SUBAREA I. MATTER AND ENERGY; HEAT, THERMODYNAMICS, AND THERMOCHEMISTRY COMPETENCY 1.0. MATTER AND ENERGY Skill 1.1 Organization of matter Molecules have kinetic energy (they move around), and they also have intermolecular attractive forces (they stick to each other). The relationship between these two determines whether a collection of molecules will be a gas, liquid, or solid. A gas has an indefinite shape and an indefinite volume. The kinetic model for a gas is a collection of widely separated molecules, each moving in a random and free fashion, with negligible attractive or repulsive forces between them. Gases will expand to occupy a larger container so there is more space between the molecules. Gases can also be compressed to fit into a small container so the molecules are less separated. Diffusion occurs when one material spreads into or through another. Gases diffuse rapidly and move from one place to another. A liquid assumes the shape of the portion of any container that it occupies and has a specific volume. The kinetic model for a liquid is a collection of molecules attracted to each other with sufficient strength to keep them close to each other but with insufficient strength to prevent them from moving around randomly. Liquids have a higher density and are much less compressible than gases because the molecules in a liquid are closer together. Diffusion occurs more slowly in liquids than in gases because the molecules in a liquid stick to each other and are not completely free to move. A solid has a definite volume and definite shape. The kinetic model for a solid is a collection of molecules attracted to each other with sufficient strength to essentially lock them in place. Each molecule may vibrate, but it has an average position relative to its neighbors. If these positions form an ordered pattern, the solid is called crystalline. Otherwise, it is called amorphous. Solids have a high density and are almost incompressible because the molecules are close together. Diffusion occurs extremely slowly because the molecules almost never alter their position.

Skill 1.2 Physical and chemical properties and changes of matter Physical changes are also known as phase changes and include condensation, melting, freezing, evaporation and sublimation. These concepts will be reviewed in Skill 2.4. Below are several important physical properties of matter. Viscosity Viscosity measures the ability of a liquid to flow. Liquids with high viscosity flow less easily because they have strong intermolecular forces relative to kinetic energy. The viscosity of liquids decreases with temperature because it is easier for rapidly moving molecules to flow into the spaces between them. For most liquids (water is an exception), viscosity increases with pressure because the molecules are squeezed together, which forces a greater interaction, but this dependence is not as strong as the dependence on temperature. Vapor Pressure When a liquid is placed in a container that it does not fill entirely, there are always some molecules at the surface of the liquid (e.g., the half-shaded molecule to the left of the diagram) with enough kinetic energy to overcome the attraction of their neighbors and escape into the gas. This process is known as evaporation. In a closed container, these gas molecules develop a pressure until a dynamic equilibrium occurs because the rate of their return to the liquid phase by condensation (e.g., the half-shaded molecule on the right in the diagram) equals the rate of their escape by evaporation:

evaporation

condensationLiquid Vapor

At equilibrium, the partial pressure of the substance in the gas phase is at its saturated vapor pressure. Solids are also in equilibrium with vapor and have a saturated vapor pressure, though much lower due to the attraction between the molecules of a solid. There is no real difference between the terms gas and vapor, but gas is often used to describe a substance that appears in the gaseous state under standard temperature and pressure and vapor to describe the gaseous state of a substance that appears ordinarily as a liquid or solid. The saturated vapor pressure of a liquid is often simply called its vapor pressure. This term can sometimes lead to confusion when equilibrium is not present, but equilibrium is usually assumed

An increase in temperature raises vapor pressure (making the liquid more volatile) because kinetic energy opposes intermolecular attractions and permits more molecules to escape from the liquid phase. More information on vapor pressure may be found at: http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/vappre.html. A flash animation of liquid/vapor equilibrium showing how vapor pressure is measured is located at: http://www.mhhe.com/physsci/chemistry/essentialchemistry/flash/vaporv3.swf. Surface Tension The molecules on the surface of a liquid are affected by two type of intermolecular forces. One attraction is to the molecules that have evaporated and are in the air surrounding the liquid, and the other attraction is to other molecules in the liquid. The latter attraction is many times stronger than the first. So, there is a preference for the surface molecules to remain in the liquid phase. There is a net inwards pull away from the interface between liquid and gas, which has the effect of minimizing the liquid’s surface area. This is not the case for molecules in the interior of the liquid because here the forces are balanced.

