals for the hydrogen atom can be calculated explicitly and analytically n = 1, l = 0

Atomic Structure Quantum Mechanics: The Details n = 3, l = 2

Atomic Structure n = 4, l = 3

Atoms, Molecules and Ions
s block p block 1 H He 2 Li 3 Be 4 B 5 C 6 N 7 O 8 F 9 Ne 10 Na11 Mg12 d block Al 13 Si 14 P 15 S 16 Cl 17 Ar 18 K 19 Ca 20 Sc 21 Ti 22 V 23 Cr 24 Mn 25 Fe 26 Co 27 Ni 28 Cu 29 Zn 30 Ga 31 Ge 32 As 33 Se 34 Br 35 Kr 36 Rb 37 Sr 38 Y 39 Zr 40 Nb 41 Mo 42 Tc 43 Ru 44 Rh 45 Pd 46 Ag 47 Cd 48 In 49 Sn 50 Sb 51 Te 52 I 53 Xe 54 Cs 55 Ba 56 Lu 71 Hf 72 Ta 73 W 74 Re 75 Os 76 Ir 77 Pt 78 Au 79 Hg 80 Tl 81 Pb 82 Bi 83 Po 84 At 85 Rn 86 Fr Ra 88 Lr 103 Rf 104 Db 105 Sg 106 Bh 107 Hs 108 Mt 109 110 111 112 f block La 57 Ce 58 Pr 59 Nd 60 Pm 61 Sm 62 Eu 63 Gd 64 Tb 65 Dy 66 Ho 67 Er 68 Tm 69 Yb 70 Ac 89 Th 90 Pa 91 U 92 Np 93 Pu 94 Am 95 Cm 96 Bk 97 Cf 98 Es 99 Fm 100 Md 101 No 102 The S block

s block p block 1 H He 2 Li 3 Be 4 B 5 C 6 N 7 O 8 F 9 Ne 10 Na11 Mg12 d block Al 13 Si 14 P 15 S 16 Cl 17 Ar 18 K 19 Ca 20 Sc 21 Ti 22 V 23 Cr 24 Mn 25 Fe 26 Co 27 Ni 28 Cu 29 Zn 30 Ga 31 Ge 32 As 33 Se 34 Br 35 Kr 36 Rb 37 Sr 38 Y 39 Zr 40 Nb 41 Mo 42 Tc 43 Ru 44 Rh 45 Pd 46 Ag 47 Cd 48 In 49 Sn 50 Sb 51 Te 52 I 53 Xe 54 Cs 55 Ba 56 Lu 71 Hf 72 Ta 73 W 74 Re 75 Os 76 Ir 77 Pt 78 Au 79 Hg 80 Tl 81 Pb 82 Bi 83 Po 84 At 85 Rn 86 Fr Ra 88 Lr 103 Rf 104 Db 105 Sg 106 Bh 107 Hs 108 Mt 109 110 111 112 f block La 57 Ce 58 Pr 59 Nd 60 Pm 61 Sm 62 Eu 63 Gd 64 Tb 65 Dy 66 Ho 67 Er 68 Tm 69 Yb 70 Ac 89 Th 90 Pa 91 U 92 Np 93 Pu 94 Am 95 Cm 96 Bk 97 Cf 98 Es 99 Fm 100 Md 101 No 102 The S block and P block

s block p block 1 H He 2 Li 3 Be 4 B 5 C 6 N 7 O 8 F 9 Ne 10 Na11 Mg12 d block Al 13 Si 14 P 15 S 16 Cl 17 Ar 18 K 19 Ca 20 Sc 21 Ti 22 V 23 Cr 24 Mn 25 Fe 26 Co 27 Ni 28 Cu 29 Zn 30 Ga 31 Ge 32 As 33 Se 34 Br 35 Kr 36 Rb 37 Sr 38 Y 39 Zr 40 Nb 41 Mo 42 Tc 43 Ru 44 Rh 45 Pd 46 Ag 47 Cd 48 In 49 Sn 50 Sb 51 Te 52 I 53 Xe 54 Cs 55 Ba 56 Lu 71 Hf 72 Ta 73 W 74 Re 75 Os 76 Ir 77 Pt 78 Au 79 Hg 80 Tl 81 Pb 82 Bi 83 Po 84 At 85 Rn 86 Fr Ra 88 Lr 103 Rf 104 Db 105 Sg 106 Bh 107 Hs 108 Mt 109 110 111 112 f block La 57 Ce 58 Pr 59 Nd 60 Pm 61 Sm 62 Eu 63 Gd 64 Tb 65 Dy 66 Ho 67 Er 68 Tm 69 Yb 70 Ac 89 Th 90 Pa 91 U 92 Np 93 Pu 94 Am 95 Cm 96 Bk 97 Cf 98 Es 99 Fm 100 Md 101 No 102 The S block , P block and D block

