# THERMOCHEMISTRY

Thermodynamics – The study of the relationship between heat, work, and other forms of energy

Thermochemistry – A branch of thermodynamics which focuses on the study of heat given off or absorbed in a chemical reaction.

Temperature – An intensive property of matter; a quantitative measurement of the degree to which an object is either “hot” or “cold”.

1. There are 3 scales for measuring temperature
• Fahrenheit – relative
• 32F is the normal freezing point temperature of water; 212F is the normal boiling point temperature of water.
• 0C is the normal freezing point temperature of water; 100C is the normal boiling point temperature of water.
• Kelvin – absolute
• 0 K is the temperature at which the volume and pressure of an ideal gas extrapolate to zero.

Conversion Factors for Temperature
Heat (q)

• A form of energy associated with the random motion of the elementary particles in matter.

Heat capacity – The amount of heat needed to raise the temperature of a defined amount of a pure substance by one degree.

• Specific heat – The amount of heat needed to raise the temperature of one gram of a substance by 1C (or 1 K)
• SI unit for specific heat is joules per gram-1 Kelvin-1 (J/g-K)
• Calorie – The specific heat of water = 4.184 J/g-K
• Molar heat capacity – The amount of heat required to raise the temperature of one mole of a substance by 1C (or 1 K)
• SI unit for molar heat capacity is joules per mole-1 Kelvin-1 (J/mol-K)
• Btu (British thermal unit) – The amount of heat needed to raise the temperature of 1 lb water by 1F.

NOTE:  The specific heat of water (4.184 J/g-K) is very large relative to other substances.  The oceans (which cover over 70% of the earth) act as a giant “heat sink,” moderating drastic changes in temperature.  Our body temperatures are also controlled by water and its high specific heat.  Perspiration is a form of evaporative cooling which keeps our body temperatures from getting too high.

Latent Heat versus Sensible Heat

Sensible heat – Heat that can be detected by a change in the temperature of a system.

Latent heat – Heat that cannot be detected because there is no change in temperature of the system.

• e.g.  The heat that is used to melt ice or to evaporate water is latent heat.

There are two forms of latent heat:

• Heat of fusion – The heat that must be absorbed to melt a mole of a solid.
• e.g.  melting ice to liquid water
• Heat of vaporization – The heat that must be absorbed to boil a mole of a liquid.
• e.g.  boiling liquid water to steam

Caloric Theory of Heat

• Served as the basis of thermodynamics.
• Is now known to be obsolete
• Based on the following assumptions
• Heat is a fluid that flows from hot to cold substances.
• Heat has a strong attraction to matter which can hold a lot of heat.
• Heat is conserved.
• Sensible heat causes an increase in the temperature of an object when it flows into the object.
• Latent heat combines with particles in matter (causing substances to melt or boil)
• Heat is weightless.
• The only valid part of the caloric theory is that heat is weightless.
• Heat is NOT a fluid, at it is NOT conserved.

1798 – Sir Benjamin Thompson (Count Rumford)

 Canon-boring experiment showed that friction was an inexhaustible source of heat.  He concluded that heat, therefore, was not conserved. This experiment served as a starting point for the development of a new theory, the kinetic theory of heat.

Kinetic Theory of Heat

1. Divides the universe into two parts:
1. System – The small portion of the universe in which we are interested.
2. Surroundings – Everything not included in the system, i.e. the rest of the universe.
• BOUNDARY separates the system and the surroundings from each other and can be tangible or imaginary.
• Heat is something that is transferred back and forth across boundary between a system and its surroundings
• Heat is NOT conserved.
• The kinetic theory of heat is based upon the last postulate in the kinetic molecular theory which states that the average kinetic energy of a collection of gas particles is dependent only upon the temperature of the gas.

where R is the ideal gas constant (0.0821 L-atm/mol-K) and T is temperature (Kelvin)

• The kinetic theory of heat can be summarized as follows:

 When heat enters a system, it causes an increase in the speed at which the particles in the system move.

Work (w)

• Defined as mechanical energy equal to the product of the force (F) applied to an object and the distance (d) that the object is moved:

• Work, like heat, results from interaction between a system and its surroundings.
• Chemical reactions can do two types of work:
• Electrical work – When a reaction is used to drive an electric current through a wire.
• e.g.  a light bulb
• Work of expansion – When a reaction causes a change in the volume of the system.
• e.g.  a gas pushing up a piston
• The magnitude of work done when a gas expands is equal to the product of the pressure of the gas and the change in volume of the gas:

Heat and Work

• Thompson’s canon-boring experiment showed how work (boring the canon) could produce heat.

1838 – James Prescott Joule

 Did several experiments measuring how much heat could be produced from a given amount of heat. In his most well-known experiment, Joule used falling weights connected to a rope wrapped around rotating paddles.  The paddles were placed in either water, mercury, or oil and he measured the change in temperature of these liquids when the weights were dropped. One joule is by definition the work done when a force of one newton (N) is used to move an object one meter (m):

Thermochemistry is the study of energy changes accompanying chemical and physical reactions. The purpose of this page is to give a brief summary of concepts on thermochemistry to be tested in the quiz.

