chapter 5 thermochemistry - sogang

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Chapter 5Thermochemistry

▶ SOLAR PANELS. Each panel consists of an assembly of solar cells, also known as photovoltaic cells. Various materials have been used in solar cells, but crystalline silicon is most common.

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What’s Ahead5.1 THE NATURE OF ENERGY

We begin by considering the nature of energy and the forms it takes, notably kinetic energy and potential energy. We discuss the units used in measuring energy and the fact that energy can be used to do work or to transfer heat. To study energy changes, we focus on a particular part of the universe, which we call the system. Everything else is called the surroundings.

5.2 THE FIRST LAW OF THERMODYNAMICSWe then explore the first law of thermodynamics: Energy cannot be created or destroyed but can be transformed from one form to another or transferred between systems and surroundings. The energy possessed by a system is called its internal energy. Internal energy is a state function, a quantity whose value depends only on the current state of a system, not on how the system came to be in that state.

5.3 ENTHALPYNext, we encounter a state function called enthalpy that is useful because the change in enthalpy measures the quantity of heat energy gained or lost by a system in a process occurring under constant pressure.

5.4 ENTHALPIES OF REACTIONWe see that the enthalpy change associated with a chemical reaction is the enthalpies of the products minus the enthalpies of the reactants. This quantity is directly proportional to the amount of reactant consumed in the reaction.

Thermochemistry

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What’s Ahead5.5 CALORIMETRY

We next examine calorimetry, an experimental technique used to measure heat changes in chemical processes.

5.6 HESS’S LAWWe observe that the enthalpy change for a given reaction can be calculated using appropriate enthalpy changes for related reactions. To do so, we apply Hess’s law.

5.7 ENTHALPIES OF FORMATIONThen we discuss how to establish standard values for enthalpy changes in chemical reactions and how to use them to calculate enthalpy changes for reactions.

5.8 FOODS AND FUELSFinally, we examine foods and fuels as sources of energy and discuss some related health and social issues.

Thermochemistry

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• Our modern society depends on energy for its existence.

• Most of the energy used in our daily lives comes from chemical reactions.

• Thermodynamics: The study of energy and its transformations.– Greek: thérme-, “heat”; dy’namis, “power”.

• Thermochemistry: A portion of thermodynamics, the study of the relationships between chemical reactions and energy changes that involve heat.

ThermochemistryThermochemistry

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• Energy is the capacity to do work or transfer heat.

• Work is the energy used to cause an object with mass to move against a force.

• Heat is the energy used to cause the temperature of an object to increase.

Energy

Figure 5.1 Work and heat, two forms of energy. (a) Workis energy used to cause an object to move. (b) Heat is energyused to cause the temperature of an object to increase.

5.1 THE NATURE OF ENERGY

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• Kinetic energy (Ek) is energy an object possesses by virtue of its motion.

• Potential energy (Ep) is energy an object possesses by virtue of its position or chemical composition.– Gravitational potential energy is energy an object possesses by virtue

of its elevation.

– Electrostatic potential energy (Eel ) is one of the most important form of potential energy in chemistry.

Kinetic Energy and Potential Energy

Figure 5.2 Potential energy and kinetic energy. The potential energyinitially stored in the motionless bicycle at the top of the hill is converted to kinetic energy as the bicycle moves down the hill and loses potential energy.


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• The most important form of potential energy in molecules.

Electrostatic Potential Energy

Figure 5.3 Electrostatic potential energy. At finite separation distances for two charged particles, Eel is positive for like charges and negative for opposite charges. As the particles move farther apart, their electrostatic potential energy approaches zero.

KQ1Q2

dEel =

κ: A constant of proportionality, 8.99 × 109 J-m/C2.Q1 and Q2: Electrical charges on the two interacting objects.d: The distance separating them.


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• The SI unit for energy is the joule (J).– In honor of James Joule (1818–1889), a British scientist who

investigated work and heat.1 J = 1 kg-m2/s2

– A mass of 2 kg moving at a speed of 1 m/s possesses a kinetic energy of 1 J: Ek = ½mv2 = ½(2 kg)(1 m/s)2 = 1 kg-m2/s2 = 1 J.

• A traditional non-SI unit, calorie (cal), is still in widespread use.

