chapter six 1 hall © 2005 prentice hall © 2005 thermochemistry chapter six

Chapter Six

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Prentice Hall © 2005

Thermochemistry

Chapter Six

Chapter Six

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• Energy is the capacity to do work (to displace or move matter).

• Energy literally means “work within”; however, an object does not contain work.

• Potential energy is energy of position or composition.

• Kinetic energy is the energy of motion.Ek = ½ mv2

Energy has the units of joules (J or kg . m2/s2)

Energy

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Potential Energy and Kinetic Energy

At what point in each bounce is the potential energy of the ball at a

maximum?

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• Thermochemistry is the study of energy changes that occur during chemical reactions.

• System: the part of the universe being studied.

• Surroundings: the rest of the universe.

Thermochemistry: Basic Terms

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• Open: energy and matter can be exchanged with the surroundings.

• Closed: energy can be exchanged with the surroundings, matter cannot.

• Isolated: neither energy nor matter can be exchanged with the surroundings.

Types of Systems

A closed system; energy (not matter) can be exchanged.

After the lid of the jar is unscrewed, which kind of system is it?

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• Internal energy (U) is the total energy contained within a system

• Part of U is kinetic energy (from molecular motion)– Translational motion, rotational motion,

vibrational motion.– Collectively, these are sometimes called thermal

energy

Internal Energy (U)

• Part of U is potential energy– Intermolecular and intramolecular forces of

attraction, locations of atoms and of bonds.– Collectively these are sometimes called

chemical energy

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• Technically speaking, heat is not “energy.”

• Heat is energy transfer between a system and its surroundings, caused by a temperature difference.

More energetic molecules …

… transfer energy to less energetic molecules.

Heat (q)

How do the root-mean-square speeds of the Ar atoms and the N2 molecules compare at the point of

thermal equilibrium?

• Thermal equilibrium occurs when the system and surroundings reach the same temperature and heat transfer stops.

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• Like heat, work is an energy transfer between a system and its surroundings.

• Unlike heat, work is caused by a force moving through a distance (heat is caused by a temperature difference).

• A negative quantity of work signifies that the system loses energy.

• A positive quantity of work signifies that the system gains energy.

• There is no such thing as “negative energy” nor “positive energy”; the sign of work (or heat) signifies the direction of energy flow.

Work (w)

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For now we will consider only pressure-volume work.

work (w) = –PDV

Pressure-Volume Work

How would the magnitude of DV compare to the original gas

volume if the two weights (initial and final) were identical?

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• The state of a system: its exact condition at a fixed instant.• State is determined by the kinds and amounts of matter

present, the structure of this matter at the molecular level, and the prevailing pressure and temperature.

• A state function is a property that has a unique value that depends only the present state of a system, and does not depend on how the state was reached (does not depend on the history of the system).

• Law of Conservation of Energy – in a physical or chemical change, energy can be exchanged between a system and its surroundings, but no energy can be created or destroyed.

State Functions

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• “Energy cannot be created or destroyed.”• Inference: the internal energy change of a system

is simply the difference between its final and initial states:

DU = Ufinal – Uinitial

• Additional inference: if energy change occurs only as heat (q) and/or work (w), then:

DU = q + w

First Law of Thermodynamics

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• Energy entering a system carries a positive sign:– heat absorbed by the system, or– work done on the system

• Energy leaving a system carries a negative sign– heat given off by the system– work done by the system

First Law: Sign Convention

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Example 6.1A gas does 135 J of work while expanding, and at the same time it absorbs 156 J of heat. What is the change in internal energy?

Example 6.2: A Conceptual ExampleThe internal energy of a fixed quantity of an ideal gas depends only on its temperature. If a sample of an ideal gas is allowed to expand against a constant pressure at a constant temperature,(a) what is DU for the gas? (b) Does the gas do work? (c) Is any heat exchanged with the surroundings?

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• qrxn is the quantity of heat exchanged between a reaction system and its surroundings.

• An exothermic reaction gives off heat– In an isolated system, the temperature increases.– The system goes from higher to lower energy; qrxn is

negative.• An endothermic reaction absorbs heat

– In an isolated system, the temperature decreases.– The system goes from lower to higher energy; qrxn is

positive.

Heats of Reaction (qrxn)

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Conceptualizing an Exothermic Reaction

Surroundings are at 25 °C

Hypothetical situation: all heat is instantly released to the surroundings. Heat = qrxn

Typical situation: some heat is released to the surroundings,

some heat is absorbed by the solution.

