Plan for Wed, 15 Oct 08 Lecture –The nature of energy (6.1) –Enthalpy and calorimetry (6.2)

Thermodynamics The study of energy and its interconversion. –Energy is the capacity to do work or to produce heat –Energy is neither created nor destroyed…it is only converted from one form to another. Some examples of energy interconversion... –sunlight: radiant (electromagnetic) energy...plants harvest sunlight and convert it to sugars (chemical energy) –heat: EM radiation is converted to kinetic energy when it “excites” the motion of molecules –food: the sugars (chemical energy content) from plants are metabolized by animals (different chemical energy content), allowing them to move around and stay alive (kinetic energy) –gas: long-dead plants and animals (chemical energy) are distilled and refined and delivered to your car where they are burned up and converted to kinetic energy and heat.

Energy: Kinetic vs. Potential Potential Energy (PE) – the energy an object has by virtue of its placement in a field of force, like gravity. –PE = mgh, where m = mass, g = acceleration due to gravity, h = height Ball A has higher PE than ball B. Kinetic Energy (KE) – the energy an object has by virtue of its motion –KE = ½ mv 2, where m = mass, v = velocity ball A’s PE is converted to KE when it rolls down the hill... ball A transfers its KE to ball B by doing work it also loses some of its PE to frictional heating of the hill.

Energy = KE + PE Total Energy is the sum of kinetic energy and potential energy. Energy is readily converted between these two forms. If the system of interest is isolated (no exchange with surroundings), then total energy of the system is constant.

Example: Mass on a Spring Initial PE = ½ kx 2 At x = 0: –PE = 0 –KE = ½ mv 2 = ½ kx 2 Units of Energy Joule = kg.m 2 /s 2 Example: –Init. PE = 10 J –M = 10 kg –V max = [2(PE)/M] 1/2 = 1.4m/s x = 0 x PE

Molecular Potential Energy Petrucci, Fig. 7.9 Molecules are subject to more forces than just gravity. (and Chemical Bonds)

Molecular Kinetic Energy Petrucci, Fig. 7.9 How do molecules move around? Translation: motion through space Rotation: motion about the center of mass Vibration: motion directed through chemical bonds

Petrucci, Fig. 7.9 Molecular Potential Energy Molecular Kinetic Energy Internal Energy: E = E k + E p (and chemical bonds) Chemical reactions and phase changes involve changes in both the kinetic and potential energy of molecules.

Conservation of Energy First Law of Thermodynamics: Total energy of the universe is constant. To help keep track of energy flow let’s define... System: that one part of the universe you are interested in (i.e., you define it). Surroundings: everything else in the universe. Energy gained by the system must be lost by the surroundings. Energy exchange can be in the form of heat (q), work (w), or both.

Heat vs. Work Heat: a transfer of energy between two objects due to a temperature gradient (heat is measured in J). Work: a force acting over a distance to move an object (work is measured in J). What do these have to do with molecular KE and PE? We can think of KE and PE as an accounting of the energy that exists in a system… Heat and work are the modes by which a system can exchange energy with its surroundings. By measuring the heat absorbed or evolved, and the work performed on or by the system, we can obtain information about how the internal energy of the system changes during a process.

Heat Exchange: Exothermic Exothermic Process: evolution of the system that results in heat transfer to the surroundings. q < 0 (heat is lost)

Another Example of Exothermic

Heat Exchange: Endothermic Endothermic Process: evolution of the system that results in heat transfer to the system. q > 0 (heat is gained)

Another Example of Endothermic

Defining Work In chemical processes, a common type of work is the expansion of gas against a constant external pressure Let’s isolate this system; no heat exchange with the surroundings: q = 0 System does “work” on the surroundings by pushing back the atmosphere: w < 0

Defining Work (cont) Work: energy transferred as a force applied over a distance. How much work does the system do? P ext = force/area |w| = force x distance = P ext x A x  h = P ext  V w = - P ext  V (note sign)

Heat and Work q = heat > 0 w = work < 0 system System gains energy as heat (q), causing the gas to expand. The expanding gas exerts force on the piston, causing it to move, doing work (w) on the surroundings. System loses energy as work done on surr. w = F x d = -P  V P = P surr  V of sys!!!