1 cal = 4.184 J (exactly)– A calorie was originally defined as the amount of energy required

to raise the temperature of 1 g of water from 14.5 ˚C to 15.5 ˚C.– This is not the same as the Calorie of foods (note the capital C);

1 Cal = 1000 cal = 1 kcal.

Units of Energy5.1 THE NATURE OF ENERGY

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• System: The portion we single out for study; Surroundings: Everything else.– In a chemical reaction, the

reactants and products constitute the system (here, the hydrogenand oxygen molecules).

– The container and everything beyond it are considered the surroundings (here, the cylinder, piston, and everything beyond).

System and Surroundings

Figure 5.4 A closed system.


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• Systems may be open, closed, or isolated.– Open system: Matter and energy can be exchanged with the

surroundings.• Ex) An uncovered pot of boiling water on a stove (Figure 5.1(b)).

– Closed system: The systems can exchange energy but not matter with their surroundings.• The systems we can most readily study in thermochemistry.• Ex) A cylinder fitted with a piston (Figure 5.4).

– Isolated system: Neither energy nor matter can be exchangedwith the surroundings.• Ex) A completely insulated thermos containing hot coffee.

System and Surroundings5.1 THE NATURE OF ENERGY

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• Work, w, is defined as the energy transferred when a force moves an object.– The magnitude of this work equals

the product of the force, F, andthe distance, d, the object moves:w = F × d.

• Energy can also be transferredas heat, q.– Heat flows from warmer objects to

cooler objects.

Transferring Energy: Work and Heat

Figure 5.1 Work and heat, two forms of energy. (a) Workis energy used to cause an object to move. (b) Heat is energyused to cause the temperature of an object to increase.


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Figure 5.2 Potential energy and kinetic energy. The potential energyinitially stored in the motionless bicycle at the top of the hill is converted to kinetic energy as the bicycle moves down the hill and loses potential energy.

• Energy can be converted from one type to another.

• Ex) The cyclist in Figure 5.2.– She has potential energy as she sits on top of the hill.– As she coasts down the hill, her potential energy is converted

to kinetic energy.– At the bottom, all the potential energy she had at the top of the

hill is now kinetic energy.

Conversion of Energy5.1 THE NATURE OF ENERGY

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• The first law of thermodynamics: Energy is conserved.

• Energy is neither created nor destroyed.

• In other words, the total energy of the universe is constant; if the system loses energy, it must be gained by the surroundings, and vice versa.

First Law of Thermodynamics5.2 THE FIRST LAW OF THERMODYNAMICS

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• The internal energy of a system is the sum of all kinetic and potential energies of all components of the system; we call it E.

Internal Energy

E = Ek + Ep

5.2 THE FIRST LAW OF THERMODYNAMICS

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• By definition, the change in internal energy, ∆E, is the final energy of the system minus the initial energy of the system:

∆E = Efinal − Einitial

Internal Energy5.2 THE FIRST LAW OF THERMODYNAMICS

Figure 5.5 Changes in internal energy.

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• If ∆E > 0, Efinal > Einitial.– Therefore, the system absorbed energy from the surroundings.

• If ∆E < 0, Efinal < Einitial.– Therefore, the system released energy to the surroundings.

Internal Energy

Figure 5.5 Changes in internal energy.


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• In a chemical reaction, the initial state of the system refers to the reactants and the final state refers to the products.

– The initial state is the 2 H2(g) + O2(g) and the final state is the 2 H2O(l).

• When hydrogen and oxygen form water at a given temperature, the system loses energy to the surroundings.– The internal energy of the products

(final state) is less than that of the reactants (initial state).

– ∆E for the process is negative.

Internal Energy

Figure 5.6 Energy diagram for the reaction 2 H2(g) + O2(g) 2 H2O(l).


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• When energy is exchanged between the system and the surroundings, it is exchanged as either heat (q) or work (w).

• That is, ∆E = q + w.

Relating ∆E to Heat and Work

Figure 5.7 Sign conventions for heat and work. Heat, q, gained by a system and work, w, done on a systemare both positive quantities, corresponding to “deposits” of internal energy into the system. Conversely, heattransferred from the system to the surroundings and work done by the system on the surroundings are both “withdrawals” of internal energy from the system.


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• When heat is absorbed by the system from the surroundings, the process is endothermic.

Endothermic and Exothermic Processes

Figure 5.8 Endothermic and exothermic reactions. (a) When ammonium thiocyanate and barium hydroxide octahydrate are mixedat room temperature, the temperature drops. (b) The reaction of powdered aluminum with Fe2O3 (the thermite reaction) proceeds vigorously, releasing heat and forming Al2O3and molten iron.


