Download Internal Energy, Heat, Enthalpy, and Calorimetry

The Relationships Between …
Internal Energy, Heat, Enthalpy,
and Calorimetry
Recap of Last Class
 Last class, we began our discussion about
energy changes that accompany chemical
reactions
 Chapter 5 discusses:
 Thermodynamics
 The study of energy transformations
 Thermochemistry
 Study of energy transformations specific the field
to chemical reactions
Internal Energy
 Recall that energy is often defined as the ability to do work or
produce heat
 The sum of all potential energy and kinetic energy in a system is
known as the internal energy of the system
 We call it E
Internal Energy
 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
Changes in Internal Energy
 If E > 0, Efinal > Einitial
 Therefore, the system absorbed energy from the surroundings
 This energy change is called endergonic
Changes in Internal Energy
 If E < 0, Efinal < Einitial
 Therefore, the system released energy to the surroundings.
 This energy change is called exergonic
Changes in Internal Energy
 When energy is exchanged between the system and the
surroundings, it is exchanged as either heat (q) or work
(w)
 Mathematically, this can be represented by:
E = q + w
Sign Conventions for q, w, and ∆E
For q
+ means heat
- means heat
absorbed by system released by system
For w
+ means work done
ON system
- means work done
BY the system
For ∆E
+ means net gain of
energy by system
- means net loss of
energy by system
Relation of Work to Gases
 When related to gases, work is a function of
pressure
 Pressure is defined as force per unit area
 So when the volume is changed:
 Work was done ON the gas
 Compression (decrease in volume)
 +w
 OR work was done BY the gas
 Expansion (increase in volume)
 -w
Work and Gases
 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)
Work and Gases
 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
State Functions
 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
 Called a state function
 A state function is formally defined as a property of the system
that depends only on its present state
 Does not depend in any way on the system’s past (or future)
 A change in this function in going from one state to another state is
independent of the particular pathway taken between the two states
Examples of State Functions
 Internal energy, pressure, and volume are all state
functions
 Example
 In the system below, the water could have reached room
temperature from either direction
Illustration of a State Function
 Examples
 Energy
 Enthalpy
 Elevation (non-scientific
analogy)
 Non-examples
 Work
 Heat
 Distance travelled (nonscientific analogy)
What is Enthalpy and How Does it
Relate to Internal Energy (E)?
 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 a thermodynamic function that is mathematically
defined as:
H = E + PV
Enthalpy
When the system changes at constant
pressure, the change in enthalpy, H, is
H = (E + PV)
This can be written
H = E + PV
Enthalpy
 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 = q
 So, at constant pressure, the change in enthalpy is the
heat gained or lost
 The change in enthalpy is better defined as the heat
content of a substance at constant atmospheric pressure
Enthalpy and State Functions
 Since ∆H is derived from E, P, and V – all
of which are state functions - then ∆H is
also a state function
The Truth about Enthalpy
1. Enthalpy is an extensive property
 This means that ΔH depends directly on amount
of substance
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
Various Depictions of Enthalpy
 ΔHrxn (in kJ/ molrxn)
 Heat absorbed (+) or released (-) by a chemical reaction
 ΔHcomb (in kJ/ molrxn)
 Heat absorbed or released when ONE mole of a substance is completely
burned in oxygen, O2
 ΔHf (in kJ/ molrxn)
 Heat absorbed or released when ONE mole of a compound is formed from
elements in their standard states
 ΔHfus (in kJ/ molrxn)
 Heat absorbed to melt ONE mole of solid to liquid at melting point
 ΔHvap (in kJ/ molrxn)
 Heat absorbed to change ONE mole of a liquid to a gas at boiling point
How do We Calculate ∆H?