In an isolated system, all heat is absorbed by the solution.

Maximum temperature rise.

25 °C

32.2 °C 35.4 °C

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• For a system where the reaction is carried out at constant volume, DV = 0 and DU = qV.

Internal Energy Change at Constant Volume

• All the thermal energy produced by conversion from chemical energy is released as heat; no P-V work is done.

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lnternal Energy Change at Constant Pressure

• For a system where the reaction is carried out at constant pressure, DU = qP – PDV or DU + PDV = qP

• Most of the thermal energy is released as heat.

• Some work is done to expand the system against the surroundings (push back the atmosphere).

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Enthalpy is the sum of the internal energy and the pressure-volume product of a system:

H = U + PV

Enthalpy and Enthalpy Change

Most reactions occur at constant pressure, so for most reactions, the heat

evolved equals the enthalpy change.

The evolved H2 pushes back the atmosphere;

work is done at constant pressure.

For a process carried out at constant pressure,

qP = DU + PDV so qP = DH

Mg + 2 HCl MgCl2 + H2

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• Enthalpy is an extensive property.– It depends on how much of the

substance is present.

• Since U, P, and V are all state functions, enthalpy H must be a state function also.

• Enthalpy changes have unique values. DH = qP

Properties of Enthalpy

Enthalpy change depends only on the initial and

final states. In a chemical reaction we call the initial

state the ____ and the final state the ____.

Two logs on a fire give off twice as much heat

as does one log.

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• Values of DH are measured experimentally.• Negative values indicate exothermic reactions.• Positive values indicate endothermic reactions.

Enthalpy Diagrams

A decrease in enthalpy during the reaction;

DH is negative.

An increase in enthalpy during the reaction;

DH is positive.

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• DH changes sign when a process is reversed. • Therefore, a cyclic process has the value DH = 0.

Reversing a Reaction

Same magnitude; different signs.

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Example 6.3Given the equation

(a) H2(g) + I2(s) 2 HI(g) DH = +52.96 kJ

calculate DH for the reaction

(b) HI(g) ½ H2(g) + ½ I2(s).

Example 6.4The complete combustion of liquid octane, C8H18, to produce gaseous carbon dioxide and liquid water at 25 °C and at a constant pressure gives off 47.9 kJ of heat per gram of octane. Write a chemical equation to represent this information.

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• For problem-solving, heat evolved (exothermic reaction) can be thought of as a product. Heat absorbed (endothermic reaction) can be thought of as a reactant.

• We can generate conversion factors involving DH.• For example, the reaction:

ΔH in Stoichiometric Calculations

H2(g) + Cl2(g) 2 HCl(g) DH = –184.6 kJ

can be used to write:

–184.6 kJ ———— 1 mol H2

–184.6 kJ ———— 1 mol Cl2

–184.6 kJ ———— 2 mol HCl

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Example 6.5What is the enthalpy change associated with the formation of 5.67 mol HCl(g) in this reaction?

H2(g) + Cl2(g) 2 HCl(g) DH = –184.6 kJ

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• We measure heat flow using calorimetry.• A calorimeter is a device used to make this

measurement.• A “coffee cup” calorimeter may be used for

measuring heat involving solutions.

A “bomb” calorimeter is used to find heat of combustion; the “bomb” contains oxygen and a sample of the material to be burned.

Calorimetry

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• Heat evolved in a reaction is absorbed by the calorimeter and its contents.

• In a calorimeter we measure the temperature change of water or a solution to determine the heat absorbed or evolved by a reaction.

• The heat capacity (C) of a system is the quantity of heat required to change the temperature of the system by 1 °C.

C = q/DT (units are J/°C)• Molar heat capacity is the heat capacity of one mole of a

substance.• The specific heat (s) is the heat capacity of one gram of a

pure substance (or homogeneous mixture).s = C/m = q/(mDT)

q = s m DT

Calorimetry, Heat Capacity, Specific Heat

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Heat Capacity: A Thought Experiment

• Place an empty iron pot weighing 5 lb on the burner of a stove.

• Place an iron pot weighing 1 lb and containing 4 lb water on a second identical burner (same total mass).

• Turn on both burners. Wait five minutes.• Which pot handle can you grab with your bare

hand?• Iron has a lower specific heat than does water. It

takes less heat to “warm up” iron than it does water.