• When heat is releasedby the system into the surroundings, the process is exothermic.

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• Usually we have no way of knowing the internal energy of a system; finding that value is simply too complex a problem.

• However, we do know that the internal energy of a system is independent of the path by which the system achieved that state.– In the system depicted in Figure 5.9, the water could have reached

room temperature from either direction.

State Functions

Figure 5.9 Internal energy, E, a state function. Any state function depends only on the present state of the system and not on the path by which the system arrived at that state.


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• Therefore, internal energy is a state function.• The value of a state function (internal energy, E, in this

case) depends only on the present state of the system, not on the path the system took to reach that state.

• And so, ∆E depends only on Einitial and Efinal.

State Functions

Figure 5.9 Internal energy, E, a state function. Any state function depends only on the present state of the system and not on the path by which the system arrived at that state.


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• However, q and w are not state functions.

• Whether the battery is shorted out or is discharged by running the fan, its ∆E is the same.– But q and w are different in the

two cases.

State Functions

Figure 5.10 Internal energy is a state function, but heat and work are not. (a) A battery shorted out by a wire loses energy to the surroundings only as heat; no work is performed. (b) A battery discharged through a motor loses energy as work (to make the fan turn) and also loses some energy as heat. The value of ∆Eis the same for both processes even though the values of q and w in (a) are different from those in (b).


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• Usually in an open container the only work done is by a gas pushing on the surroundings (or by the surroundings pushing on the gas).

• We can measure the work done by the gas if the reaction is done in a vessel that has been fitted with a piston:

w = −P∆V

Work

Figure 5.11 A system that does work on its surroundings.

5.3 ENTHALPY

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• Enthalpy is a measure of the total energy of a system.

• If a process takes place at constant pressure (as the majority of processes we study do) and the only work done is this pressure–volume work, we can account for heat flow during the process by measuring the enthalpy of the system.

• Enthalpy is defined as the internal energy plus the product of pressure and volume:

H = E + PV (state function)

Enthalpy5.3 ENTHALPY

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• When the system changes at constant pressure, the change in enthalpy, ∆H, is

∆H = ∆(E + PV)• This can be written

∆H = ∆E + P∆V + V∆P = ∆E + P∆V• Since ∆E = q + w and w = −P∆V, we can substitute these

into the enthalpy expression:∆H = ∆E + P∆V∆H = (q + w) − w∆H = qP

• So, at constant pressure, the change in enthalpy is the heat gained or lost.

Enthalpy5.3 ENTHALPY

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• A process is endothermicwhen ∆H is positive.

• A process is exothermicwhen ∆H is negative.

Endothermicity and Exothermicity

Figure 5.12 Endothermic and exothermic processes. (a) An endothermic process (∆H > 0) deposits heat into the system. (b) An exothermic process (∆H < 0) withdraws heat from the system.

5.3 ENTHALPY

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ENERGY, ENTHALPY, AND P-V WORK• Let’s consider a gas confined to a cylinder with a movable piston of

cross-sectional area A (Figure 5.13).– A downward force F acts on the piston.– The pressure, P, on the gas is the force per area: P = F/A.– Suppose the gas expands and the piston moves a distance.

Figure 5.13 Pressure-volume work. The amount of work done by the system on the surroundings is w = −P∆V.

– The magnitude of the work done by the system is

– Because the system (the confined gas) does work on the surroundings, the work is a negative quantity:

– Now, if P-V work is the only work that can be done,

5.3 ENTHALPY

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ENERGY, ENTHALPY, AND P-V WORK

– When a reaction is carried out in a constant-volume container (∆V = 0), therefore, the heat transferred equals the change in internal energy:

– Most reactions are run under constant pressure, so that

– The right side of the above equation is the enthalpy change under constant-pressure conditions. Thus,

– At constant V, the change in E is equal to the heat gained or lost.– At constant P, the change in H is equal to the heat gained or lost.– The difference between ∆E and ∆H is the amount of P-V work done by the

system when the process occurs at constant P, −P∆V.– In many reactions, ∆V is close to zero, which makes P∆V (the difference between

∆E and ∆H) small.– Generally, ∆H can be used to measure energy changes during most chemical

processes.

