• The relationships between chemical reactions and energy changes that involve heat. This portion of thermodynamics is called thermochemistry

Chapter 6

Thermochemistry

許富銀 ( Hsu Fu-Yin)

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Thermodynamics

• The study of energy and its transformations is known as thermodynamics

• The relationships between chemical reactions and energy changes that involve heat. This portion of thermodynamics is called thermochemistry

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Energy

• Energy is the capacity to do work or transfer heat

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

• Heat is the energy used to cause the temperature of an object to increase. Heat passes spontaneously from the region of

higher temperature to the region of lower temperature

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Work = force × distance

Kinetic Energy and Potential Energy

• Kinetic energy (E_k) is energy an object possesses by virtue of its motion:

• Potential energy is energy an object possesses by virtue of its position or chemical composition.

The most important form of potential energy in molecules is electrostatic potential energy, E_el:

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Potential Energy

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Kinetic Energy and Potential Energy

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Units of Energy

• The SI unit of energy is the joule (J):

• An older, non-SI unit is still in widespread use, the calorie (cal):

• 1 cal = 4.184 J

• (Note: this is not the same as the calorie of foods; the food calorie is 1 kcal!)

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System and Surroundings

• The system includes the molecules we want to study

Types of Systems:

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

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

 Isolated system: neither energy nor matter can be exchanged with the surroundings

• The surroundings are everything else

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Closed system

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• It can exchange energy with its

surroundings in the form of work

and heat

First Law of Thermodynamics

• Energy can be neither created nor destroyed.

Any energy that is lost by a system must be gained by the surroundings, and vice versa.

Energy is conserved—is known as the first law of thermodynamics.

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Internal Energy

• The internal energy, E, of a system is the sum of all the kinetic and potential energies of the components of the system.

• We generally do not know the numerical value of a system’s internal energy.

• In thermodynamics, we are mainly concerned with the change in E (and, as we shall see, changes in other quantities as well) that accompanies a change in the system.

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The change in internal energy:

Internal Energy

• A positive value of ΔE results when E_final > E_initial, indicating that the system has gained energy from its surroundings.

• A negative value of ΔE results when E_final < E_initial, indicating that the system has lost energy from its surroundings.

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Relating E to Heat and Work

• When a system undergoes any chemical or physical change, the accompanying change in internal energy, ΔE, is the sum of the heat added to or liberated from the system, q, and the work done on or by the system, w:

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When heat is added to a system or work is done on a

system, its internal energy increases.

Ex:

• A 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?

Sol:

14 Heat is absorbed by the system; this means q is a positive quantity

∴ q = +156 J

Work is done by the system; this means w is a negative quantity

∴

w = –135 J

∴∆E = q + w = +156 J + (–135 J) = +21 J

Work

• 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).

• Calculating Work for gas

15 We will consider only pressure-volume work.

work (w) = –P△V

 When a gas expands, △V is positive and the work is negative (system loses energy).

 When a gas is compressed, △V is

negative and w is positive, signifying that energy (as work) enters the system.

(system gains energy).

Sample

Exercise 5.3

• A fuel is burned in a cylinder equipped with a piston. The

initial volume of the cylinder is 0.250 L, and the final volume is 0.980 L. If the piston expands against a constant pressure of 1.35 atm, how much work (in J) is done?

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Endothermic and Exothermic Processes

• When a process occurs in which the system absorbs heat, the process is called endothermic.

• A process in which the system loses heat is called exothermic.

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State function

• The value of a state function depends only on the present state of the system, not on the path the system took to reach that state.

• q and w are not state functions.

• ΔE is not state functions.

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Enthalpy

• Under conditions of constant pressure, a thermodynamic quantity called enthalpy

• Enthalpy, which we denote by the symbol H, is defined as the internal energy plus the product of the pressure, P, and

volume, V, of the system:

• Like internal energy E, both P and V are state functions. H

• Enthalpy (H) is also state function

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Enthalpy Change

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

ΔH = Δ(E + PV)= ΔE + PΔ V (constant pressure)

ΔE = q + w = q-PΔ V [w = -P V (at constant pressure)]

ΔH =Δ E + P ΔV = (q_P + w) - w = q_P

The change in enthalpy equals the heat q_P gained or lost at constant pressure.

• When H is positive (that is, when q_P is positive), the system has gained heat from the surroundings, which means the process is endothermic.

• When H is negative, the system has released heat to the

surroundings, which means the process is exotherm

ic.

Enthalpies of Reaction

• Because ΔH = H_final – H_initial, the enthalpy change for a chemical reaction is given by

ΔH = H_products – H_reactants

• ΔH is called enthalpy of reaction or the heat of reaction and is sometimes written ΔH_rxn

EX:

• Balanced chemical equations that show the associated enthalpy change in this way are called thermochemical equations.