 Enthalpy can be calculated from several sources
including:





Stoichiometry
Calorimetry
Heats of formation (∆Hf)
Hess’ Law
Bond energies
Chemical Reactions and ∆H
 Most chemical
reactions involve a
change in enthalpy
 Endothermic reaction
 Net ABSORPTION of
energy (heat) by the
system
 Enthalpy of products is
greater than enthalpy
of reactants
 ΔH is positive
 Energy is considered a
reactant
Chemical Reactions and ∆H
 Exothermic reaction
 Net RELEASE of
energy (heat) by the
system
 Enthalpy of products is
less than enthalpy of
reactants
 ΔH is negative
 Energy is considered a
product
Determining ∆H using Stoichiometry
 As stated before:
 ΔH depends on the amount of substance present
 ΔH can be represented as a product or a reactant in a balanced
chemical equation
 When ΔH is included in a chemical equation, it is called a
thermochemical equation
KOH (s) → KOH (aq) + 43 kJ/mol
 You would read the above equation as:
“43 kJ are released for every 1 mole of potassium hydroxide that
is decomposed at 250C and 1 atm”
Determining ∆H using Stoichiometry
 But, what if you don’t have the amounts of substance
as described in the balanced equation? How much
energy would be transferred?
 Use stoichiometry!
 Practice!
 # 2 on page 157
Determining ΔH using Calorimetry
 Since we cannot know the exact enthalpy of the
reactants and products, we measure H through
calorimetry, the measurement of heat flow
 Specifically, calorimetry is the process of measuring heat
based on observing the temperature change when a
body absorbs or releases energy as heat energy
 Based on First Law of Thermodynamics
qsystem + qsurroundings = 0
Some Terms to Know when Using
Calorimetry
 Heat capacity (C)
 Energy required to raise temperature
by 1 degree
 Units are J/°C or J/K
 Specific heat capacity (Cp)
 Energy required to raise temperature of
1 gram of substance by 1 degree
 Units are J/g ∙°C or J/g ∙ K
 Specific heat of water is 4.184 J/g ∙°C or
1.00 cal /g ∙°C
 Molar heat capacity
 Energy required to raise temperature of
1 mole of substance by 1 degree
 Units are J/mol∙K or J/mol ∙°C
More on Specific Heat
 Specific heat, then, is represented mathematically by
the following equation:
Specific heat capacity Cp
quantity of heat transferred
=
(g of material)(degrees of temperature change)
Determination of ΔH using
Calorimetry
 Calorimetry is done using a calorimeter!
 A device used to measure heat flow
 Coffee-cup calorimeter
 Experiment is done at constant pressure
 Bomb calorimeter
 Experiment is done at constant volume
Calorimetry at Constant Pressure
Coffee-Cup Calorimetry
 Constant-pressure
calorimetry is used in
determining the changes in
enthalpy (∆Hrxn) for
reactions occurring in
solution
 By carrying out a reaction in
aqueous solution in a simple
calorimeter, the heat
change for the system can
be found by measuring the
heat change for the water in
the calorimeter
Coffee-Cup Calorimetry
 Recall that under constant pressure, the change in enthalpy equals heat
 Also recall that enthalpy follows the First Law of Thermodynamics
 Thus,
∆H = q at constant pressure
qsystem + qsurroundings = 0
−qsystem = qsurroundings
 In other words,
Energy (heat) released by the reaction = Energy (heat) absorbed by the solution
 Assume that the calorimeter does not absorb or leak any heat and that the
solution can be treated as if it were pure water with a density of 1.0 g/mL
 So,
Energy (heat) released by substance = Energy (heat) gained by water
Practice!
 #7 on page
Quantifying Energy Exchanges using
Constant-Pressure Calorimetry
 Since the change in enthalpy is dependent on amount of
substance, the energy exchanged during a reaction is
expressed as:
∆H = q
= specific heat capacity × mass of solution × increase in tempearture
∆H = q = mC∆T
 Where:
q = heat
m = mass (g)
C = Specific heat capacity (J/g∙°C)
T = °C
Practice!
 #8 on page
Quantifying Energy Exchanges using
Constant-Pressure Calorimetry
 Remember, enthalpies of reactions are often
expressed in terms of energy per moles of reacting
substances or moles of produced substances
 Divide calculated energy by amount of substance
 May need to use stoichiometry to find amount of
substance
Bomb Calorimeters and ConstantVolume Calorimetry
 Bomb calorimeters are used
to measure heats of
combustion
 The steel jacket isolates the
system so that the heat
produced by the combustion
is taken up by calorimeter
−qrxn = qcalorimeter
qrxn = – Ccal × ∆T
Bomb Calorimetry
 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
−∆Erxn = Ccal ∆T
Practice!
 # 11 on page