5.3 ENTHALPY

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• The change in enthalpy, ∆H, is the enthalpy of the products minus the enthalpy of the reactants:

∆H = Hproducts − Hreactants

• This quantity, ∆H, is called the enthalpy of reaction, or the heat of reaction.

Enthalpy of Reaction5.4 ENTHALPIES OF REACTION

• Thermochemical equations are balanced chemical equations that show the associated enthalpy change.

• The exothermic nature of this reaction is also shown in the enthalpy diagram (next page).

Enthalpy diagram

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Enthalpy of Reaction

Figure 5.14 Exothermic reaction of hydrogen with oxygen. When a mixture of H2(g) and O2(g) is ignited to form H2O(g), the resultant explosion produces a ball of flame. Because the system releases heat to the surroundings, the reaction is exothermic as indicated in the enthalpy diagram.

5.4 ENTHALPIES OF REACTION

Enthalpy diagram

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• Enthalpy is an extensive property.– The magnitude of ∆H is proportional to

the amount of reactant consumed in the process.

– Ex) 890 kJ of heat is produced when 1 mol of CH4 is burned in a constant-pressure system:

• ∆H for a reaction in the forward direction is equal in size, but opposite in sign, to ∆H for the reverse reaction.– Ex) ∆H for the reverse of the above

equation is +890 kJ:

The Truth about Enthalpy

Figure 5.15 ∆H for a reverse reaction. Reversing a reaction changes the sign but not the magnitude of the enthalpy change: ∆H2 = –∆H1.

5.4 ENTHALPIES OF REACTION

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• ∆H for a reaction depends on the states of the reactants and products.

– If the product in the above equation were H2O(g) instead of H2O(l), ∆Hrxn would be −802 kJ instead of −890 kJ because the enthalpy of H2O(g) is greater than that of H2O(l). The conversion of 2 mol H2O(l) to 2 mol H2O(g) is an endothermic process that absorbs 88 kJ:

– Thus, it is important to specify the states of the reactants and products in thermochemical equations.

– The reactants and products are both at the same temperature, 25 ˚C, unless otherwise indicated.

The Truth about Enthalpy5.4 ENTHALPIES OF REACTION

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• Since we cannot know the exact enthalpies of the reactants and products, we measure ∆H,through calorimetry, the measurement of heat flow.

• The instrument used to measure heat flow is called a calorimeter.

• We can determine the magnitude of the heat flow by measuring the magnitude of the temperature change the heat flow produces.

Calorimetry5.5 CALORIMETRY

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• Heat capacity (C): The amount of heat required to raise the temperature of a substance by 1 K (1 ˚C).

• Molar heat capacity (Cm): The heat capacity of one mole of a substance.

• Specific heat capacity or simply Specific heat (Cs): The heat capacity of one gram of a substance.

Heat Capacity and Specific Heat5.5 CALORIMETRY

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– Ex) 209 J is required to increase the temperature of 50.0 g of water by 1.00 K. What is the specific heat of water?

– We can calculate the quantity of heat a substance gains or loses by using the rearranged equation:

Heat Capacity and Specific Heat

Figure 5.16 Specific heat of water.

5.5 CALORIMETRY

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• By carrying out a reaction in an aqueous solution in a simple “coffee-cup” calorimeter, the heat change for the system can be indirectly measured by measuring the temperature changefor the water in the calorimeter.

– System: Reactants and products.– Surrounding: Water and calorimeter.

Constant Pressure Calorimetry

Figure 5.17 Coffee-cup calorimeter. This simple apparatus is used to measure temperature changes of reactions at constant pressure.

• Because the specific heat for water is well known (4.184 J/g-K), we can measure ∆H (qP) for the reaction with this equation: q = Cs × m × ∆T.

• The heat gained or lost by the solution, qsoln, is therefore equal in magnitude but opposite in sign to the heat absorbed or released by the reaction, qrxn: qsoln = –qrxn.

5.5 CALORIMETRY

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• Combustion reactions are most accurately studied using a bomb calorimeter.– Reactions are carried out in a sealed reaction chamber called a “bomb”.

Bomb Calorimetry (Constant-Volume Calorimetry)

Figure 5.18 Bomb calorimeter.

– The bomb is designed to withstand high pressures.

– The bomb has an inlet valve for adding oxygen and electrical leads for initiating the reaction.

