thermodynamic processes and thermochemistry · 2017. 1. 7. · therefore, internal energy is a...

Thermodynamic Processes and

Thermochemistry

박준원 교수(포항공과대학교 화학과)

General Chemistry

• Systems, states, and processes

• The first law of thermodynamics: internal energy, work, and

heat

• Heat capacity, calorimetry, and enthalpy

• The first law and ideal gas processes

• Thermochemistry

이번 시간에는!


Thermochemistry (I-1)


General Chemistry

Thermodynamics is a broad and general subject with

applications in all branches of the physical and biological

sciences and engineering; thus we limit our discussion to

those aspects necessary for 𝐜𝐡𝐞𝐦𝐢𝐜𝐚𝐥 𝐞𝐪𝐮𝐢𝐥𝐢𝐛𝐫𝐢𝐮𝐦.

For example, with thermodynamics we can answer the following types of chemical questions:

Thermodynamics can determine whether a process is possible, but it cannot say how rapidly the process will occur.

1. If hydrogen and nitrogen are mixed, is it possible for them to react? If so, what will be the percentage yield of ammonia?

2. How will a particular change in temperature or pressure affect the extent of the reaction?

3. How can the conditions for the reaction be optimized to maximize its yield?

Systems, states, and processes

System: a part of universe of immediate interest in a particular experiment or study.

Closed system: the boundaries prevent the flow of matter into or out of it.

Open system: the boundaries permit such flow.

1

Isolated system: exchanges neither matter nor energy with the rest of the universe.

• Rigid walls prevent the system from gaining energy by mechanical processes such as compression.

• Adiabatic walls prevent the system from gaining or losing thermal energy.

• Diathermal walls permit thermal energy transfer.

Surroundings: the portion of the remainder of the universe that can exchange energy and matter with the system.

Thermodynamic universe: the system + the surroundings

An extensive property of the system can be written as the sum of the corresponding property in the two subsystems. Ex) volume, mass, energy

An intensive property of the system is the same as the corresponding property of each of the subsystem. Ex) temperature, pressure

A thermodynamic state is a macroscopic condition of a system in which the properties of the system are held at selected fixed values independent of time.

A thermodynamic process changes the thermodynamic state of a system. A process may be 𝑝ℎ𝑦𝑠𝑖𝑐𝑎𝑙, such as changing the pressure of a gaseous system or boiling a liquid. A 𝑐ℎ𝑒𝑚𝑖𝑐𝑎𝑙 process involves a chemical reaction.

Suppose a gas is confined by a piston in a cylinder with volume

𝑉1 (thermodynamic state A in Fig 12.2). If the piston is abruptly

pulled out to increase the volume to 𝑉2 (thermodynamic state B),

chaotic gas currents arises (Fig 12.2 b), and the intermediate

stage is not thermodynamic state because the properties are not

independent of time.

[ F I G U R E 1 2 . 2 ]

Oxtoby, D. W.; Gillis, H. P.; Campion, A., Principles of modern chemistry, 7th ed.; Cengage Learning: Boston, 2012; p 523.

In contrast, a reversible process proceeds through a continuous

series of thermodynamic states. The term reversible is used

because an infinitesimal change in external conditions suffices to

reverse the direction of motion of the system. Such a process is

an idealization. If a real process is conducted slowly enough and

in sufficiently small steps, the real (irreversible) process can be

𝑎𝑝𝑝𝑟𝑜𝑥𝑖𝑚𝑎𝑡𝑒𝑑 by an idealized reversible process.

Certain properties of a system, called state functions, are

uniquely determined by the thermodynamic state of the system.

Ex) volume, temperature, pressure, and the internal energy 𝑈

The change in any state function between two states is

independent of path.

The change of altitude, latitude, and longitude by going from

Chicago to Denver is independent of path, and other properties

such as the total distance traveled are dependent of path.


[ F I G U R E 1 2 . 3 ]


Thermochemistry (I-2)


General Chemistry

The first law of thermodynamics: internal energy, work, and heat

<Work>

The mechanical definition of work is the product of the external

force on a body times the distance through which the force acts.

