Chapter 6 Energy Thermodynamics. Energy is... The ability to do work. Conserved. made of heat and...

Chapter 6

EnergyThermodynamics

Energy is...• The ability to do work.• Conserved.• made of heat and work.• a state function.• independent of the path, or how you get

from point A to B.• Work is a force acting over a distance.• Heat is energy transferred between objects

because of temperature difference.

Energy

Chapter 6: Thermochemistry 3

Literally means “work within,” however no object contains work

Energy refers to the capacity to do work– that is, to move or displace matter

EOS

2 basic types of energy: – Potential (possibility of doing work because of composition or position) – Kinetic (moving objects doing work)

Energy

Chapter 6: Thermochemistry 4

Potential Energy – in a gravitational field (= position)

Kinetic Energy – energy of motion

PE = mghm = mass (kg)g = gravity constant (m s-2)h = height (m)

KE = 1/2mv2

m = mass (kg)v = velocity (m s–1)v2 = (m2 s–2)

EOS

units are kg m2 s–2

Junits are kg m2 s–2 = J

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

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Kinetic EnergyKinetic energy is energy an object possesses by virtue of its motion.

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12

KE = mv2

Conversion of Energy

• Energy can be converted from one type to another.

• For example, the cyclist above has potential energy as she sits on top of the hill.

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Conversion of Energy

• 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.

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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

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1 J = 1 kg m2

s2

The universe

• is divided into two halves.• the system and the surroundings.• The system is the part you are concerned with.• The surroundings are the rest.• Exothermic reactions release energy to the

surroundings.• Endo thermic reactions absorb energy from the

surroundings.

Thermochemistry

Chapter 6: Thermochemistry 11

EOS

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

UniverseFocus is on heat and matter transfer between the system ...

System

Surroundings

Su

rrou

nd

ing

sS

urro

un

din

gs

and the surroundings

Definitions:System and Surroundings

• The system includes the molecules we want to study (here, the hydrogen and oxygen molecules).

• The surroundings are everything else (here, the cylinder and piston).

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Thermochemistry

Chapter 6: Thermochemistry 13

Types of systems one can study:

OPEN

MatterMatter

EnergyEnergy

CLOSED

Matter

EnergyEnergy

Matter

EOS

ISOLATED

MatterMatter

EnergyEnergy

Definitions: Work

• Energy used to move an object over some distance is work.

• w = F dwhere w is work, F is the force, and d is the distance over which the force is exerted.

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Internal Energy

Chapter 6: Thermochemistry 15

Internal Energy (U) is the total energy contained within the system, partly as kinetic energy and partly as potential energy

EOS

Kinetic involves three types of molecular motion ...

Internal Energy

Chapter 6: Thermochemistry 16

Internal Energy (U) is the total energy contained within the system, partly as kinetic energy and partly as potential energyPotential energy involves intramolecular interactions ...

EOS

and intermolecular interactions ...

Heat

• Energy can also be transferred as heat.

• Heat flows from warmer objects to cooler objects.

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Heat (q)

Chapter 6: Thermochemistry 18

Heat is energy transfer resulting from thermal differences between the system and surroundings

“flows” spontaneously from higher T lower T

EOS

“flow” ceases at thermal equilibrium

CH + 2O CO + 2H O + Heat4 2 2 2

CH + 2O 4 2

CO + 2 H O 2 2

Pote

nti

al en

erg

y

Heat

N + O2 2

Pote

nti

al en

erg

y

Heat

2NO

N + O 2NO2 2 + heat

Same rules for heat and work

• Heat given off is negative.• Heat absorbed is positive.• Work done by system on surroundings is

positive.• Work done on system by surroundings is

negative.• Thermodynamics- The study of energy and the

changes it undergoes.

Work (w)

Chapter 6: Thermochemistry 22

Work is an energy transfer between a system and its surroundings

Recall from gas laws … the product PV = energy

EOS

Pressure–volume work is the work of compression (or expansion) of a gas

Calculating Work (w)

Chapter 6: Thermochemistry 23

PV work is calculated as follows:

w = –PV

Sign conventions: think from the perspective of the system

SYSTEM WORK

EOS

If work is done by the system, the system loses energy equal to –w

Calculating Work (w)

Chapter 6: Thermochemistry 24

SYSTEM WORKExpansion is an example of work done by the system—the weight above the gas is lifted

EOS

compression (or expansion) of a gas

ExpansionWork

What is work?

• Work is a force acting over a distance.• w= F x d• P = F/ area• d = V/area• w= (P x area) x (V/area)= PV• Work can be calculated by multiplying

pressure by the change in volume at constant pressure.

• units of liter - atm L-atm

Work needs a sign

• If the volume of a gas increases, the system has done work on the surroundings.