– After the sample has been placed in the bomb, the bomb is sealed and pressurized with oxygen. It is then placed in the calorimeter.

– When the wire becomes sufficiently hot, the sample ignites.

– Surroundings: The water and the various components of the calorimeter.

5.5 CALORIMETRY

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• The heat absorbed (or released) by the water is a very goodapproximation of the enthalpy change (∆H) for the reaction.– Because the volume in the bomb calorimeter is constant, what is

measured is really the change in internal energy, ∆E, not ∆H.– For most reactions, the difference is very small.

• The total heat capacity of the calorimeter is measured by combusting a standard sample.– Ex) Combustion of exactly 1 g of benzoic acid (C6H5COOH) produces

26.38 kJ of heat. Suppose 1.000 g of benzoic acid is combusted in a calorimeter, leading to a temperature increase of 4.857 ˚C. The heat capacity of the calorimeter is then Ccal = 26.38 kJ/4.857 ˚C = 5.431 kJ/˚C.

• We can measure temperature changes produced by other reactions, and from these we can calculate the heat evolved in the reaction (qrxn): qrxn = –Ccal × ∆T.

Bomb Calorimetry (Constant-Volume Calorimetry)5.5 CALORIMETRY

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THE REGULATION OF BODY TEMPERATURE

Figure 5.19 Perspiration.

• Optimal body temperature for muscle function and biochemical reactions in our body generally ranges from 35.8 ˚C to 37.2 ˚C (very narrow range).

– “Are you running a fever?”: A deviation in body temperature of only a few degrees indicates something amiss.

– It is difficult to maintain a solution at a constant temperature. Yet, our bodies maintain a near-constant temperature.

• Hypothalamus (the portion of the human brain stem) regulates body temperature.

– It triggers mechanisms to increase the temperature if body temperature drops too low.– When the body produces too much heat, it dissipates the excess heat.

• We can view the body as a thermodynamic system.– The body increases its internal energy content by ingesting foods from the surroundings.

The foods, such as glucose (C6H12O6), are metabolized—a process that is essentially controlled oxidation to CO2 and H2O:

– Heat is transferred from the body to its surroundings primarily by radiation, convection, and evaporation. Evaporative cooling occurs when perspiration is generated. Perspiration is predominantly water (high heat capacity), so the process is the endothermic conversion of liquid water into water vapor:

5.5 CALORIMETRY

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• Consider the combustion of CH4(g) to form CO2(g) and H2O(l):– It can be thought of as occurring in one step (on

the left in Figure 5.20).

– It can be thought of as occurring in two step (on the right in Figure 5.20).

The net equation is

– The enthalpy change for the overall process is the sum of the enthalpy changes for these two steps.

Hess’s Law

Figure 5.20Enthalpy diagram for combustion of 1 mol of methane. The enthalpy change of the one-step reaction equals the sum of the enthalpy changes of the reaction run in two steps: –890 kJ = –802 kJ + (–88 kJ).

5.6 HESS’S LAW

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• Hess’s law: If a reaction is carried out in a series of steps, ∆H for the overall reaction will be equal to the sum of the enthalpy changes for the individual steps.

• Because ∆H is a state function, the total enthalpy changedepends only on the initial state(reactants) and the final state (products) of the reaction.

Hess’s Law

Figure 5.20 Enthalpy diagram for combustion of 1 mol of methane. The enthalpy change of the one-step reaction equals the sum of the enthalpy changes of the reaction run in two steps: –890 kJ = –802 kJ + (–88 kJ).

5.6 HESS’S LAW

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• Hess’s law provides a useful means of calculating energy changes that are difficult to measure directly.– Ex) A different two-step path of

CH4 combustion, with the initial formation of CO (A reaction that is hard to carry out in the laboratory, Figure 5.21).

• We can estimate ∆H using published ∆H values and the properties of enthalpy.

Hess’s Law

Figure 5.21 Enthalpy diagram illustrating Hess’s law. The net reaction is the same as in Figure 5.21, but here we imagine different reactions in our two-step version. As long as we can write a series of equations that add up to the equation we need, and as long as we know a value for ∆H for all intermediate reactions, we can calculate the overall ∆H.

5.6 HESS’S LAW

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• An enthalpy of formation, ∆Hf, is defined as the enthalpy change for the reaction in which a compound is made from its constituent elements in their elemental forms.– The temperature, pressure, and state (gas, liquid, or solid

crystalline form) of the reactants and products should be defined.

