Thermodynamics The First Law Work, Heat, Energy

Transcription

1 The Basic Concepts: the system Thermodynamics The First Law Work, Heat, Energy System Matter Energy System Matter Energy Thermodynamics is the study of the transformations of energy. Surroundings (a) open System Matter Surroundings (b) closed Oxtoby, Chapter 10 ( ) Energy Surroundings (c) isolated The Basic Concepts: state and path fns A state function, X, is a property that depends only on the current state of the system, and not on how it was prepared. Changes in a state function depend only on the start and end points of an experiment DX = X final X initial e.g. the duration of this lecture depends only when I start and when I finish A path function, Y, is a property that depends on the history of the system. e.g. the boredom/interest factor for this lecture depends on a lot more than just my first and last sentence The Conservation of Energy: Energy can neither be created not destroyed (experimental observation) fl Energy is a state function The principle of conservation of energy can be used to assess the energy changes that accompany physical and chemical processes. ICE SOLID + heat + heat Melting Liquid water Liquid Heat, q When the energy of a system changes as a result of a temperature difference between it and its surroundings, it is said that energy has been transferred as Heat, q Processes that release energy as heat are exothermic; A B + heat C + O 2 CO 2 + heat Combustion reactions Processes that absorb energy as heat are endothermic; A + heat B Melting, Vaporization of Water 1

2 Work, Heat and Energy Work, w, is done when an object is moved against an opposing force Work, w In general: w = F. d work distance Force along path Work is a path function (how strong is gravity?) Expanding gas pushes out piston against (e.g, atmospheric) pressure More specifically, for thermodynamics: w = - F. d We focus on the force the system has to push against Work is done on system by the surroundings Work and pressure Pressure - Volume Work: External pressure, p The First Law In thermodynamics, the total energy of a system is called the internal energy, E. Experiments measure the change in energy between start and finish: Area A h w = - F. ext d w = - F ext h E = E f - E i The change in internal energy E is the sum of work done on a system and the energy transferred as heat to a system according to; E = w + q w = - p ext A h w = - p ext V Heat must be a path function: the system can gain/lose energy either as heat or as work. & E = w + q w = - p ext V If the system is kept at constant volume: E = q v We measure E usually using Calorimetry (the measurement of amounts of heat flowing into or out of a system and the accompanying temperature changes) Calorimetry Adiabatic Bomb Calorimeter Adiabatic means no heat is transferred from calorimeter to surroundings The change in temperature, T, of the calorimeter is proportional to the heat that the reaction releases or absorbs. q = C cal T Calorimeter Constant Calibrated using a process of known energy output (eg, burning of a substance of known mass) or from an electrical current, I, of known potential, V q = V I t 2

3 Heat Capacity Heat Capacity q Generally: C = Units: J K T -1, cal K -1 1 cal = J Molar Heat Capacity (J K -1 mol -1 or cal K -1 mol -1 ) q C c = = Heat capacity of a sample divided by the T n n chemical amount of substance, n The heat capacity C of a substance is the heat required to change its temperature by one Kelvin, and has units of energy per Kelvin. The heat capacity is an extensive variable: the quantity is proportional to the amount of matter present. Specific Heat Capacity (in J K -1 kg -1 or cal K -1 kg -1 ) q C c s = = Heat capacity of a sample divided by the T m m mass of substance, m c = M c s Spontaneous Changes: Entropy Why do some processes happen spontaneously? Why does a hot body get cooler (rather than hotter) when surrounded by a cooler medium? Why does a gas expand into all available volume of a container rather than contract? The driving force for spontaneous change (change that happens without intervention doing work or heating) is described in the second law of Thermodynamics Chapter 11 No process is possible in which the sole result is the absorption of heat from a reservoir and its complete conversion into work. Kinetic energy converted into thermal motion Energy is not accumulated in ball and thermal motion is not directional Entropy, S, and the second law These spontaneous changes happen because they increase the randomness with which energy is spread through an isolated system The Entropy, S, a thermodynamic state function, is a measure of molecular disorder, or freedom of movement molecules have, and helps us to define the direction of spontaneous change The Entropy of an isolated system increases in the course of a spontaneous change S system + S surroundings = S total > 0 Hence, in a spontaneous process: S universe > 0 3

4 Entropy and Equilibrium Nothing changes when a system is at equilibrium, including the entropy of the system So, for any process S system + S surroundings = S universe r 0 But, equilibrium is dynamic at a microscopic level reactants Ý products This introduces the idea that changes can be reversible, i.e. a change can be made, and then exactly undone ( reversed ), so S universe = 0 for a reversible process Entropy and Heat Entropy measures dispersal of energy in a system Heat changes kinetic energy of molecules, i.e. disperses energy by increasing the velocities of all the molecules fl heat and entropy are related? For a reversible process DS = q rev / T For an irreversible process DS > q rev / T = DU / T (at constant volume) In practice, reversible changes are an idealised limit in which changes happen infinitely slowly via a series of imperceptible shifts in the equilibrium Entropy and Disorder The Entropy of the System Reversible (infinitesimal) Changes q rev = TdS First law becomes du = TdS PdV Solid Liquid Gas Entropy of system increases Other Energies Legendre transformations enable us to define other energies which have exact differentials in terms of other state variables Enthalpy H = U+ PV Gibbs Free Energy G= U + PV TS Helmholtz Free Energy A= U TS dh = TdS+ VdP dg= SdT + VdP da = SdT PdV Enthalpy 4