interior molecule

surface molecule

Surface tension is the energy required to increase the surface area of a liquid by a unit amount. Because of surface tension, friction exists at the liquid-gas interface that makes it more difficult to move a solid object through the surface than to move it when it’s completely submerged. Temperature decreases surface tension because kinetic energy acts in opposition to intermolecular attractive forces. Chemicals with strong intermolecular attractive forces have a high surface tension. Surface tension can also be altered by adding other substances. For example, NaOH added to water will raise its surface tension and adding soap to water will lower its surface tension. Boiling Point as a Function of Pressure For a liquid in an open container, vapor pressure increases with temperature until it is equal to the external pressure, and the boiling point occurs at that temperature. Boiling is defined as the process of vapor bubbles forming and evolving from the liquid. Substances with stronger intermolecular attractive forces have a higher boiling point. An increase in the surrounding pressure forces molecules closer together and increases their intermolecular attractive forces. More kinetic energy is required to break these bonds, so boiling point increases with pressure.

Critical Point In this section, we’ve seen how rising temperature at a gas-liquid interface increases vapor pressure and decreases surface tension. All the liquid will become a gas at the boiling point, but if the external pressure is increased above the vapor pressure, material will remain in the liquid phase and the boiling point will increase. A pressure cooker is a good example of this. Finally, however, a temperature is reached at which no amount of pressure will keep the material in a liquid state. The highest temperature at which a substance can exist as a liquid is its critical temperature. Critical pressure is the vapor pressure of a liquid at its critical temperature. Surface tension shrinks to zero and there is no longer a gas-liquid interface when critical conditions are reached. Above its critical temperature and pressure, a substance takes the shape and volume of its container, like a gas, but it has a density and intermolecular attractive forces similar to a liquid. This phase is called a supercritical fluid. Like liquids and gases, supercritical fluids are able to flow from one place to another. Summary The following table summarizes the properties of a liquid as temperature and pressure are altered. The speed and kinetic energy of molecules are only dependant on temperature.

– = decrease, 0 = no change, + = increase, NA=not applicable Effect on a liquid of an increase in one variable

with the other constant

Average speed of

molecules

Average translational

kinetic energy of molecules

Viscosity Vapor pressure

Surface tension

Boiling point

Temperature + + – + – NA External pressure 0 0 +/–1 NA2 NA2 +

1A slight increase for most materials but a slight decrease for water at some temperatures. 2Not applicable. For a pure substance in a closed container at equilibrium, external pressure forces more vapor into the liquid phase. The volume of each phase is altered but conditions at the interface remain unchanged.

Skill 1.3 Forms and transformations of matter and energy The forms of matter are discussed in Skill 1.1. It is important to recognize that matter is conserved (see Skill 1.4) and so while it may undergo phase (see Skill 2.4) and chemical changes and even nuclear decay, it will never be created nor destroyed. The forms of energy include chemical, electrical, thermal, and mechanical. All types of energy are important for the study of chemistry and some are discussed elsewhere in this guide (thermal energy in Competency 2.0 and electric energy in Skill 7.5). Like matter, energy is conserved and cannot be created or destroyed (see Skill 1.4). Energy can be converted from one type to another. For instance, living things convert the chemical energy stored in adenosine-tri-phosphate (ATP) to mechanical energy to perform a variety of tasks. Further, mass and energy are related to one another via special relativity. The total energy (E) of particle or object is related to its mass (m) via the famous equation E = mc (where c is a constant, the speed of light in a vacuum). Note that in this equation, mass is specifically rest mass or mass measured independent of the observer (i.e., rest mass does not change with a change in reference).

2

Therefore, in modern physics, all forms of energy exhibit mass and all mass is a form of energy. Skill 1.4 Laws of conservation of mass and energy The law of conservation of mass states that the mass of a closed system will remain constant, regardless of the processes acting inside the system. This means that matter can change form, but it cannot be created or destroyed. This implies that for any chemical process in a closed system, the mass of the reactants must equal the mass of the products. Likewise, the law of conservation of energy states that the total amount of energy in an isolated system remains constant. The energy may be converted from one form to another, but will not be created or destroyed. Note that the conservation of energy is also the first law of thermodynamics (Skill 2.5).