𝑤 = 𝐹 𝑟f − 𝑟i (force along direction of path)

2

𝑤 = 𝐹 𝑟f − 𝑟i = 𝑀𝑎 𝑟f − 𝑟i 𝑤 = 𝑀𝑣f − 𝑣i

𝑡

𝑣i+𝑣f

2𝑡

𝑟f − 𝑟i = 𝑣i+𝑣f

2𝑡 =

𝑀

2(𝑣f − 𝑣i)(𝑣f + 𝑣i)

𝑎 = (𝑣f − 𝑣i)/𝑡 =𝑀

2𝑣f2 −

𝑀

2𝑣i2

= ∆𝐸kin

1) Consider a block of mass, 𝑀, moving with initial velocity 𝑣i along a frictionless surface. If a constant force, 𝐹, is exerted on it in the direction of its motion, it will experience a constant acceleration, 𝑎. After a time, 𝑡, the velocity of the block will have increased from 𝑣i to 𝑣f. The work done on the block is

The work done in the moving block from 𝑟i to 𝑟f is equal to the change in energy of the block.

2) Consider the work done in lifting an object in a gravitational

field. To raise a mass, 𝑀, from an initial height, ℎi, to a final

height, ℎf, an upward force sufficient to counteract the

downward force of gravity, 𝑀g, must be exerted. The work

done on the object is

The mechanical work done in moving a body is equal to the

change in potential energy.

𝑤 = 𝑀g ℎf − ℎi = 𝑀g∆ℎ = ∆𝐸pot

3) Imagine that a gas has pressure 𝑃i and is confined in a cylinder

by a frictionless piston of cross-sectional area 𝐴 and negligible

mass (Fig 12.4). The piston is exerted by an external pressure

𝑃ext, and the pressure is less than the initial pressure exerted

by the gas inside of the cylinder, then the gas will expand and

lift the piston from ℎi to ℎf.


[ F I G U R E 1 2 . 4 ]

The work is

For an expansion, ∆𝑉 > 0, thus 𝑤 < 0 and the system does work.

For a compression, the work is done on the system. If 𝑃ext = 0, no

pressure-volume work can be performed even for the expansion

(called 𝑓𝑟𝑒𝑒 𝑒𝑥𝑝𝑎𝑛𝑠𝑖𝑜𝑛).

𝑤 = −𝑃ext∆𝑉 [12.1]

𝑤 = −𝐹ext(ℎf − ℎi)

𝑤 = −𝑃ext𝐴∆ℎ

so the work is

International System of Units (SI) unit for pressure is pascals, the

unit for volume is cubic meters, and the unit for their product is

joules (J). For many purposes, it is more convenient to express

pressures in atmospheres and volumes in liters.

1 L atm = 10−3m3 1.01325 × 105 kg m−1s−2 = 101.325 J

<Internal energy>

The internal energy is defined as the total energy content of a

system arising from the potential energy between molecules,

from the kinetic energy of molecular motions, and chemical

energy stored in chemical bonds.

𝑃 − 𝑉 work is a means of changing the internal energy of a

macroscopic system through purely mechanical interaction

between the system and its surroundings.

<Heat>

A means of increasing the internal energy of a system without mechanical interaction.

The amount of energy transferred between two objects initially at different temperatures is called heat, or thermal energy.

The specific heat capacity of a material is the amount of heat required to increase the temperature of a 1-g mass by 1℃.

𝑞 = 𝑀𝑐s∆𝑇 [12.2]

One calorie was defined as the amount of heat required to increase the temperature of 1 g water from 14.5℃ to 15.5℃, and the calorie is now defined as

1 cal = 4.184 J (exactly)

<The first law of thermodynamics>

In many processes, both heat and work cross the boundary of a system, and

the change in the internal energy, 𝑈, is the sum of the two contributions. This

statement, called the first law of thermodynamics, takes the mathematical

form

Because 𝑞 and 𝑤 depend on the particular process (or path) connecting states,

they are not state functions. But their sum (∆𝑈) is independent of path;

therefore, internal energy is a function of state.

