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.
• Celsius (centigrade) - relative
• 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

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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.

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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.

• A 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.  (See Kinetic Molecular Theory notes)

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.

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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) First Law of Thermodynamics Energy can neither be created nor destroyed. The energy of the universe does not change. The energy in a system may change, but it must be complemented by a change in the energy of its surroundings to balance the change in energy. The term internal energy is often used synonymously with the energy of a system.  It is the sum of the kinetic and potential energies of the particles that form the system.  The last postulate in the kinetic molecular theory states that the average kinetic energy of a collection of gas particles is dependent only upon the temperature of the gas.  Since ideal gases have no potential energy, the internal energy is directly proportional to the temperature: where R is the ideal gas constant (0.0821 L-atm/mol-K) and T is temperature (Kelvin) If a system is more complex than an ideal gas, then the internal energy must be measured indirectly by observing any changes in the temperature of the system.  The change in the internal energy of a system is equal to the difference between the final and initial energies of the system: The equation for the first law of thermodynamics can be rearranged to show the energy of a system in terms of the energy of its surroundings. This equation indicates that the energy lost by one must equal the energy gained by the other: The energy of a system can change by the transfer of work and or heat between the system and its surroundings.  Any heat that is taken, given off, or lost must be complemented by an input of work to make up for the loss of heat.  Conversely, a system can be used to do any amount of work as long as there is an input of heat to make up for the work done. This equation can be used to explain the two types of heat that can be added to a system: Heat can increase the temperature of a system.  This is sensible heat. Heat that does ONLY WORK on a system is latent heat. The diagram above illustrates the sign (positive or negative) of the change in the energy of a system when heat and work are transferred between a system and its surroundings. When heat enters a system,  resulting in an increase in the temperature, E is positive. When heat leaves a system resulting in a decrease in the temperature, E is negative. When a system does work on its surroundings, energy is lost, therefore E is negative. When the surroundings do work on a system, the internal energy increases, therefore E is positive.   State Functions A property of a system is a state function if it depends on the state of the system and not the path used to get to that state. Equations of state - Equations that connect two or more properties that describe the state of a system. e.g.  The ideal gas law, PV = nRT is an equation of state. Are the following properties state functions? TEMPERATURE:  YES.  The net change in the temperature of a system (T) depends only on the initial and final temperatures of the system.  It does not matter what changes in temperature happened in between these stages. INTERNAL ENERGY:  YES.  Since the internal energy of a system is directly proportional to the temperature of a system, internal energy is also a state function. WORK:  NO.  By definition, work is the product of the force and the distance that an object moves.  This means that it does depend on the path use to get to the final state, and therefore work cannot be a state function. HEAT:  NO.  It was determined earlier that the change in the internal energy of a system is equal to the work and the heat transferred between the system and its surroundings: We already determined that the internal energy of a system is a state function, but work is not.  Since the change heat must complement the path that the work followed, heat cannot be a state function. Properties that ARE state functions generally have CAPITALIZED variables. e.g.  E, P, T, V, etc. Properties that ARE NOT state functions generally have LOWER-CASE variables. e.g.  q and w Enthalpy (H) - The sum of the internal energy of the system plus the product of the pressure of the gas in the system and its volume: After a series of rearrangements, and if pressure if kept constant, we can arrive at the following equation:   where H is the Hfinal minus Hinitial and q is heat Enthalpy of Reaction (H) The difference between the sum of the enthalpies of the products and the sum of the enthalpies of the reactants: In the above reaction, n and m are the coefficients of the products and the reactants in the balanced equation. Exothermic - Reaction in which a system RELEASES heat to its surroundings. H  is negative (H < 0)Ea is the activation energy which is discussed in more detail in the kinetics unit.  (See Activation Energy notes) Endothermic - Reaction in which a system ABSORBS heat from its surroundings. H  is positive (H > 0) Let's distinguish various phase changes of water as either endothermic or exothermic. 