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Example 6.6Calculate the heat capacity of an aluminum block that must absorb 629 J of heat from its surroundings in order for its temperature to rise from 22 °C to 145 °C.

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q = mass x specific heat x DT• If DT is positive (temperature increases), q is

positive and heat is gained by the system.• If DT is negative (temperature decreases), q is

negative and heat is lost by the system.• The calorie, while not an SI unit, is still used to

some extent.• Water has a specific heat of 1 cal/(g oC).• 4.184 J = 1 cal• One food calorie (Cal or kcal) is actually equal to

1000 cal.

More on Specific Heat

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Many metals have low specific heats.

The specific heat of water is higher than that of almost any other substance.

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Example 6.7

How much heat, in joules and in kilojoules, does it take to raise the temperature of 225 g of water from 25.0 to 100.0 °C?

Example 6.8

What will be the final temperature if a 5.00-g silver ring at 37.0 °C gives off 25.0 J of heat to its surroundings? Use the specific heat of silver listed in Table 6.1.

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Example 6.9A 15.5-g sample of a metal alloy is heated to 98.9 °C and then dropped into 25.0 g of water in a calorimeter. The temperature of the water rises from 22.5 to 25.7 °C. Calculate the specific heat of the alloy.

Example 6.10: An Estimation ExampleWithout doing detailed calculations, determine which of the following is a likely approximate final temperature when 100 g of iron at 100 °C is added to 100 g of 20 °C water in a calorimeter:

(a) 20 °C (b) 30 °C (c) 60 °C (d) 70 °C.

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For a reaction carried out in a calorimeter, the heat evolved by a reaction is absorbed by the calorimeter and its contents.

Measuring Enthalpy Changes for Chemical Reactions

qrxn = – qcalorimeter

qcalorimeter = mass x specific heat x DT

By measuring the temperature change that occurs in a calorimeter, and using the specific heat and mass of the contents, the heat evolved (or absorbed) by a reaction can be determined and the enthalpy change calculated.

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Example 6.11A 50.0-mL sample of 0.250 M HCl at 19.50 °C is added to 50.0 mL of 0.250 M NaOH, also at 19.50 °C, in a calorimeter. After mixing, the solution temperature rises to 21.21 °C. Calculate the heat of this reaction.

Example 6.12Express the result of Example 6.11 for molar amounts of the reactants and products. That is, determine the value of DH that should be written in the equation for the neutralization reaction:

HCl(aq) + NaOH(aq) NaCl(aq) + H2O(l) DH = ?

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• Some reactions, such as combustion, cannot be carried out in a coffee-cup calorimeter.

• In a bomb calorimeter, a sample of known mass is placed in a heavy-walled “bomb,” which is then pressurized with oxygen.

• Since the reaction is carried out at constant volume,

Bomb Calorimetry: Reactions at Constant

Volume

–qrxn = qcalorimeter = DU

… but in many cases the value of DU is a good approximation of DH.

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• Some reactions cannot be carried out “as written.”• Consider the reaction:

C(graphite) + ½ O2(g) CO(g).

• If we burned 1 mol C in ½ mol O2, both CO and CO2 would probably form. Some C might be left over. However …

Hess’s Law of Constant Heat Summation

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• … enthalpy change is a state function.• The enthalpy change of a reaction is the same

whether the reaction is carried out in one step or through a number of steps.

• Hess’s Law: If an equation can be expressed as the sum of two or more other equations, the enthalpy change for the desired equation is the sum of the enthalpy changes of the other equations.

Hess’s Law of Constant Heat Summation

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Hess’s Law: An Enthalpy Diagram

We can find DH(a) by subtracting DH(b) from DH(c)

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Example 6.14Calculate the enthalpy change for reaction (a) given the data in equations (b), (c), and (d).

(a) 2 C(graphite) + 2 H2(g) C2H4(g) DH = ?

(b) C(graphite) + O2(g) CO2(g) DH = –393.5 kJ

(c) C2H4(g) + 3 O2 2 CO2(g) + 2 H2O(l) DH = –1410.9 kJ

(d) H2(g) + ½ O2 H2O(l) DH = –285.8 kJ

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Standard Enthalpies of Formation

• It would be convenient to be able to use the simple relationship

ΔH = Hproducts – Hreactants

to determine enthalpy changes.• Although we don’t know absolute values of enthalpy, we don’t

need them; we can use a relative scale.