s block p block 1 H He 2 Li 3 Be 4 B 5 C 6 N 7 O 8 F 9 Ne 10 Na11 Mg12 d block Al 13 Si 14 P 15 S 16 Cl 17 Ar 18 K 19 Ca 20 Sc 21 Ti 22 V 23 Cr 24 Mn 25 Fe 26 Co 27 Ni 28 Cu 29 Zn 30 Ga 31 Ge 32 As 33 Se 34 Br 35 Kr 36 Rb 37 Sr 38 Y 39 Zr 40 Nb 41 Mo 42 Tc 43 Ru 44 Rh 45 Pd 46 Ag 47 Cd 48 In 49 Sn 50 Sb 51 Te 52 I 53 Xe 54 Cs 55 Ba 56 Lu 71 Hf 72 Ta 73 W 74 Re 75 Os 76 Ir 77 Pt 78 Au 79 Hg 80 Tl 81 Pb 82 Bi 83 Po 84 At 85 Rn 86 Fr Ra 88 Lr 103 Rf 104 Db 105 Sg 106 Bh 107 Hs 108 Mt 109 110 111 112 f block La 57 Ce 58 Pr 59 Nd 60 Pm 61 Sm 62 Eu 63 Gd 64 Tb 65 Dy 66 Ho 67 Er 68 Tm 69 Yb 70 Ac 89 Th 90 Pa 91 U 92 Np 93 Pu 94 Am 95 Cm 96 Bk 97 Cf 98 Es 99 Fm 100 Md 101 No 102 The S block , P block , D block and F block

Atomic Structure The Aufbau Principle and the Periodic Table The quantum mechanical rules the relate n, l and ml dictate the structure of the periodic table through the aufbau prinicple, when used in conjunction with the Exclusion principle The rules are that, given n, l = n – 1 and ml = +/- l including 0

Atomic Structure The Aufbau Principle and the Periodic Table For each value of n, l ml there are two possibilities for s the spin of the electron - + ½ and - ½. Each orbital can therefore accommodate two and only two electrons. We can therefore write the electronic configurations of the atoms in terms of the occupations of each orbital.

Atomic Structure The Aufbau Principle and the Periodic Table For hydrogen, n = 1, l = n – 1= 0 and ml = 0. The only possibilities are therefore ± ½ and we write that H has a configuration of 1s2, showing the prinicipal quantum number, the l quantum number and the number of electrons.

Atomic Structure The Aufbau Principle and the Periodic Table All the orbitals that we can calculate from the Schrödinger equation are hydrogenic as we can only solve the Schrödinger equation for a two particle system. In hydrogen all the orbitals with the same n with non-zero l and ml have the same energies, the only energy differences between orbitals being n. Such orbitals are termed degenerate.

Atomic Structure The Aufbau Principle and the Periodic Table In atoms heavier than hydrogen, the l quantum number does effect the energy slightly and the orbitals are no longer degenerate. This becomes more important for heavier atoms and effects the order of filling in the periodic table.

Atomic Structure The Aufbau Principle and the Periodic Table A second and highly important factor is the distribution of the electrons with in the atom. Any orbital with non-zero l has an angular node that runs through the nucleus – the density of the electrons at the nucleus is zero for these orbitals. s orbitals have density at the nucleus and the force on these from the nucleus is higher, so they are more strongly bound

s before p before d before f
Atomic Structure The Aufbau Principle and the Periodic Table In general, the higher l the less penetrating the orbitals are and the order of filling is s before p before d before f Anomalies appear at the 3d sub-shell. After Ar (3p6), the 4s shell fills first, before the 3d. A similar feature occurs before the filling of the 4f shell.

Atomic Structure The Aufbau Principle and the Periodic Table Hund’s rule is the final rule for the configuration of the atom. Orbitals are filled such that all spins are parallel and all orbitals are singly filled first, before doubling filling the orbitals with paired spins. Spin-parallel electrons cannot occupy the same space and so the repulsion between electrons is reduced. Spin-paired electrons can occupy the same region of space and the repulsion is higher.