Heat and Work in a Chemical Reaction Zn (s) + 2HCl (aq)  Zn 2+ (aq) + H 2 (g) + 2H 2 O + Cl  (aq) System loses energy as heat. Production of H 2 (g) causes piston to move... system loses energy as work done on surroundings.

Conservation of Energy Revisited If system gives heat q < 0 (q is negative) If system gets heat q > 0 (q is positive) If system does work w < 0 (w is negative) If work done on system w > 0 (w is positive)  E = q + w

Zumdahl, Ex 6.3 A hot-air balloon is inflated from 4 x 10 6 L to 4.5 x 10 6 L by the addition of 1.3 x 10 8 J of heat. If the balloon expands against an external pressure of 1 atm, what is  E for this process? First, define the system: the balloon.

 E = q + w = (1.3 x 10 8 J) + (-P  V) = (1.3 x 10 8 J) + (-1 atm (V final  V init )) = (1.3 x 10 8 J) + (-0.5 x 10 6 L.atm) Conversion: J per L.atm  (-0.5 x 10 6 L.atm) x (101.3 J/L.atm) = -5.1 x 10 7 J  E = (1.3 x 10 8 J) + (-5.1 x 10 7 J) = 8 x 10 7 J In English: the system gained more energy through heat than it lost doing work. Therefore, the overall energy of the system has increased.

Energy and Sign Convention If system loses energy: E final < E initial E final -E initial =  E < 0. If system gains energy: E final > E initial E final -E initial =  E > 0.

Suppose that you have two identical 500-mL bottles of water sitting on your desk at equilibrium. Bottle 1 has been kept at 25°C since bottling. Bottle 2 came from the same spring, but has been frozen, thawed, transported by air in an unpressurized compartment, and allowed to fluctuate wildly in temperature before being at equilibrium on your desk. Which bottle has the higher internal energy?

State Functions A State Function is a function in which the value only depends on the initial and final state….NOT on the pathway taken. In this example, start in Seattle, end in Denver, but you take different paths to get from one place to the other. Los Alamos

U as a state fxn  U = q + w Combustion of gas in a bomb calorimeter:  V = 0  w = -P  V = 0 All the energy produced in the combustion rxn is evolved as heat. Combustion of gas in your car:  V > 0  w = -P  V < 0 Some of the energy produced is evolved as heat, and some is evolved as work done on the surroundings. BUT IN BOTH CASES  U IS THE SAME.

Measuring  E On an earlier slide, I mentioned that by measuring: –the heat (q) exchanged between a system and its surroundings –the work (w) performed on or by a system we could determine how the internal energy of a system changes during a process. How exactly do we go about measuring q and w? It is kind of a pain, actually, to measure w, so let’s concentrate on ways to measure q…

Enthalpy Define Enthalpy: the heat transferred at constant pressure. H = E + PV or  H =  E + P  V  H accounts for  E P-V work q p =  H reaction Note that since E, P, and V are all state fxns, H is also a state fxn.

Enthalpy is defined as: Consider a process carried out at constant P (w = - P  V): Note similarity to our definition of enthalpy: Enthalpy What is this telling us? We can track the heat flow in a process occurring at constant P and that will give us direct info about  E.

Heat Capacity Heat Capacity (C): the energy required to raise the temp. of a sample of a substance by 1 o C; the ability of a substance to absorb heat. Specific heat (s): the energy required to raise the temperature of 1 gram of a substance by 1 o C. If we know the specific heat of a substance, the mass, and the temperature change, we can determine the heat flow.

NaOH + HCl  H 2 O + NaCl;  H = -58 kJ The heat evolved in this reaction is trapped in the water…this heat increases the average E k of the water molecules, leading to an increase in the temperature of the water. Formally, q is the amount of heat that must be exchanged with the surroundings to return the system to its original temperature. In calorimetry we don’t let it escape… q goes into raising the temperature of the water. q system = - q surroundings Constant P Calorimetry