COMPETENCY 2.0 HEAT AND THERMODYNAMICS Skill 2.1 Heat and temperature; concepts; measurements and units Energy Energy is the driving force for change. Energy has units of joules (J). Temperature remains constant during phase changes, so the speed of molecules and their translational kinetic energy do not change during a change in phase. The internal energy of a material is the sum of the total kinetic energy of its molecules and the potential energy of interactions between those molecules. Total kinetic energy includes the contributions from translational motion and other components of motion such as rotation. The potential energy includes energy stored in the form of resisting intermolecular attractions between molecules. The enthalpy (H) of a material is the sum of its internal energy and the mechanical work it can do by driving a piston. We usually don't deal with mechanical work in high school chemistry, so the differences between internal energy and enthalpy are not important. The key concept is that a change in the enthalpy of a substance is the total energy change caused by adding or removing heat at constant pressure. When a material is heated and experiences a phase change, thermal energy is used to break the intermolecular bonds holding the material together. Similarly, bonds are formed with the release of thermal energy when a material changes its phase during cooling. Therefore, the energy of a material increases during a phase change that requires heat and decreases during a phase change that releases heat. For example, the energy of H2O increases when ice melts and decreases when water freezes. Entropy Entropy may be thought of as the disorder in a system or as a measure of the number of states a system may occupy. Changes due to entropy occur in one direction with no driving force. For example, a small volume of gas released into a large container will expand to fill it, but the gas in a large container never spontaneously collects itself into a small volume. This occurs because a large volume of gas has more disorder and has more places for gas molecules to be. This change occurs because processes increase in entropy when given the opportunity to do so. A brief definition will not help you master these concepts. But it is important that you can utilize them sufficiently to apply them to phase changes and to chemical reactions. Entropy has units of Joules/Kelvin.

Also see Skill 14.1 for more information on units and temperature scales. Skill 2.2 Measurement and transfer of thermal energy and its effects on matter In the solid phase, each molecule may vibrate a little, but it is otherwise locked in place in an ordered position and may only be in a relatively small number of locations. In the gas phase, however, each molecule could be almost anywhere and there is greater disorder. Therefore, the entropy of a material increases during a phase change that raises the freedom of molecular motion and decreases during a phase change that prevents molecular motion. Entropy also increases with temperature because molecules experience more disorder when they have a wider range of energy states to occupy. Raw phase change data is often charted by recording the temperature over time when heat is added at a constant rate. A diagram for water at 1 atm from –50°C to 150°C is shown below. Note that temperature does not change during melting and boiling. Also note the difference in the length of time required for melting compared to boiling. This is a result of greater energy requirements to boil a substance than to melt it. 150 vapor

-50

0

50

100

Time→

ice

melting

liquid

vaporization (boiling)

Tem

pera

ture

ºC

The relationship of the translational kinetic energy, enthalpy, and entropy of water to temperature is charted below under the same conditions.

-50 0 50 100 150Temperature °C

Enth

alpy

-50 0 50 100 150Temperature °C

Tran

slat

iona

lki

netic

ene

rgy

-50 0Te

Entr

opy

50 100 150mperature °C

Skill 2.3 Kinetic molecular theory and gas laws In a solid, the energy of intermolecular attractive forces is much stronger than the kinetic energy of the molecules. As temperature increases in a solid, the vibrations of individual molecules grow more intense and the molecules spread slightly further apart, decreasing the density of the solid. In a liquid, the energy of intermolecular attractive forces is about as strong as the kinetic energy of the molecules and both play a role in the properties of liquids. In a gas, the energy of intermolecular forces is much weaker than the kinetic energy of the molecules. Kinetic molecular theory is most commonly used to understand gases and is best applied by imagining ourselves shrinking down to become a molecule and picturing what happens when we bump into other molecules and into container walls. Gas pressure results from molecular collisions with container walls. The number of molecules striking an area on the walls and the average kinetic energy per molecule are the only factors that contribute to pressure. A higher temperature increases speed and kinetic energy. There are more collisions at higher temperatures, but the average distance between molecules does not change, and thus density does not change in a sealed container. Kinetic molecular theory explains how pressure and temperature influences behavior of gases the way they do by making a few assumptions, namely:

1) The energies of intermolecular attractive and repulsive forces may be neglected.

2) The average kinetic energy of the molecules is proportional to absolute temperature.