• The standard enthalpy of formation of a compound, ∆Hf˚, is the change in enthalpy for the reaction that forms one mole of the compound from its elements with all substances in their standard states.If: elements (in standard state) compound (1 mol in standard state)Then: ∆H = ∆Hf˚

Enthalpies of Formation5.7 ENTHALPIES OF FORMATION

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• The standard enthalpy change (∆H˚) of a reaction is defined as the enthalpy change when all reactants and products are in their standard states.– The standard state of a substance is its pure form at atmospheric

pressure (1 atm)* and the temperature of interest (usually 298 K(25 ˚C)).

*The definition of the standard state for gases has been changed to 1 bar (1 atm = 1.013 bar), a slightly lower pressure than 1 atm. For most purposes, this change makes very little difference in the standard enthalpy changes.

– The superscript (˚) indicates standard-state conditions.

Standard Enthalpy Change5.7 ENTHALPIES OF FORMATION

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• Values at 298 K (25 ˚C) are usually reported.• If an element exists in more than one form under standard

conditions, the most stable form of the element is usually used for the formation reaction.– Ex) The standard enthalpy of formation (∆Hf) for ethanol (C2H5OH).

• The most stable forms: O2(g) (not O or O3), graphite (not diamond), H2(g).– The ∆Hf of the most stable form of any element is zero.

Standard Enthalpies of Formation5.7 ENTHALPIES OF FORMATION

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• Imagine this as occurring in three steps:

Calculation of ∆H5.7 ENTHALPIES OF FORMATION

Figure 5.22 Enthalpy diagram for propane combustion.

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• The sum of these equations is

• We can use Hess’s law in this way:

– The symbol Σ (sigma) means “the sum of”.– n and m are the stoichiometric coefficients of the relevant chemical

equation.

Calculation of ∆H5.7 ENTHALPIES OF FORMATION

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Calculation of ∆H using Values from the Standard Enthalpy Table

5.7 ENTHALPIES OF FORMATION

Figure 5.22 Enthalpy diagram for propane combustion.

∆H = [3(−393.5 kJ) + 4(−285.8 kJ)] – [1(−103.85 kJ) + 5(0 kJ)]= [(−1180.5 kJ) + (−1143.2 kJ)] – [(−103.85 kJ) + (0 kJ)]= (−2323.7 kJ) – (−103.85 kJ) = −2219.9 kJ

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• Fuel value: The energy released when 1 g of a substance is combusted.– The fuel value of carbohydrates: 17 kJ/g (4 kcal/g).

– The fuel value of fats: 38 kJ/g (9 kcal/g).

– The fuel value of proteins: 17 kJ/g (4 kcal/g).– Most of the fuel in the food we eat comes from carbohydrates and fats.

Foods5.8 FOODS AND FUELS

Figure 5.23 Nutrition label for whole milk.

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• Fossil fuels: The world’s major sources of energy.– Natural gas: It consists of gaseous hydrocarbons (primarily CH4).– Petroleum: Liquid composed of hundreds of compounds, mostly

hydrocarbons and some organic compounds containing S, N, or O.– Coal: Solid containing hydrocarbons of high molecular weight as

well as compounds containing S, N, or O.• When coal is combusted, the sulfur is converted mainly to sulfur dioxide,

SO2, a troublesome air pollutant.

Fuels5.8 FOODS AND FUELS

Figure 5.24 Energy consumption in the United States. In 2011 the United States consumed a total of 1.03 × 1017 kJ of energy.

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• Nonrenewable energy sources.– Fossil fuels and nuclear energy.– They are limited resources that we are consuming at a

much greater rate than they can be regenerated.

• Renewable energy sources.– Because nonrenewable energy sources will eventually be

used up, a great deal of research is being conducted on renewable energy sources.

– They include solar energy from the Sun, wind energyharnessed by windmills, geothermal energy from the heat stored inside Earth, hydroelectric energy from flowing rivers, and biomass energy from crops and biological waste matter.

– Currently, they provide about 7.4% of the U.S. annual energy consumption, with hydroelectric and biomass sources the major contributors.

Other Energy Sources5.8 FOODS AND FUELS

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Chapter 5. HomeworkExercises 5.6

5.205.235.265.435.485.515.595.615.665.685.735.1035.108

chapter 5 thermochemistry - sogang

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