This page is very similar to weekly skill review. Using either page will be fine.

### Energy

Energy is the potential to do work, such as accelerating an object (kinetic energy), lifting things up (potential energy), producing electric power (electric energy), raising the temperature of a system (heat) and producing sound (waves of energy). In physics, work is formally defined as force times the distance in the direction of the force, and such a definition defines the very basic idea of energy.

Energy is the driving force of changes. All changes are caused by energy, and the cause or energy can be in many forms: light, heat, work, electrical, mechanical (energy stored in a spring), chemical, etc. The changes are phenomena caused by energy, but more importantly, forms of energy inter-convert into one another during the changes.

Unlike some of these changes, forms of energy convert into one another always at a fixed rate. Exactly 4.184 J of mechanical work converts into 1.00 cal measured as heat, and vice versa.

#### Conservation of Energy

Energy can neither be destroyed, nor created; it converts from one form (for example heat) to another form (say mechanical work) at a fixed rate. This is the fundamental principle of conservation of energy.

To indicate changes, we use d to represent the delta (D) commonly used in text books, because using the delta will cause the loading of this page into your computer to be very slow.

The internal energy E accounts for energy and work transferred to a system. This concept is another form of the principle of conservation of energy. The change in internal energy dE of a closed system increases by the amount of energy input to the system. Such input can be in the form of heat (q) or (mechanical or any other form) of work (w). Usually, it is formulated as

dE=q+w

dE=q+w.

Heat transferred out and work done by the system are assigned negative signs by convention. This relationship is usually referred to as the first law of thermodynamics.

When energy is transferred from system A to system B, what happens to the energy? Does energy disappear? The internal energy as defined above shows that energy does not disappear, because the internal energy loss of system A equals the internal energy gain of system B. The change in internal energy, dE, is negative for system A, but positive for system B. Energy is neither destroyed, nor created.

#### Heats of Reactions

The enthalpy of reaction, dH, is the energy [heat (q) and work (d(P V))] released in a reaction. The thermochemical equation is usually written in the form:

2H2(g,1atm)+O2(g)2H2O(l),dH=571.7kJ

2H2(g,1atm)+O2(g)→2H2O(l),dH=−571.7kJ

This equation means that when 2 moles of H2

H2 gas react with 1 mole of O2

O2 gas, 571.7 kJ of energy is released (lost to the surrounding). Thus, if 1 mole of H2

H2 and one half mole of O2

O2 react, half of 571.7 kJ or 285.9 kJ of energy is released.

H2(g,1atm)+0.5O2H2O(l),dH=285.9kJ

H2(g,1atm)+0.5O2→H2O(l),dH=−285.9kJ

On the other hand, if double amounts of reactants (i.e. 4 moles of H2

H2 and 2 moles of O2

O2) are used, twice the amount of energy (2*(-571.7) =) -1043.4 kJ is released.

If dH is positive, at least that much energy must be supplied to carry out the endothermic reaction.

#### The Standard Enthalpy of Reaction

For convenience in application, 1 atm for gas and 1.0 M for solutions were considered the “standard conditions”, and data collected at standard conditions were called standard data such as standard enthalpy of reaction and standard enthalpy of formation. These values are condensed and summarized in handbooks for scientists and engineers in their applications.

Because temperature, pressure, and concentration of reactants and products affect the amount of measured energy, the scientific community has agree upon a temperature of 273 K and 1 atm as the standard temperature and and pressure (STP). However, standard enthalpies are often given for data collected at 298 K.

The most stable state at the standard condition is the standard state. The enthalpy of an element at its standard state is assigned 0 for reference.

For example, at 1 atm, graphite is the most stable state of carbon. The standard enthalpy of combustion of carbon is the energy released (-394 kJ) when 1 mole of graphite reacts with oxygen in the reaction

C(graphite)+O2CO2,dHo=394kJ

C(graphite)+O2→CO2,dHo=−394kJ.

Since the measurement is done at the standard condition, a superscript o is usually placed on the right side of H in most literature. Incidentally, the above equation is for the formation of CO2

CO2, and the enthalpy of reaction happens to be the enthalpy of formation of CO2

CO2, designated as dHof = -394 kJ, as reviewed in the next paragraph.

As another example, when 1.0 mole Zn

Zn reacts with sufficient amount of HCl

HCl solution (1.0 M), 150 kJ is released. Thus, we write standard energy of reaction for Zn

Zn as,

Zn+2HCl(aq)H2(g)+ZnCl2(aq),dHo=150kJ

Zn+2HCl(aq)→H2(g)+ZnCl2(aq),dHo=−150kJ.

