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Internal Energy, Heat, Enthalpy, and Calorimetry
The Relationships Between …
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
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
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
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
Changes in Internal Energy
Sign Conventions for q, w, and ∆E
For q + means heat absorbed by system
- means heat 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
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
Relation of Work to Gases
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 = −PV
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
Internal energy, pressure, and volume are all state functions
Example
In the system below, the water could have reached room temperature from either direction
Examples of State Functions
Illustration of a State Function
Examples
Energy
Enthalpy
Elevation (non-scientific analogy)
Non-examples
Work
Heat
Distance travelled (non-scientific analogy)
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
What is Enthalpy and How Does it Relate to Internal Energy (E)?
Enthalpy
When the system changes at constant pressure, the change in enthalpy, H, is
H = (E + PV)
This can be written
H = E + PV
Enthalpy
Since E = q + w and w = −PV, we can substitute these into the enthalpy expression:
H = E + PV
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
Since ∆H is derived from E, P, and V – all of which are state functions - then ∆H is also a state function
Enthalpy and State Functions
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
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
Various Depictions of Enthalpy
Enthalpy can be calculated from several sources including:
Stoichiometry
Calorimetry
Heats of formation (∆Hf)
Hess’ Law
Bond energies
How do We Calculate ∆H?
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
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 ∆H using Stoichiometry
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
Determining ΔH using Calorimetry
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
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)
More on Specific Heat
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
Determination of ΔH using Calorimetry
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
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
Coffee-Cup Calorimetry
#7 on page
Practice!
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
Quantifying Energy Exchanges using Constant-Pressure Calorimetry
#8 on page
Practice!
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
Quantifying Energy Exchanges using Constant-Pressure Calorimetry
Bomb Calorimeters and Constant-Volume 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
# 11 on page
Practice!