3) Energy can be transferred between molecules during collisions and the collisions are elastic, so the average kinetic energy of the molecules doesn’t change due to collisions.

4) The volume of all molecules in a gas is negligible compared to the total volume of the container.

Strictly speaking, molecules also manifest some kinetic energy by rotating or experiencing other motions. The motion of a molecule from one place to another is called translation. Translational kinetic energy is the form that is transferred by collisions, and kinetic molecular theory ignores other forms of kinetic energy because they are not proportional to temperature.

The following table summarizes the application of kinetic molecular theory to an increase in container volume, number of molecules, and temperature:

Impact on gas: – = decrease, 0 = no change, + = increase Effect of an increase in one variable

with other two constant

Average distance between

molecules

Density in a

sealed containe

r

Average speed of molecule

s

Average translationa

l kinetic energy of molecules

Collisions with

container walls per second

Collisions per unit area of wall per second

Pressure (P)

Volume of container (V) + – 0 0 – – –

Number of molecules – + 0 0 + + +

Temperature (T) 0 0 + + + + +

Additional details on the kinetic molecular theory may be found at http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/ktcon.html. An animation of gas particles colliding is located at http://comp.uark.edu/~jgeabana/mol_dyn/. Charles’s law states that the volume of a fixed amount of gas at constant pressure is directly proportional to absolute temperature, or:

∝V T

V ∝1P

. Boyle’s law states that the volume of a fixed amount of gas at constant temperature is inversely proportional to the gas pressure, or:

.

Gay-Lussac’s law states that the pressure of a fixed amount of gas in a fixed volume is proportional to absolute temperature, or:

∝P T

V ∝TP

. The combined gas law uses the above laws to determine a proportionality expression that is used for a constant quantity of gas:

.

The combined gas law is often expressed as an equality between identical amounts of an ideal gas at two different states (n1=n2):

=P2V2

T2

P1V1

T1

.

Avogadro’s hypothesis states that equal volumes of different gases at the same temperature and pressure contain equal numbers of molecules. Avogadro’s law states that the volume of a gas at constant temperature and pressure is directly proportional to the quantity of gas, or:

∝ n

∝nTP

where n is the number of moles of gas. V

Avogadro’s law and the combined gas law yieldV . The proportionality

constant R--the ideal gas constant--is used to express this proportionality as the ideal gas law:

= PV nRT

PV = nRT

1 2 3totalP P P P= + + +K

( )

. The ideal gas law ( ) is useful because it contains all the information of Charles’s, Avogadro’s, Boyle’s, and the combined gas laws in a single expression. For mixtures of gases in a container, each gas exerts a partial pressure that it would have if it were present in the container alone. Dalton’s law of partial pressures states that the total pressure of a gas mixture is simply the sum of these partial pressures:

Dalton's law may be applied to the ideal gas law:

( )1 2 3totalP V P P P V n n n RT= + + + = + + +K K

M

. 1 2 3

Effusion occurs when gas escapes through a tiny opening into a vacuum or into a region at lower pressure. Graham’s law states that the rate of effusion (r) for a gas is inversely proportional to the square root of its molecular weight (M).

r ∝1

Graham’s law may be used to compare the ratios of effusion rates and molecular weights for two different gases.

r1r2

=M2

M1

Graham’s law uses the same two expressions above to describe the dependence of the diffusion rate on molecular weight.

Solving gas law problems using these formulas is a straightforward process of algebraic manipulation. Errors commonly arise from using improper units, particularly for the ideal gas constant R. An absolute temperature scale must be used (never ºC) and is usually reported using the Kelvin scale, but volume and pressure units often vary from problem to problem. Temperature in Kelvin is found from:

T (in K) = T(in °C)+273.15

V =nRT

P

If pressure is given in atmospheres and volume is given in liters, a value for R of 0.08206 L-atm/(mol-K) is used. If pressure is given in Pascal (newtons/m2) and volume in cubic meters, then the SI value for R of 8.314 J/(mol-K) may be used. This is because a joule is defined as a Newton-meter. A value for R of 8.314 m3-Pa/(mol-K) is identical to the ideal gas constant using joules. Many problems are given at “standard temperature and pressure” or “STP.” Standard conditions are exactly 1 atm (101.325 kPa) and 0 ºC (273.15 K). At STP, one mole of an ideal gas has a volume of:

=( ) L-atm1 mole 0.08206

mol-K⎛ ⎞ ( )⎝⎜ ⎠⎟

273 K

1 atm= 22.4 L.