• ΔH<0 tells us that this reaction is exothermic.

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Guidelines for Enthalpy

• Enthalpy is an extensive property.

 When reaction is multiplied by a factor, ΔH_rxn is multiplied by that factor

• If a reaction is reversed, then the sign of ΔH is changed.

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Exercise 5.5

• How much heat is released when 4.50 g of methane gas is burned in a constant-pressure system?

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Sol:

Guidelines for Enthalpy

• ΔH is state function. Hence, if a reaction can be expressed as a series of steps, then the ΔH_rxn for the overall reaction is the sum of the heats of reaction for each step. (Hess’s Law)

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Exercise 5.10

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Sol:

Calorimetry

• Since we cannot know the exact enthalpy of the reactants and

products, we measure ΔH through calorimetry, the measurement of heat flow.

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

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

C = q/ΔT (units are J/°C)

• Molar heat capacity (C_m) is the heat capacity of one mole of a substance.

• The specific heat (C_s) is the heat capacity of one gram of a pure substance (or homogeneous mixture)

C_s=C/m=q/(mΔT) q = C_smΔT

• Water has a specific heat of 1 cal/(g℃).

• 4.184 J = 1 cal

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Specific heat

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Exercise 5.6

• (a) How much heat is needed to warm 250 g of water (about 1 cup) from 22 °C (about room temperature) to 98 °C (near its boiling point)? (b) What is the molar heat capacity of water?

Sol:

(a) ΔT = 98 °C - 22 °C = 76 °C = 76 K

q = CsmΔ T = (4.18 J/gK)(250 g)(76 K) = 7.9 * 10⁴ J

(b) Water has a specific heat of 1 cal/(gK), 4.184 J = 1 cal

C_m = (18 g/mole)[ 4.18 J/(gK) ]=75.2 J/mole K

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Coffee-cup calorimeter

• Reactions done in aqueous solution are at constant pressure.

• The calorimeter is often nested foam cups containing the solution.

q_reaction = - q_solution = -(mass_solution × Cs, solution × ΔT)

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Exercise 5.7

• When a student mixes 50 mL of 1.0 M HCl and 50 mL of 1.0 M NaOH in a coffee-cup calorimeter, the temperature of the resultant

solution increases from 21.0 to 27.5 °C. Calculate the enthalpy

change for the reaction in kJ/mol HCl, assuming that the calorimeter loses only a negligible quantity of heat, that the total volume of the solution is 100 mL, that its density is 1.0 g/mL, and that its specific heat is 4.18 J/gK.

Sol:

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Bomb Calorimeter

• Reactions can be carried out in a sealed “bomb”

such as this one.

• The heat absorbed (or released) by the water is

a very good approximation of the enthalpy change for the reaction.

q_rxn = – C_cal × ∆T

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Exercise 5.8

32 Sol:

ΔH=-2.6x10³ KJ

Standard enthalpy change

• The standard state is the state of a material at a defined set of conditions.

• Pure gas at exactly 1 atm pressure

• Pure solid or liquid in its most stable form at exactly 1 atm pressure and temperature of interest (Usually 25 °C)

• Substance in a solution with concentration 1 M

• The standard enthalpy change, △H°, is the enthalpy change when all reactants and products are in their standard states.

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Standard enthalpy of formation

• The standard enthalpy of formation, ΔH

°, is the enthalpy change for the reaction forming 1 mole of a pure

compound from its constituent elements.

• The elements must be in their standard states.

• The ΔH

°, for a pure element in its standard state = 0 kJ/mol.

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Calculating Standard Enthalpy Change for a Reaction

• The standard enthalpy of formation corresponds to the formation of a compound from its constituent elements in their standard states

• The decomposition of a compound into its constituent elements in their standard states:

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Calculating Standard Enthalpy Change for a Reaction

• The ΔH° for the reaction is then the sum of the Δ H_f° for the component reactions.



The ΔH° for the reaction is then the sum of the ΔH

° for the component reactions.

ΔH°

= Σ n ΔH

°(products) − Σ n ΔH

°(reactants)

Σ means sum.

n is the coefficient of the reaction.

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Standard Enthalpies of Formation

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Using Enthalpies of Formation to Calculate Enthalpies of Reaction

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EX:

Exercise 5.12

• (a) Calculate the standard enthalpy change for the

combustion of 1 mol of benzene, C

H

( l ^{), to CO}

^{(g) and} H

O( l ^).

Sol:

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Energy in Foods

• Most of the fuel in the food we eat comes from carbohydrates and fats.

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Energy in Fuels

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Other Energy Sources

• Nuclear fission produces 8.5% of the U.S. energy needs.

• Renewable energy sources, like solar, wind, geothermal,

hydroelectric, and biomass sources produce 7.4% of the U.S.

energy needs.

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