5 The Enthalpy, H Enthalpy of Reaction - H r For a system kept at constant pressure: Example 1 A B H = q p where H = H f - H i H A Enthalpy of Reaction: H r = H B - H A H B The Enthalpy, like the internal Energy, is a state function Example 2 2 C + D E + 3 F 2 H C H D H E 3 H F Enthalpy of Reaction: H r = H E + 3 H F - H D -2 H C The Reaction Enthalpy, H r In General: H r = H products - H reactants Standard Enthalpies Enthalpy normally tabulated for substances in their standard state; these are called the standard enthalpy, H o. Denotes standard condition Example: H r = Σ ν H products - Σ ν H reactants Sum over all standard molar enthalpies taking into account their stochiometric factors, ν 2 C 2 H O 2 4 CO H 2 O ν= 2 ν= 7 ν= 4 ν= 6 H r = 6H(H 2 O) + 4H(CO 2 ) -7H(O 2 ) -2H(C 2 H 6 ) The standard state of a substance at a specified temperature is its pure form at 1 atm (should now be 1 bar). For dissolved species, the standard state is the concentration of 1M under a pressure of 1 atm at a specified temperature. Standard enthalpies at T = 298 K are often denoted Hʅ Hence, the standard enthalpy of reaction is H ro = Σ ν H o products - Σ ν H o reactants Enthalpies of phase change Being a state function: path doesn t matter Enthalpy changes also occur when a substance melts/freezes or condenses/evaporates H o fus = +6.0 kj mol 1 Fusion (melting): Vaporisation (boiling): H o fus (273)=+6.0 kj mol H o vap (373)=+40.7 kj mol Overall: H o vap = kj mol 1 H o sub = kj mol 1 endothermic! = kj mol 1 Sublimation (direct conversion from solid to gas) H o kj sub (298.15)=+46.7 mol Because enthalpy is a state function, these rules apply to every type of reaction or change 5

6 Hess s Law The enthalpy of an overall reaction is the sum of the enthalpies of the individual reactions into which the reaction can be divided. Example:Calculate the enthalpy of combustion of benzene (C 6 H 6 ) from its enthalpy of hydrogenation (-205 kj/mol) to cyclohexane, and the enthalpy of combustion of cyclohexane ( H o (C 6 H 12 ) = 3920 kj/mol)). The enthalpy of the combustion for H 2 is -286 kj/mol. Standard Molar Enthalpies of Formation, H o f The enthalpy of formation is the enthalpy change when a compound is formed from its elements, and those elements are in their most stable form under the prevailing conditions. When the prevailing conditions are the standard state, this is called the standard enthalpy of formation, H o f H 2(g) O 2(g) H o f = kj/mol 6 C (s, graphite) + 3 H 2(g) C 6 H 6(l) H o f = + 49 kj/mol The standard enthalpies of elements in their reference states are zero at all temperatures (graphite is the reference state of carbon!). Bond enthalpies A B (g) A (g) + B (g) H rxn = energy of the A B bond But bond enthalpies are affected by the neighbouring bonds CH 4(g) CH 3(g) + H (g) H = 439 kj mol 1 C 2 H 6(g) C 2 H 5(g) + H (g) H = 410 kj mol 1 CHCl 3(g) CCl 3(g ) + H (g) H = 380 kj mol 1 Gibbs Free Energy, G fl usually tabulate average bond enthalpies (determined from A B bond enthalpies in many different A B containing molecules) Average bond enthalpies can be used to estimate the enthalpy of a compound: just count the number and type of bonds involved. The Gibbs Free Energy, G The Gibbs Free Energy: criterion for spontaneity S uni = S system + S surroundings Requires knowledge of both system and surroundings At constant pressure and temperature, and for reversible changes: T S surroundings = q p,rev = H system Define a new form of the energy function G = H TS Called the Gibbs free energy. G is a state function At constant T: But also: G sys = (H sys - T sys S sys ) = H sys - T S sys H sys T G = H - T S = - S surr Resulting in: G sys = - T S surr -T S sys = - T ( S surr + S sys ) and as S uni > 0 = - T ( S uni ) < 0 for spontaneous pr. 6

7 Criterion for Spontaneity S uni > 0 S uni = 0 S uni < 0 Spontaneous Equilibrium Not spontaneous (reverse reaction is spontaneous) G sys < 0 G sys = 0 G sys > 0 N.B. left hand describes the whole universe, but right hand is just the system. We can drive the system in the wrong direction (hence can have reactions where DG is positive, but cannot force the universe to show negative entropy Driving forces in chemistry Two driving forces underpin Chemistry: Systems tend to a state of minimum enthalpy Systems tend to a state of maximum entropy The Gibbs free energy expresses the balance between these two driving forces DG = DH T DS (b 0?) Gibbs Energy for Chemical Reaction Standard Molar Gibbs Energy of Formation As the Gibbs energy is a state function, the (standard) Gibbs energy of reaction is defined (in analogy to Hess law for the enthalpy) as: G ro = Σ ν G o products - Σ ν Go reactants Where o as before indicates that all substances are in their standard states at the specified temperature. G ro = H ro - T S r o By analogy with the definition of the standard molar Enthalpy of formation we define G fo = H fo -T S f o as the standard molar Gibbs energy of formation when 1 mole of a substance forms in a standard state at a specified temperature from the most stable forms of its constituent elements in standard states at the same temperature. 7