The value of 22.4 L is known as the standard molar volume of any gas at STP. Tutorials for gas laws may be found online at: http://www.chemistrycoach.com/tutorials-6.htm. A flash animation tutorial for problems involving a piston may be found at http://www.mhhe.com/physsci/chemistry/essentialchemistry/flash/gasesv6.swf. Skill 2.4 Phase changes Phase changes occur when the relative importance of kinetic energy and intermolecular forces is altered sufficiently for a substance to change its state. The transition from gas to liquid is called condensation and from liquid to gas is called vaporization. The transition from liquid to solid is called freezing and from solid to liquid is called melting. The transition from gas to solid is called deposition and from solid to gas is called sublimation.

Heat removed from a substance during condensation, freezing, or deposition permits new intermolecular bonds to form, and heat added to a substance during vaporization, melting, or sublimation breaks intermolecular bonds. During these phase transitions, this latent heat is removed or added with no change in the temperature of the substance because the heat is not being used to alter the speed of the molecules or the kinetic energy when they strike each other or the container walls. Latent heat alters intermolecular bonds.

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Solid

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Freezing Melting

Deposition Sublimation

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The kinetic energy of molecules is unaltered during phase changes, but the freedom of molecules to move relative to one another increases dramatically. The following table summarizes the application of kinetic molecular theory to the addition of heat to ice, first changing it to liquid water and then to water vapor.

0 = no change, + = increase, ++ = strong increase Effect at 1 atm of the addition of

heat to:

Temperature Average speed of

molecules

Average translational

kinetic energy of molecules

Intermolecular freedom of motion

Ice at less than 0 ºC

+ + + +

Ice at 0 ºC 0 0 0 ++ (melting) Liquid water

at 0 ºC + + + +

Liquid water at 100 ºC

0 0 0 ++ (boiling)

Water vapor at 100 ºC

+ + + 0 (complete freedom for an ideal gas)

The term vaporization is used for any process of liquid becoming a gas. This includes evaporation and boiling. Evaporation takes place at a gas/liquid interface when the temperature is lower than the boiling point. Equilibrium develops between the gas and liquid phases when the rates of evaporation and condensation are equal. An increase in the external pressure forces molecules closer to each other and may cause condensation, freezing, or deposition for most substances. Water is an exception because liquid water is denser than ice, so pressure favors the liquid state. A pressure increase for water may cause condensation, melting, or deposition.

Whether a substance exists as a gas, liquid, or solid depends on the nature of its intermolecular attractive forces and on temperature and pressure. This information is often visualized as a phase diagram for the substance. A region on the phase diagram represents each phase. Solid lines dividing these regions are located at conditions under which two phases may exist at equilibrium and a phase change may occur. All three phases may coexist at the triple point of a substance. The triple point pressure of CO2 is greater than 1 atm, so dry ice sublimates at atmospheric pressure with no liquid phase. Vapor pressure at a given temperature is the pressure of the phase transition line to a gas at that temperature. Normal melting point (Tm) and normal boiling point (Tb) are defined at 1 atm. Note that freezing point and melting point refer to an identical temperature approached from different directions, but they represent the same concept. At temperatures and pressures above the critical point, the substance becomes too dense with too much kinetic energy for a gas-liquid interface to form. Matter under these conditions forms a supercritical fluid with properties of gases and of liquids.

Gas

Liquid

Supercritical fluid

Solid 1 atm

Pcritical

Ptriple

Ttriple Tm Tb Tcritical

Pres

sure

melting

freezing

sublimation

deposition

vaporization

condensation

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Temperature

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The phase diagram for water (shown below) is unusual. The solid/liquid phase boundary slopes to the left with increasing pressure because the melting point of water decreases with increasing pressure. Note that the normal melting point of water is lower than its triple point. The diagram is not drawn to a uniform scale. Many anomalous properties of water are discussed here: http://www.lsbu.ac.uk/water/anmlies.html.

