The Relationships Between. Internal Energy, Heat, Enthalpy, and Calorimetry

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1 The Relationships Between Internal Energy, Heat, Enthalpy, and Calorimetry

2 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

3

4 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

5 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 = E final E initial

6 Changes in Internal Energy If E > 0, E final > E initial Therefore, the system absorbed energy from the surroundings This energy change is called endergonic

7 Changes in Internal Energy If E < 0, E final < E initial Therefore, the system released energy to the surroundings. This energy change is called exergonic

8 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 For q Sign Conventions for q, w, and E + 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

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10 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

11 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)

12 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

13 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

14 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

15 Illustration of a State Function Examples Energy Enthalpy Elevation (non-scientific analogy) Non-examples Work Heat Distance travelled (nonscientific analogy)

16 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

17 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

18 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

19 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

20 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

21 Various Depictions of Enthalpy ΔH rxn (in kj/ mol rxn ) Heat absorbed (+) or released (-) by a chemical reaction ΔH comb (in kj/ mol rxn ) Heat absorbed or released when ONE mole of a substance is completely burned in oxygen, O 2 ΔH f (in kj/ mol rxn ) Heat absorbed or released when ONE mole of a compound is formed from elements in their standard states ΔH fus (in kj/ mol rxn ) Heat absorbed to melt ONE mole of solid to liquid at melting point ΔH vap (in kj/ mol rxn ) Heat absorbed to change ONE mole of a liquid to a gas at boiling point

22 How do We Calculate H? Enthalpy can be calculated from several sources including: Stoichiometry Calorimetry Heats of formation ( H f ) Hess Law Bond energies

23 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

24 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

25 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 25 0 C and 1 atm

26 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

27 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 q system + q surroundings = 0

28 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 (C p ) 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 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

29 More on Specific Heat Specific heat, then, is represented mathematically by the following equation: Specific heat capacity C p = quantity of heat transferred (g of material)(degrees of temperature change)

30 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

31 Calorimetry at Constant Pressure Coffee-Cup Calorimetry Constant-pressure calorimetry is used in determining the changes in enthalpy ( H rxn ) 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

32 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 q system + q surroundings = 0 q system = q surroundings 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

33 #7 on page Practice!

34 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 Where: H = q = mc T q = heat m = mass (g) C = Specific heat capacity (J/g C) T = C

35 #8 on page Practice!

36 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

37 Bomb Calorimeters and Constant- 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 Volume Calorimetry q rxn = q calorimeter q rxn = C cal T

38 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 E rxn = C cal T

39 # 11 on page Practice!

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