#### The Standard Enthalpy of Formation

Combination of elements at their standard states resulting in one compound is called a formation reaction. When enthalpy of formation is measured at the standard condition, it is called the standard enthalpy of formation. The standard enthalpy of combustion of carbon mentioned earlier

C(graphite)+O2CO2,dHof=394kJ

C(graphite)+O2→CO2,dHfo=−394kJ

is the formation of CO2

CO2 from elements at their standard states. Thus, dHof of -394 kJ is also the standard enthalpy of formation of CO2

CO2.

Similarly, a few more examples are given below. The enthalpies can be both positive and negative values.

12O2=O,dHof=249.17kJ

12O2=O,dHfo=249.17kJ       (also bond energy of O=O

O=O).
12H2=H,dHof=217.96kJ

12H2=H,dHfo=217.96kJ       (also bond energy of HH

H−H).
H2+O2=H2O2(aq),dHof=191.17kJ

H2+O2=H2O2(aq),dHfo=−191.17kJ12H2+12Cl2=HCl(g),dHof=92.31kJ

12H2+12Cl2=HCl(g),dHfo=−92.31kJ12H2+12Br2=HBr(g),dHof=36.40kJ

12H2+12Br2=HBr(g),dHfo=−36.40kJ

#### Hess’s Law

Hess’s law is another interpretation of the principle of conservation of energy. Since the changes in energy are independent of path, they depend on the initial and final state of the system. Thus, if it takes several steps to reach the final state from the initial state, the changes in energy are additive. The law states:

The total enthalpy change in a reaction is the same whether the reaction occurs in one or several steps.

However, one should recognize that the enthalpy change is related to the amounts of reactants and products in the equation.

A simple application of Hess’s law is to give the standard enthalpy of decomposition of CO2

CO2 from its standard enthalpy of formation,

CO2(g)C(graphite)+O2(g),dHo=394kJ

CO2(g)→C(graphite)+O2(g),dHo=394kJ.

Note that we change the sign of dHo if the reaction is reversed.

#### Measurements of Energy Changes

Various experimental techniques have been designed to measure energy changes in a chemical reaction. It is necessary to know the heat capacity of a system. Precise measurements require carefully designed calorimeters.

Enthalpy of reaction (dH) is measured when the reaction is carried out at constant pressure. When a bomb calorimeter is used, the volume does not change. The amount of energy measured is the internal energy dE. To convert dE into dH, we use the defined relationship,

dH=dE+d(PV)

dH=dE+d(PV).

The changes in pressure and volume (P V) work can be evaluated by the application of ideal gas law,

d(PV)=dnRT

d(PV)=dnRT,

where dn is the total number of moles of gas of product Sn(products) minus the total number of moles of gas of reactants, Sn(reactants).

dn=Sn(products)Sn(reactants)

dn=Sn(products)−Sn(reactants)

EXAMPLE 1

Will the reaction

P4O10(s)+6H2O(l)4H2PO4(aq)

P4O10(s)+6H2O(l)→4H2PO4(aq)

be exothermic or endothermic?

Solution
The enthalpy of a reaction can be evaluated from the standard enthalpies of formation of all products and reactants.

dHo=dHof(allproducts)dHof(allreactants)

dHo=dHfo(allproducts)−dHfo(allreactants)

Thus, it is desirable to find the dHof of all products and reactants: P4O10

P4O10, -3110 kJ/mol; H2

H2, -286 kJ/mol; H3PO4

H3PO4, -1288 kJ/mol.

dHo=4×1288(3110286×6)=326kJ/mol(5)(6)

(5)dHo=−4×1288−(−3110−286×6)(6)=−326kJ/mol

Discussion
The entropy (dS) is another important piece of thermodynamic data, which is often listed together with dHof. The entropies are: P4O10

P4O10, 229 J/(K mol); H2

H2, 70 J/(K mol); H3PO4

H3PO4, 158 J/(K mol); and the entropy of the reaction is thus:

dS=4×158(6×70+229)kJ/mol=17J/(Kmol)(7)(8)

(7)dS=4×158−(6×70+229)kJ/mol(8)=−17J/(Kmol)

and the Gibb’s free energy dG=dHTdS

dG=dH−TdS,

dG=[326298×(0.017)]kJ/mol=321kJ/mol(9)(10)

(9)dG=[−326−298×(−0.017)]kJ/mol(10)=−321kJ/mol

A negative value for dG indicates that the reaction will be spontaneous.

Don’t worry. General chemistry students are not expected to know entropy and Gibb’s free energy yet.

A summary of thermochemistry has been given. Thermochemistry deals with the energy aspect of chemical reactions. A more complete study of energy is Thermodynamics. This link is divided into 7 units: Energy, Enthalpy, Hess’s Law, Enthalpy of Formation, Entropy, Gibbs Free Energy and Conclusion. You may find its simple approach interesting. Some of the aspect has been included in the discussion of the above example.

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