s block p block 1 H He 2 Building the Periodic Table

s block p block 1 H He 2 Li 3 Be 4 B 5 C 6 N 7 O 8 F 9 Ne 10 Building the Periodic Table

s block p block 1 H He 2 Li 3 Be 4 B 5 C 6 N 7 O 8 F 9 Ne 10 Na11 Mg12 Al 13 Si 14 P 15 S 16 Cl 17 Ar 18 Building the Periodic Table

s block p block 1 H He 2 Li 3 Be 4 B 5 C 6 N 7 O 8 F 9 Ne 10 Na11 Mg12 d block Al 13 Si 14 P 15 S 16 Cl 17 Ar 18 K 19 Ca 20 Sc 21 Ti 22 V 23 Cr 24 Mn 25 Fe 26 Co 27 Ni 28 Cu 29 Zn 30 Ga 31 Ge 32 As 33 Se 34 Br 35 Kr 36 The Periodic Table

s block p block 1 H He 2 Li 3 Be 4 B 5 C 6 N 7 O 8 F 9 Ne 10 Na11 Mg12 d block Al 13 Si 14 P 15 S 16 Cl 17 Ar 18 K 19 Ca 20 Sc 21 Ti 22 V 23 Cr 24 Mn 25 Fe 26 Co 27 Ni 28 Cu 29 Zn 30 Ga 31 Ge 32 As 33 Se 34 Br 35 Kr 36 Rb 37 Sr 38 Y 39 Zr 40 Nb 41 Mo 42 Tc 43 Ru 44 Rh 45 Pd 46 Ag 47 Cd 48 In 49 Sn 50 Sb 51 Te 52 I 53 Xe 54 The Periodic Table

s block p block 1 H He 2 Li 3 Be 4 B 5 C 6 N 7 O 8 F 9 Ne 10 Na11 Mg12 d block Al 13 Si 14 P 15 S 16 Cl 17 Ar 18 K 19 Ca 20 Sc 21 Ti 22 V 23 Cr 24 Mn 25 Fe 26 Co 27 Ni 28 Cu 29 Zn 30 Ga 31 Ge 32 As 33 Se 34 Br 35 Kr 36 Rb 37 Sr 38 Y 39 Zr 40 Nb 41 Mo 42 Tc 43 Ru 44 Rh 45 Pd 46 Ag 47 Cd 48 In 49 Sn 50 Sb 51 Te 52 I 53 Xe 54 Cs 55 Ba 56 Lu 71 Hf 72 Ta 73 W 74 Re 75 Os 76 Ir 77 Pt 78 Au 79 Hg 80 Tl 81 Pb 82 Bi 83 Po 84 At 85 Rn 86 f block La 57 Ce 58 Pr 59 Nd 60 Pm 61 Sm 62 Eu 63 Gd 64 Tb 65 Dy 66 Ho 67 Er 68 Tm 69 Yb 70 The Periodic Table

s block p block 1 H He 2 Li 3 Be 4 B 5 C 6 N 7 O 8 F 9 Ne 10 Na11 Mg12 d block Al 13 Si 14 P 15 S 16 Cl 17 Ar 18 K 19 Ca 20 Sc 21 Ti 22 V 23 Cr 24 Mn 25 Fe 26 Co 27 Ni 28 Cu 29 Zn 30 Ga 31 Ge 32 As 33 Se 34 Br 35 Kr 36 Rb 37 Sr 38 Y 39 Zr 40 Nb 41 Mo 42 Tc 43 Ru 44 Rh 45 Pd 46 Ag 47 Cd 48 In 49 Sn 50 Sb 51 Te 52 I 53 Xe 54 Cs 55 Ba 56 Lu 71 Hf 72 Ta 73 W 74 Re 75 Os 76 Ir 77 Pt 78 Au 79 Hg 80 Tl 81 Pb 82 Bi 83 Po 84 At 85 Rn 86 Fr Ra 88 Lr 103 Rf 104 Db 105 Sg 106 Bh 107 Hs 108 Mt 109 110 111 112 f block La 57 Ce 58 Pr 59 Nd 60 Pm 61 Sm 62 Eu 63 Gd 64 Tb 65 Dy 66 Ho 67 Er 68 Tm 69 Yb 70 Ac 89 Th 90 Pa 91 U 92 Np 93 Pu 94 Am 95 Cm 96 Bk 97 Cf 98 Es 99 Fm 100 Md 101 No 102 The Periodic Table

Atomic Structure Periodic Trends As the number of electrons in an atom rises, the size of the atom increases. As the binding energy of the electrons rises, the size of the atom decreases. These two factors mean that the size of the atom increases right to left and top to bottom in the Periodic Table. Cs is the largest stable atom and F the smallest.

Atomic Structure Periodic Trends Ionic radii also follow the same trends. Cations are smaller than the neutral atoms and anions are larger than the neutral atoms, though the trend in ion sizes follow those of the atoms.

Atomic Structure Periodic Trends The energy required to remove electrons from the atoms is termed the ionization energy. In breaking a subshell there is a large jump in ionization energy. In breaking a shell, there is a huge jump in ionization energy.

Thermochemistry Energy Energy is defined as the ability to do work.

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Thermochemistry Energy Energy is defined as the ability to do work.

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