The laws of thermodynamics cannot be derived or proved; they are

generalizations of the results of countless experiments on a tremendous

variety of substances.

∆𝑈 = 𝑞 + 𝑤 [12.3]

In any process, the heat added to the system is removed from the surroundings: thus

In the same way,

Adding these two gives

The total energy change of the thermodynamic universe remains unchanged (conservation of the total energy).

𝑞sys = −𝑞surr

𝑤sys = −𝑤surr

∆𝑈sys = −∆𝑈surr

∆𝑈univ = ∆𝑈sys + ∆𝑈surr = 0 [12.4]


Thermochemistry (II-1)


General Chemistry

<Heat capacity and specific heat capacity>

Heat capacity, 𝑪, is defined as the amount of energy that must

be added to the system to increase its temperature by 1 K and

has units of J K−1.

Heat capacity, calorimetry, and enthalpy

𝑞 = 𝐶∆𝑇

3

The molar heat capacity 𝐶v is the amount of heat required to increase the temperature of 1 mol of substance by 1 K at constant volume, the molar heat capacity 𝑐p is that at constant pressure. If

the total heat transferred to n moles at constant volume is 𝑞V, then

If an amount 𝑞P is transferred at constant pressure, then

The specific heat capacity at constant 𝑉 or constant 𝑃 is the system heat capacity reported per gram of substance.

𝑞V = 𝑛𝑐V 𝑇2 − 𝑇1 = 𝑛𝑐V∆𝑇 [12.5]

𝑞P = 𝑛𝑐P ∆𝑇 [12.6]

<Heat transfer at constant volume: Bomb calorimeters>

Suppose some reacting species are sealed in a small closed

container (called a bomb). Because the container is sealed tightly,

its volume is constant and no 𝑃 − 𝑉 work is done. Therefore, the

change in internal energy is

∆𝑈 = 𝑞V

[ F I G U R E 1 2 . 9 ]


<Heat transfer at constant pressure: Enthalpy>

Most chemical reactions are carried out under constant pressure

rather than at constant volume.

Therefore, the change in internal energy is

If 𝑃ext = 𝑃internal

∆𝑈 = 𝑞P + 𝑤 = 𝑞P − 𝑃ext∆𝑉

∆𝑈 = 𝑞P − 𝑃∆𝑉

𝑞P = ∆𝑈 + 𝑃∆𝑉

Because 𝑃 is constant,

The above equation becomes

The combination 𝑈 + 𝑃𝑉 is now defined as the enthalpy 𝐻:

Because 𝑈, 𝑃, and 𝑉 are state functions, 𝐻 must be also a state function.

𝑃∆𝑉 = ∆(𝑃𝑉)

𝑞P = ∆ 𝑈 + 𝑃𝑉

𝐻 = 𝑈 + 𝑃𝑉 [12.7a]

𝑞P = ∆ 𝑈 + 𝑃𝑉 = ∆𝐻 [12.7b]

The first law and ideal gas processes

<Heat capacities of ideal gases>

The pair of molar heat capacities of 𝑐V and 𝑐P for an ideal monoatomic gas can be calculated from the results of the kinetic theory of gases and the ideal gas equation of state.

To find the value of 𝑐P,

∆𝑈 = 𝑞V = 𝑛𝑐V∆𝑇 (ideal gas)

𝑐V = 3

2𝑅 (monatomic ideal gas) [12.8]

∆𝑈 = 𝑞P + 𝑤

𝑛𝑐V∆𝑇 = 𝑛𝑐P∆𝑇 − 𝑃∆𝑉

4

For ideal gases,

For an ideal gas processes,

𝑃𝑉1 = 𝑛𝑅𝑇1 and 𝑃𝑉2 = 𝑛𝑅𝑇2; thus

𝑛𝑐V∆𝑇 = 𝑛𝑐P∆𝑇 − 𝑛𝑅∆𝑇

𝑐V = 𝑐P − 𝑅, 𝑐P = 𝑐V + 𝑅

𝑐P = 𝑐V + 𝑅 (any ideal gas) [12.9]