Gas

LiquidSolid 1 atm

Pcritical

WATER

Ttriple0 ºC 100 ºC Tcritical

Supercritical fluid

Pres

sure

Temperature

Ptriple

Skill 2.5 Laws of thermodynamics Thermodynamics is the study of energy flow in natural systems. Findings in this area have been codified into three important physical laws that describe how energy behaves throughout the universe. In addition to the three traditional laws a zeroth law is often included: Zeroth Law: If two thermodynamic systems are in thermal equilibrium with a third, they are also in thermal equilibrium with each other. This law simply establishes equivalence in thermodynamic systems. First Law: The increase in the energy of a closed system is equal to the amount of energy added to the system by heating, minus the amount lost in the form of work done by the system on its surroundings. This law means that energy is conserved: energy can be transferred from one system to another, but not created or destroyed. Thus, the total amount of energy available in the Universe is constant. Einstein's famous equation (E=mc2) describes the relationship between energy and matter. Second Law: The total entropy (disorder) of any isolated thermodynamic system tends to increase over time, approaching a maximum value. This law indicates that disorder increases with every reaction and some energy is always lost to the increase in that disorder. As a result of this law, it is also true that energy transfer always occurs in one direction (heat can pass spontaneously only from a colder to a hotter body). Third Law: As a system asymptotically absolute zero of temperature all processes virtually cease and the entropy of the system asymptotically approaches a minimum value. This law defines absolute zero (0 K or –273° C), at which all thermal motion stops. However, absolute zero cannot be achieved and even empty outer space has a temperature around 3 K. The British scientist and author C.P. Snow had an excellent way of remembering the three laws:

1. You cannot win (that is, you cannot get something for nothing, because matter and energy are conserved).

2. You cannot break even (you cannot return to the same energy state, because there is always an increase in disorder; entropy always increases).

3. You cannot get out of the game (because absolute zero is unattainable).

Skill 2.6 Thermochemistry A substance's molar heat capacity is the heat required to change the temperature of one mole of the substance by one degree. Heat capacity has units of joules per mol-kelvin or joules per mol-°C. The two units are interchangeable because we are only concerned with differences between one temperature and another. A Kelvin degree and a Celsius are the same size. The specific heat of a substance (also called specific heat capacity) is the heat required to change the temperature of one gram or kilogram by one degree. Specific heat has units of joules per gram or joules per kilogram. These terms are used to solve thermochemistry problems involving a change in temperature by applying the formula:

where q ⇒ heat added (positive) or evolved (negative)n ⇒ amount of material

q = n ×C × ΔT

C ⇒molar heat capacity if n is in moles, specific heat if n is a massΔT ⇒ change in temperature Tfinal −Tinitial

A substance's enthalpy of fusion (ΔHfusion) is the heat required to change one mole of a substance from a solid to a liquid by freezing. This is also the heat released from the substance when it changes from a liquid to a solid (melts). A substance's enthalpy of vaporization (ΔHvaporization) is the amount of heat required to change one mole of a substance from a liquid to a gas or the heat released by condensation. A substance's enthalpy of sublimation (ΔHsublimation) is the amount of heat required to change one mole directly from a solid to a gas by sublimation or the heat released by deposition. These three values are also called "heats" or "latent heats" of fusion, vaporization, and sublimation. They have units of joules per mole, and are negative values when heat is released.

Solid Liquid Gas ΔHsublimation

–ΔHsublimation

ΔHfusion

–ΔHfusion–ΔHvaporization

ΔHvaporization

melting

freezing

vaporization

condensation

sublimation

deposition

Gas Solid

Gas Liquid Solid Gas Solid

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These terms are used to solve thermochemistry problems involving a change of phase by applying the formula:

q = n × ΔHchange

where q ⇒ heat added (positive) or evolved (negative)

Δ n ⇒ amount of material

Hchange ⇒ enthalpy of fusion, vaporization, or sublimation for heat added

⇒−(enthalpy of fusion, vaporization, or sublimation) for heat evolved

Example: What is the change in energy of 10 g of gold at 25 °C when it is heated

beyond its melting point to 1300 °C. You will need the following data for gold:

Solid heat capacity: 28 J/mol-KMolten heat capacity: 20 J/mol-K

Ent

10 g × 1 mol197 g

halpy of fusion: 12.6 kJ/molMelting point: 1064 °C

Solution: First determine the number of moles used.