• We define the standard state of a substance as the state of the pure substance at 1 atm pressure and the temperature of interest (usually 25 °C).

• The standard enthalpy change (ΔH°) for a reaction is the enthalpy change in which reactants and products are in their standard states.

• The standard enthalpy of formation (ΔHf°) for a reaction is the enthalpy change that occurs when 1 mol of a substance is formed from its component elements in their standard states.

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When we say “The standard enthalpy of formation of CH3OH(l) is –238.7 kJ”, we are saying that the reaction:

C(graphite) + 2 H2(g) + ½ O2(g) CH3OH(l)

has a value of ΔH of –238.7 kJ.

Standard Enthalpy of Formation

We can treat ΔHf° values as though they were absolute enthalpies, to determine enthalpy changes for reactions.Question: What is ΔHf° for an element in its standard state [such as O2(g)]? Hint: since the reactants are the same as the products …

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DH°rxn = Snp x DHf°(products) – Snr x DHf°(reactants)

• The symbol S signifies the summation of several terms.• The symbol n signifies the stoichiometric coefficient

used in front of a chemical symbol or formula.• In other words …

1. Add all of the values for DHf° of the products.

2. Add all of the values for DHf° of the reactants.

3. Subtract #2 from #1

(This is usually much easier than using Hess’s Law!)

Calculations Based onStandard Enthalpies of Formation

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Example 6.15Synthesis gas is a mixture of carbon monoxide and hydrogen that is used to synthesize a variety of organic compounds. One reaction for producing synthesis gas is 3 CH4(g) + 2 H2O(l) + CO2(g) 4 CO(g) + 8 H2(g) ΔH° = ?Use standard enthalpies of formation from Table 6.2 to calculate the standard enthalpy change for this reaction.

Example 6.16The combustion of isopropyl alcohol, common rubbing alcohol, is represented by the equation 2 (CH3)2CHOH(l) + 9 O2(g) 6 CO2(g) + 8 H2O(l) ΔH° = –4011 kJUse this equation and data from Table 6.2 to establish the standard enthalpy of formation for isopropyl alcohol.

Example 6.17: A Conceptual ExampleWithout performing a calculation, determine which of these two substances should yield the greater quantity of heat per mole upon complete combustion: ethane, C2H6(g), or ethanol, CH3CH2OH(l).

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Ionic Reactions in Solution

• We can apply thermochemical concepts to reactions in ionic solution by arbitrarily assigning an enthalpy of formation of zero to H+

(aq).

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Example 6.18

H+(aq) + OH–(aq) H2O(l) ΔH° = –55.8 kJ

Use the net ionic equation just given, together with ΔHf° = 0 for H+(aq), to obtain ΔHf° for OH–

(aq).

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• A reaction that occurs (by itself) when the reactants are brought together under the appropriate conditions is said to be spontaneous.

• A discussion of entropy is needed to fully understand the concept of spontaneity, and will be discussed in Chapter 17.

• A spontaneous reaction isn’t necessarily fast (rusting; diamond graphite; etc. are slow).

• The difference between the tendency of a reaction to occur and the rate at which a reaction occurs will be discussed in Chapter 13.

Looking Ahead

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• Fossil Fuels: Coal, Natural Gas, and Petroleum– A fuel is a substance that burns with the release of

heat.– These fossil fuels were formed over a period of

millions of years from organic matter that became buried and compressed under mud and water.

• Foods: Fuels for the Body– The three principal classes of foods are

carbohydrates, fats, and proteins.– 1 Food Calorie (Cal) is equal to 1000 cal (or 1

kcal).

Combustion and Respiration:Fuels and Foods

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Lower in carbon, higher in moisture, less

effective for heating.

“Hard” coal is highest in fuel value,

most expensive.

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Glyceryl Trilaurate:

A Typical Fat

Fats are esters.

This particular fat is saturated; all the C–C

bonds are single bonds.

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CUMULATIVE EXAMPLE

The human body is about 67% water by mass. What mass of sucrose, C12H22O11(s), for which ΔHf° = –2225 kJ/mol, must be metabolized by a 55-kg person with hypothermia (low body temperature) to raise the temperature of the body water from 33.5 °C to the normal body temperature of 37.0 °C? Assume the products of metabolism are in their most stable states at 25 °C. What volume of air at 37 °C having a partial pressure of O2 of 151 Torr is required for the metabolism?

chapter six 1 hall © 2005 prentice hall © 2005 thermochemistry chapter six

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