∆𝐻 = ∆𝑈 + ∆ 𝑃𝑉 = 𝑛𝑐V∆𝑇 + 𝑛𝑅∆𝑇

∆𝐻 = 𝑛𝑐P∆𝑇 (any ideal gas) [12.11]


Thermochemistry (II-2)


General Chemistry

Thermochemistry

The study of heat transfers during chemical reactions is referred

to as thermochemistry. Because chemical reactions are usually

studied at constant pressure, the heat transferred in each reaction

(𝑞P) equals with the enthalpy change (∆𝐻reaction).

<Enthalpies of Reaction>

When heat is given off by a reaction (∆𝐻 is negative), the reaction

is said to be exothermic. Reactions in which heat is taken up (∆𝐻

is positive) are called endothermic.

5

Hess’s law: If two or more chemical equations are added to give

another chemical equation, the corresponding enthalpies of

reaction must be added. The law is useful to find ∆𝐻 even if the

reaction of interest is difficult to study directly. For example,

C 𝑠, gr + 1

2O2 g → CO g ∆𝐻 = ?

Given that

Adding equations (1) and (2) gives the equation in question.

Therefore,

The corresponding internal energy change ∆𝑈 is,

C 𝑠, gr + O2 g → CO2 g ∆𝐻1 = −393.5 kJ (1)

CO2 g → CO g + 1

2O2 g ∆𝐻2 = +283.0 kJ (2)

∆𝐻 = ∆𝐻1 + ∆𝐻2 = −110.5 kJ

∆𝑈 = ∆𝐻 − ∆ 𝑃𝑉 , ∆ 𝑃𝑉 = ∆ 𝑛𝑅𝑇 = 𝑅𝑇∆𝑛g = 1

2 mol

∆𝑈 = −110.5 kJ − 1.24 kJ = −111.7 kJ

∆ 𝑃𝑉 = ∆ 𝑛𝑅𝑇 = 𝑅𝑇∆𝑛g = 1

2 mol

<Standard-state enthalpies>

Absolute values of the enthalpy of a substance cannot be measured or calculated. Only 𝑐ℎ𝑎𝑛𝑔𝑒 in enthalpy can be measured. Just as altitudes are measured relative to a standard altitude (sea level), it is necessary to adopt a reference state for the enthalpies. Chemists define standard states as follows: For solids and liquids, the standard state is the thermodynamically stable state at a pressure of 1 atm and at a specified temperature. For gases, the standard sate is the gaseous phase at a pressure of 1 atm, at a specified temperature and exhibiting ideal gas behavior. For dissolved species, the standard state is a 1-M solution at a pressure of 1 atm, at a specified temperature and exhibiting ideal solution behavior. (Most common “specified temperature” is 298.15 K.)

Once standard states have been defined, the zero of the enthalpy scale is defined by arbitrarily stetting the enthalpies of selected reference substances to zero in their standard states. Chemists agreed to the following: The chemical elements in their standard state at 298.15 𝐾 have zero enthalpy. Chemists have agreed to assign zero enthalpy to the form that is most stable at 1 atm and 298.15 K (for examples, O2(g) rather than O3(g) and graphite rather than diamond and fullerenes).

The standard enthalpy change (∆𝑯°): The enthalpy change for a chemical reaction in which all reactants and products are in their standard states and at 298.15 𝐊.

The standard enthalpy of formation (∆𝐻f°) of a compound: the enthalpy change for the

reaction that produces 1 mol of the compound from its element in their stable states, all at 25℃ and 1 atm pressure.

For example, ∆𝐻f° of liquid water is

Chemists have agreed that ∆𝐻f° of H+ 𝑎𝑞 is set to zero to establish a

reference point for the enthalpies of formation of cations and anions.