= 0.051 mol

There are then three steps that all require energy, so the results will be positive numbers. 1) Heat the solid:

= × ×Δ = × × −

×

1

3

J0.051 mol 28 (1064 °C 25 °C)mol-K

=1.4 10 J=1.4 kJ

q n C T

8 8

2) Melt the solid:

q2 = n × ΔHfusion = 0.051 mol×12.6 kJmol

= 0.64 kJ

3) Heat the liquid:

= × ×Δ = × × −

× 2

0.051 mol 20 (1300 °C 1064 °C)mol-K

.4 10 J=0.24 kJ

C T3J

=2

q n

q = q1 + q2 + q3 = 1.48 kJ+ 0.64 kJ+ 0.24 kJ = 2.36 kJ=

The sum of the three processes is the total change in energy of the gold:

2.4 kJ

Now we will consider the thermochemistry of one substance reacting to form a different substance. Energy When a chemical reaction takes place, the enthalpies of the products will differ from the enthalpies of the reactants. There is an energy change for the reaction Δ Hrxn, determined by the sum of the products minus the sum of the reactants:

( )Δ = + + − + +K Kproduct 1 product 2 reactant 1 reactant 2rxnH H H H H . The enthalpy change for a reaction is commonly called the heat of reaction. If the enthalpies of the products are greater than the enthalpies of the reactants then Δ Hrxn is positive and the reaction is endothermic. Endothermic reactions absorb heat from their surroundings. The simplest endothermic reactions break chemical bonds. If the enthalpies of the products are less than the enthalpies of the reactants then ΔHrxn is negative and the reaction is exothermic. Exothermic reactions release heat into their surroundings. The simplest exothermic reactions form new chemical bonds. The heat absorbed or released by a chemical reaction often has the impact of changing the temperature of the reaction vessel and of the chemicals themselves. The measurement of these heat effects is known as calorimetry. The enthalpy change of a reaction Δ Hrxn is equal in magnitude but has the opposite sign to the enthalpy change for the reverse reaction. If a series of reactions lead back to the initial reactants then the net energy change for the entire process is zero.

When a reaction is composed of substeps, the total enthalpy change will be the sum of the changes for each step. Even if a reaction in reality contains no substeps, we may still write any number of reactions in series that lead from the reactants to the products and their sum will be the heat of the overall reaction of interest. The ability to add together these enthalpies to form ultimate products from initial reactants is known as Hess's Law. It is used to determine one heat of reaction from others:

Δ = + +K rxn 1 rxn 2net rxnH H H

+ +For the reaction: A B Qa b pP q

ΔS = pS P( )+ qS Q

It is generally the case that exothermic reactions are more likely to occur spontaneously than endothermic reactions. Molecules usually seek the lowest possible energy state. However, entropy also plays a critical role in determining whether a reaction occurs. Entropy Remember that gases are of greater entropy than liquids, liquids are of greater entropy than solids, and matter in the same state increases in entropy with temperature. Entropy is also an extensive property of matter. A greater number of moles will have more entropy. If two different chemicals are at the same temperature, in the same state of matter, and they have the same number of molecules, their entropy difference will depend mostly on the number of ways the atoms within the two chemicals can rotate, vibrate, and flex. Most of the time, the more complex molecule will have the greater entropy because there are more energetic and spatial states in which it may exist. At zero Kelvin (0 K), there is no energy available for a chemical to sample different states. The absolute entropy, S, of a pure crystalline solid at 0 K is zero. Absolute entropy may be measured and calculated for different substances at different temperatures. The entropy change of a reaction, ΔS, is given by the sum of the absolute entropies of all the products multiplied by their stoichiometric coefficients minus the sum of all the products multiplied by their stoichiometric coefficients:

( )− aS A( )− bS B( )

Spontaneity A reaction with a negative ΔH and a positive ΔS causes a decrease in energy and an increase in entropy. These reactions will always occur spontaneously. A reaction with a positive ΔH and a negative ΔS causes an increase in energy and a decrease in entropy. These reactions never occur to an appreciable extent because the reverse reaction takes place spontaneously. Whether reactions with the remaining two possible combinations (ΔH and ΔS both positive or both negative) occur depends on the temperature. If ΔH–TΔS (known as the Gibbs Free Energy, ΔG) is negative, the reaction will take place. If it is positive, the reaction will not occur to an appreciable extent. If ΔH–TΔS=0 exactly, then at equilibrium there will be 50% reactants and 50% products. A spontaneous reaction is called exergonic. A non-spontaneous reaction is known as endergonic. These terms are used much less often than exothermic and endothermic. A standard thermodynamic value occurs with all components at 25 °C and 100 kPa. This thermodynamic standard state is slightly different from the standard temperature and pressure (STP) often used for gas law problems, (0 °C and 1 atm=101.325 kPa). Standard properties of common chemicals are listed in tables. The heat of formation ΔHf of a chemical is the heat required (positive) or emitted (negative) when elements react to form the chemical. It is also called the enthalpy of formation. The standard heat of formation ΔHf° is the heat of formation with all reactants and products at 25 °C and 100 kPa. Elements in their most stable form are assigned a value of Δ Hf° = 0 kJ/mol. Different forms of an element in the same phase of matter are known as allotropes.