• work is negative• w = - PV• Expanding work is negative.• Contracting, surroundings do work on the

system w is positive.• 1 L atm = 101.3 J

Examples

• What amount of work is done when 15 L of gas is expanded to 25 L at 2.4 atm pressure?

• If 2.36 J of heat are absorbed by the gas above. what is the change in energy?

• How much heat would it take to change the gas without changing the internal energy of the gas?

System

Surroundings

Energy

E <0

System

Surroundings

Energy

E >0

Direction

• Every energy measurement has three parts.1. A unit ( Joules of calories).2. A number how many.3. and a sign to tell direction.• negative - exothermic• positive- endothermic

First Law of Thermodynamics• Energy is neither created nor destroyed.• In other words, the total energy of the universe is a

constant; if the system loses energy, it must be gained by the surroundings, and vice versa.

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First Law of Thermodynamics

• The energy of the universe is constant.• Law of conservation of energy.• q = heat• w = work• E = q + w• Take the systems point of view to decide

signs.

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

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Internal EnergyBy definition, the change in internal energy, E, is the final energy of the system minus the initial energy of the system:

E = Efinal − Einitial

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Changes in Internal Energy

• 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.

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E, q, w, and Their Signs

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Exchange of Heat between System and Surroundings

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

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Exchange of Heat between System and Surroundings

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

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

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States of a System

Chapter 6: Thermochemistry 39

The state of a system refers to its exact condition, determined by the kinds and amounts of matter present, the structure of this matter at the molecular level, and the prevailing pressure and temperature

Example: internal energy (U) is a function of the state of the system ...

EOS

State Functions

Chapter 6: Thermochemistry 40

A state function is a property that has a unique value that depends only on the present state of a system and not on how the state was reached, nor on the history of the system

EOS

U = Uf – Ui

State Functions• 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 below, the water could have reached room

temperature from either direction.

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State Functions• Therefore, internal energy is a state function.• It depends only on the present state of the system,

not on the path by which the system arrived at that state.

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

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State Functions

• 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.

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Enthalpy• Symbol is H• Change in enthalpy is H• delta H• If heat is released the heat content of the

products is lower• H is negative (exothermic)• If heat is absorbed the heat content of the

products is higher• H is positive (endothermic)

44

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

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H = E + PV

Enthalpy

• abbreviated H• H = E + PV (that’s the definition)• at constant pressure.• H = E + PV

• the heat at constant pressure qp can be calculated

from

• E = qp + w = qp - PV

• qp = E + P V = H

Enthalpy

• Since E = q + w and w = -PV, we can substitute these into the enthalpy expression:

H = E + PVH = (q+w) − w H = q

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

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Endothermicity and Exothermicity

• A process is endothermic when H is positive.

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Endothermicity and Exothermicity

• A process is endothermic when H is positive.

• A process is exothermic when H is negative.

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Enthalpy of Reaction

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

H = Hproducts − Hreactants

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Enthalpy of Reaction

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

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The Truth about Enthalpy

1. Enthalpy is an extensive property.2. H for a reaction in the forward direction is

equal in size, but opposite in sign, to H for the reverse reaction.

3. H for a reaction depends on the state of the products and the state of the reactants.

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Calorimetry

Chapter 6: Thermochemistry 53

Calorimetry is a technique used to measure heat exchange in chemical reactions

A calorimeter is the device used to make heat measurements

EOS

Calorimetry is based on the law of conservation of energy

Calorimetry Relationships

Chapter 6: Thermochemistry 54

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

calculated from C = q/T units of J oC–1 or J K–1

Specific heat is the heat capacity of a one-gram sample

EOS

Specific heat = C/m = q/mT units of J g–1 oC–1 or J g–1 K–1

Specific Heats

Chapter 6: Thermochemistry 55

Molar heat capacity is the product of specific heat times the molar mass of a substance

units are J mol–1 K–1

A useful form of the specific heat equation is:

q = m CT If T > 0, then q > 0 and heat is gained by the system

EOS

If T < 0, then q < 0 and heat is lost by the system

Calorimetry

• Measuring heat.• Use a calorimeter.• Two kinds• Constant pressure calorimeter (called a coffee

cup calorimeter)• heat capacity for a material, C is calculated • C= heat absorbed/ T = H/ T• specific heat capacity = C/mass

Calorimetry

• molar heat capacity = C/moles• heat = specific heat x m x T• heat = molar heat x moles x T• Make the units work and you’ve done the

problem right.• A coffee cup calorimeter measures H.• An insulated cup, full of water. • The specific heat of water is 1 cal/gºC• Heat of reaction= H = sh x mass x T

Heat Capacity and Specific Heat

The amount of energy required to raise the temperature of a substance by 1 K (1C) is its heat capacity.

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Heat Capacity and Specific Heat

We define specific heat capacity (or simply specific heat) as the amount of energy required to raise the temperature of 1 g of a substance by 1 K.