1) The above reaction is EXOTHERMIC because heat is released when liquid water freezes to form ice. 2) The above reaction is ENDOTHERMIC because there must be an input of energy in order for water molecules in the liquid phase to have enough energy to escape into the gas phase. 3) The above reaction is ENDOTHERMIC because there must be an input of energy to break the bonds holding water molecules together as ice. Standard-State Enthalpy of Reaction (H) Three factors can affect the enthalpy of reaction: The concentrations of the reactants and the products The temperature of the system The partial pressures of the gases involved (if any) The effects of changes in these factors can be shown relative to the standard-state enthalpy of reaction (H) which is the change in the enthalpy during a chemical reaction that begins and ends under standard-state conditions.Standard-state conditions The partial pressures of any gases involved in the reaction is 0.1 MPa. The concentrations of all aqueous solutions are 1 M. Measurements are also generally taken at a temperature of 25C (298 K)   Hess's Law 1940 - Germain Henri Hess Hess's Law states that the heat transferred, or change in enthalpy (H), in a reaction is the same regardless whether the reaction occurs in a single step or in several steps.  The method of calculating the enthalpy of reaction developed by Hess is called Hess's Law of Heat Summation.  If a series of reactions are added together, the net change in the heat of the reaction is the sum of the enthalpy changes for each step.  Rules for using Hess's Law If the reaction is multiplied (or divided) by some factor, H must also be multiplied (or divided) by that same factor.  If the reaction is reversed (flipped), the sign of H must also be reversed.  Example Calculations1) Nitrogen and oxygen gas combine to form nitrogen dioxide according to the following reaction: Calculate the change in enthalpy for the above overall reaction, given: This problem is very simple.  If we simply add up the two reactions keeping all the reactants on the left and all the products on the right, we end up with the overall equation that we are given.  Since we didn't make any changes to the individual reactions, we don't make any changes toH.  If we add upH as well, we find the change in enthalpy: Let's try one that is a bit more complicated. 2) From the following enthalpy changes: calculate the value ofH for the reaction: If we look at the final reaction, we see that we need 2 S atoms on the reactants side.  The only reaction with S atoms is the third reaction, and in order to get 2 S atoms, we need to multiply the whole reaction by a factor of 2.  The next reactant in the final reaction is 2 OF molecules.  The only reaction with an OF molecule is the first reaction, and in order to get 2 OF molecules, we need to multiply the whole reaction by a factor of 2.  On the products side of the final reaction, there is 1 SF4 molecule, and the only possible source of the SF4 molecule is the second reaction.  However, the SF4 molecule is on the reactants side, which is not the side we need it on.  So we'll have to FLIP the second reaction to get the SF4 molecule where we need it. Now if we total up the reactions, we should end up with the given overall reaction: Remember that everything we did to each reaction, we have to do to each respectiveH.  So we have to multiply the first and thirdH values by a factor of 2.  We also have to reverse the sign of the secondH.  When we add these up we get: Enthalpy of formation (Hf) The enthalpy associated with the reaction that forms a compound from its elements in their most thermodynamically stable states.  These are measured on a relative scale where zero is the enthalpy of formation of the elements in their most thermodynamically stable states. The standard-state enthalpy of reaction is equal to the sum of the enthalpies of formation of the products minus the sum of the enthalpies of formation of the reactants: Sample enthalpy of formation calculation Calculate the heat given off when one mole of B5H9 reacts with excess oxygen according to the following reaction: Compound Hf (kJ/mol-K) B5H9(g) 73.2 B2O3(g) -1272.77 O2(g) 0 H2O(g) -241.82 In the reaction above 2 moles of B5H9 react with 12 moles of O2 to yield five moles of B2O3 and 9 moles of H2O.  We find theHf by subtracting the sum of the enthalpies of the reactant from the sum of the enthalpies of the products: NOTE: The heat of formation of O2 is zero because this is the form of the oxygen in its most thermodynamically stable state.   Bond Energy The energy required to break a bond.  Bond energy is always a positive number because the breaking of a bond requires an input of energy (endothermic).  When a bond is formed, the amount of energy equal to the bond energy is released. The bonds broken are the reactant bonds.  The bonds formed are the product bonds. Sample Calculation FindH for the following reaction given the following bond energies: Bond   Bond Energy (kJ/mol) H-H 436 O=O 499 O-H 463 We have to figure out which bonds are broken and which bonds are formed. 2 H-H bonds are broken. 1 O=O bond is broken 2 O-H bonds are formed per water molecule, and there are 2 water molecules formed, therefore 4 O-H bonds are formed Now we can substitute the values given into the equation: Bond-dissociation enthalpy - The energy needed to break an X-Y bond to give X and Y atoms in the gas phase, such as in the following reaction: EVALUATION