Example: The heat of formation for carbon as a gas is:

Δ o kJ for C( ) 718.fH g = 4 mol

. C in the solid phase exists in three

allotropes. A C60 buckyball (one face is shown to the left), contains C atoms linked with aromatic bonds and arranged in the shape of a soccer ball. C60 was discovered in 1985. Diamonds (below left) contains single C–C bonds in a three dimensional network. The most stable form at 25 °C is graphite (below right). Graphite is composed of C atoms with aromatic bonds in sheets.

Heat of combustion Δ Hc (also called enthalpy of combustion) is the heat of reaction when a chemical burns in O2 to form completely oxidized products such as CO2 and H2O. It is also the heat of reaction for nutritional molecules that are metabolized in the body. The standard heat of combustion Δ Hc° takes place at 25 °C and 100 kPa. Combustion is always exothermic, so the negative sign for values of Δ Hc is often omitted. If a combustion reaction is used in Hess's Law, the value must be negative. The standard molar entropy, S°, is the absolute entropy of a chemical at 1 atm and 25 °C. The molar entropy of a substance is expressed in units of J/mol-K.

Δ =

Δ =∞

∞

o60

kJ for C ( or ) 38.0 mol

kJ for C ( ) 1.88 mol

kJ for C ( ) 0 .mol

fH buckminsterfullerene buckyball

diamond

H graphiteΔ =

o

o

f

f

H

Example: Determine the standard heat of formation Δ Hf° for ethylene:

2C(graphite)+2H (g)→ C H (g)2 2 4 .

Use the heat of combustion for ethylene:

°Δ = + → +kJ1411.2 for C H ( ) 3O ( ) 2CO ( ) 2H O( )H g g g l2 4 2 2 2

2 4mol C Hc

and the following two heats of formation for CO2 and H2O:

°Δ = − + →2 2kJ393.5 for C( ) O ( ) CO ( )

mol Cf

f

H graphite g g

S°(C(graphite)) = 5.7 J

mol K

°Δ = − + →2 2 22

kJ 1285.9 for H ( ) O ( ) H O( ).mol H 2

H g g l

Also find the standard change in entropy Δ S° for the formation of C2H4

given:

S°(H2(g)) = 130.6 Jmol K

S°(C2H4(g)) = 219.4 Jmol K

.

Will graphite and hydrogen gas react to form C2H4 at 25 °C and 100 kPa?

Solution: Use Hess's Law after rearranging the given reactions so they cancel to

yield the reaction of interest. Combustion is exothermic, so Δ H for this reaction is negative. We are interested in C2H4 as a product, so we take the opposite (endothermic) reaction. The given Δ H are multiplied by stoichiometric coefficients to give the reaction of interest as the sum of the three:

2CO2(g) + 2H2O(l)→ C2H4(g) + 3O2(g) ΔH = 1411.2 kJmol reaction

2C(graphite) + 2O2(g)→ 2CO2(g) ΔH = −787.0 kJmol reaction

2H2(g) +O2(g)→ 2H2O(l) ΔH = −571.8mol reaction

kJ

______________________________ ____________________

2C(graphite)+2H2(g)→ C2H4(g) ΔHf° = 52.4 kJ

mol

The entropy change is found from:

ΔS° =S°(C2H4)− 2S°(C)− 2S°(H2) = 219.4 Jmol K

− 2 × 5.7 Jmol K

− 2 ×130.6 Jmol K

= −53.2 Jmol K

.

This reaction is endothermic with a decrease in entropy, so it is endergonic. Graphite and hydrogen gas will not react to form C2H4.