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Heat Capacity and Specific Heat

Specific heat, then, is

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Specific heat =heat transferred

mass temperature change

s =q

m T

Examples

• The specific heat of graphite is 0.71 J/gºC. Calculate the energy needed to raise the temperature of 75 kg of graphite from 294 K to 348 K.

• A 46.2 g sample of copper is heated to 95.4ºC and then placed in a calorimeter containing 75.0 g of water at 19.6ºC. The final temperature of both the water and the copper is 21.8ºC. What is the specific heat of copper?

Calorimetry

• Constant volume calorimeter is called a bomb calorimeter.

• Material is put in a container with pure oxygen. Wires are used to start the combustion. The container is put into a container of water.

• The heat capacity of the calorimeter is known and tested.

• Since V = 0, PV = 0, E = q

Constant Pressure Calorimetry

By carrying out a reaction in aqueous solution in a simple calorimeter such as this one, one can indirectly measure the heat change for the system by measuring the heat change for the water in the calorimeter.

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Constant Pressure Calorimetry

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

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Bomb Calorimeter

• thermometer

• stirrer

• full of water

• ignition wire

• Steel bomb

• sample

Properties

• intensive properties not related to the amount of substance.

• density, specific heat, temperature.• Extensive property - does depend on the

amount of stuff.• Heat capacity, mass, heat from a reaction.

Hess’s Law

• Enthalpy is a state function.• It is independent of the path.• We can add equations to to come up with the

desired final product, and add the H• Two rules• If the reaction is reversed the sign of H is

changed• If the reaction is multiplied, so is H

Hess’s Law

Hess’s law states that “[i]f 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.”

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Hess’s Law

Because H is a state function, the total enthalpy change depends only on the initial state of the reactants and the final state of the products.

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N2 2O2

O2 NO2

68 kJ

NO2180 kJ

-112 kJ

H (

kJ)

Standard Enthalpies

Chapter 6: Thermochemistry 71

The standard enthalpy of reaction (Ho) is the enthalpy change for a reaction in which the reactants in their standard states yield products in their standard statesThe standard enthalpy of formation (Ho

f) of a substance is the enthalpy change that occurs in the formation of 1 mol of the substance from its elements when both products and reactants are in their standard states

EOS

Standard Enthalpy

• The enthalpy change for a reaction at standard conditions (25ºC, 1 atm , 1 M solutions)

• Symbol Hº• When using Hess’s Law, work by adding the

equations up to make it look like the answer. • The other parts will cancel out.

Standard Enthalpies of Formation

Standard enthalpies of formation, Hf°, are measured under standard conditions (25 °C and 1.00 atm pressure).

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Calculation of H

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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C3H8 (g) + 5 O2 (g) 3 CO2 (g) + 4 H2O (l)

H (g) + 1

2O (g) H (l) 2 2 2O

C(s) + O (g) CO (g) 2 2Hº= -394 kJ

Hº= -286 kJ

C H (g) + 5

2O (g) 2CO (g) + H O( ) 2 2 2 2 2 l

Example

• Given

calculate Hº for this reaction

Hº= -1300. kJ

2C(s) + H (g) C H (g) 2 2 2

Example

O (g) + H (g) 2OH(g) 2 2 O (g) 2O(g)2 H (g) 2H(g)2

O(g) + H(g) OH(g)

Given

Calculate Hº for this reaction

Hº= +77.9kJHº= +495 kJ

Hº= +435.9kJ

Standard Enthalpies of Formation

• Hess’s Law is much more useful if you know lots of reactions.

• Made a table of standard heats of formation. The amount of heat needed to for 1 mole of a compound from its elements in their standard states.

• Standard states are 1 atm, 1M and 25ºC• For an element it is 0• There is a table in Appendix 4 (pg A22)

Standard Enthalpies of Formation

• Need to be able to write the equations.• What is the equation for the formation of

NO2 ?

• ½N2 (g) + O2 (g) NO2 (g)

• Have to make one mole to meet the definition.• Write the equation for the formation of

methanol CH3OH.

Since we can manipulate the equations

• We can use heats of formation to figure out the heat of reaction.

• Lets do it with this equation.

• C2H5OH +3O2(g) 2CO2 + 3H2O

• which leads us to this rule.

Since we can manipulate the equations

• We can use heats of formation to figure out the heat of reaction.

• Lets do it with this equation.

• C2H5OH +3O2(g) 2CO2 + 3H2O

• which leads us to this rule.

( H products) - ( H reactants) = Hfo

fo o

Calculations Based onStandard Enthalpies of Formation

Chapter 6: Thermochemistry 81

Ho = p × Hof (products) – r × Ho

f (reactants)General Expression:

Each coefficient is multiplied by the standard enthalpy of formation for that substanceThe sum of numbers for the reactants is subtracted from the sum of numbers for the products

EOS

With organic compounds, the measured Ho

f is often the standard enthalpy of combustion Ho

comb