For a general reaction of the form

The standard enthalpy change is

H2 g + 1

2 O2 → H2O(l) ∆𝐻° = −285.83 kJ

∆𝐻f° H2O l = −285.83 kJ mol−1

𝑎A + 𝑏B → 𝑐C + 𝑑D

∆𝐻° = 𝑐 ∆𝐻f° C + 𝑑 ∆𝐻f

° D − 𝑎 ∆𝐻f° C − 𝑏 ∆𝐻f

° C

Reversible processes in ideal gases

Most thermodynamic processes conducted in laboratory work are irreversible. Because changes in the state functions are independent of the detailed path of the process, as long as the initial and final equilibrium states are known, the changes can be directly calculated along reversible paths.

<Isothermal processes>

An isothermal process is one conducted at constant temperature.

In a reversible process,

∆𝑈 = 0, 𝑤 = −𝑞 (isothermal process, ideal gas)

𝑃ext = 𝑃gas ≡ 𝑃 = 𝑛𝑅𝑇

𝑉

6


[ F I G U R E 1 2 . 1 9 ]

𝑤 = − 𝑃 𝑑𝑉𝑉2

𝑉1

𝑤 = −𝑛𝑅𝑇 1

𝑉𝑑𝑉

𝑉2

𝑉1

𝑤 = −𝑛𝑅𝑇 ln 𝑉2𝑉1

𝑞 = −𝑤 = 𝑛𝑅𝑇 ln 𝑉2𝑉1

∆𝑈 = 0 because ∆𝑇 = 0 ∆𝐻 = ∆𝑈 + ∆ 𝑃𝑉 = ∆𝑈 + ∆ 𝑛𝑅𝑇

(reversible process) [12.14]

[12.15]

[12.16]

<Adiabatic process>

An adiabatic process is one in which there is no transfer of heat

into or out of the system.

If the process is reversible, as well as adiabatic, so that 𝑃ext = 𝑃

𝑞 = 0, ∆𝑈 = 𝑤 𝑑𝑈 = 𝑛𝑐V𝑑𝑇

𝑛𝑐V𝑑𝑇 = −𝑃ext𝑑𝑉

𝑛𝑐V𝑑𝑇 = −𝑃 𝑑𝑉 = −𝑛𝑅𝑇

𝑉𝑑𝑉

𝑐V𝑇 𝑑𝑇 = −

𝑅

𝑇 𝑑𝑉

Suppose now that the change is not infinitesimal but large.

Evaluating integrals gives

𝑐V 1

𝑇

𝑇2

𝑇1

𝑑𝑇 = −𝑅 1

𝑉

𝑉2

𝑉1

𝑑𝑉

𝑐V ln 𝑇2𝑇1= −𝑅 ln

𝑉2𝑉1= 𝑅 ln

𝑉1𝑉2

𝑇2𝑇1

𝑐V

= 𝑉1𝑉2

𝑅

= 𝑉1𝑉2

𝑐P−𝑐V

The last step used the factor that 𝑅 = 𝑐P − 𝑐V . Thus,

Where γ = 𝑐P 𝑐V

𝑇2𝑇1=

𝑉1𝑉2

𝑐P 𝑐V−1

= 𝑉1𝑉2

γ−1

𝑇1𝑉1γ−1 = 𝑇2𝑉2

γ−1

𝑃1𝑉1γ = 𝑃2𝑉2

γ

∆𝑈 = 𝑛𝑐V 𝑇2 − 𝑇1 = 𝑤 (reversible adiabatic process for ideal gas)

∆𝐻 = ∆𝑈 + ∆ 𝑃𝑉 = ∆𝑈 + 𝑃2𝑉2 − 𝑃1𝑉1

or simply ∆𝐻 = 𝑛𝑐P∆𝑇

[12.17]

[12.18]

Because 𝛄 > 𝟏 , the adiabatic line falls more rapidly with increasing volume than the isothermal line.

The adiabatic work (𝑞 = 0 , no heat transfer into the system) is 40% of the isothermal work.


[ F I G U R E 1 2 . 2 0 ]

thermodynamic processes and thermochemistry · 2017. 1. 7. · therefore, internal energy is a...

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