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# Chapter 17

### Free Energy and Thermodynamics

Term | Definition |
---|---|

Spontaneous Process | A process that occurs without ongoing outside intervention such as the performance of work by some external force |

Mechanical Potential | Mechanical potential energy predicts the direction in which a mechanical system will spontaneously move |

Chemical Potential | We seek a chemical potential that predicts the direction in which a chemical system will spontaneously move |

Difference Between Spontaneity of a Chemical Reaction and the Speed of a Chemical Reaction | In thermodynamics, we study the spontaneity of a reaction - the direction in which and the extent to which a chemical reaction proceeds. In kinetics, we study the speed of the reaction - how fast the reaction takes place |

Catalyst's Effect on Spontaneous Reaction | Although the rate of a spontaneous process can be increase by the use of a catalyst, a nonspontaneous process cannot be made spontaneous by the use of a catalyst. Catalysts affect only rate of reaction, not sponteneity |

Entropy (S) | Entropy (S) is a thermodynamic function that increases with the number of energetically equivalent ways to arrange the components of a system to achieve a particular state |

Entropy Mathematical Expression | S = k * ln(w)... where k is the Boltzmann constant(the gas constant (divided by Avogadro's number) and W is the number of energetically equivalent ways to arrange the components of the system with units of joules per kelvin (J/K) |

Microstate | The exact energy distribution among the particles at any one instant is sometimes referred to as a microstate. A snapshot of the system at any given instant in time. A given macrostate can exist as a result of a large number of different microstates |

The Quantity W | The number of possible microstates that can result in a given macrostate |

Energy Dispersal or Energy Randomization | A state in which a given amount of energy is more highly dispersed(or more highly randomized) has more entropy than a state in which the same energy is more highly concentrated. The state with the highest entropy has the greatest dispersal energy |

Second Law of Thermodynamics | A law stating that for any spontaneous process, the entropy of the universe increases (ΔSuniverse > 0). The criterion for spontaneity is the entropy of the universe. |

Spontaneous and Nonspontaneous Reaction Occurance | Processes that increase the entropy of the universe - those that result in greater dispersal or randomization of energy - occur spontaneously. Processes that decrease the entropy of the universe do not occur spontaneously |

State Function | Entropy is state function. Its value depends only on state of system, not on how it arrived at that state. Therefore, for any process, the change in entropy is entropy of the final state minus entropy of the initial state... ΔS = Sfinal - Sinitial |

Entropy and Direction of Chemical and Physical Changes | A chemical system proceeds in a direction that increases the entropy of the universe - it proceeds in a direction that has the largest number of energetically equivalent ways to arrange its components |

Entropy and State Change | Entropy increases in going from a solid to a liquid and in going from a liquid to a gas |

Entropy Change for the Universe | Is the sum of the entropy changes for the system and the surroundings... ΔSuniv = ΔSsyst + ΔSsurr |

Summarizing Entropy Changes in the Surroundings | 1. An exothermic process increases the entropy of the surroundings.. 2. An endothermic process decreases the entroyp of the surroundings |

1. Quantifying Entropy Changes in the Surroundings | 1. A process that emits heat in the surroundings(qsys negative) increases the entropy of the surroundings(positive ΔSsurr).. 2. A process that absorbs heat from the surroundings(qsys positive) decreases the entropy of the surroundings(negative ΔSsurr) |

2. Quantifying Entropy Changes in the Surroundings | 3. The magnitude of the change in entropy of the surroundings is proportional to the magnitude of qsys... These three points summarized with the proportionality.. ΔSsurr ∝ -qsys |

Entropy and Temperature Relationship | For given amount of heat exchanged with surroundings, the magnitude of ΔSsurr is inversely proportional to the temperature. In general, the higher the temperature, the lower the magnitude of the ΔSsurr for a given amount of heat exchanged.. ΔSsurr ∝ 1/T |

Combining Heat and Temperature Proportionalities for Entropy | ΔSsurr ∝ -qsys / T |

Expression for Calculating Entropy Changes in the Surroundings | Under conditions of constant pressure, qsys = ΔHsys, therefore... ΔSsurr = -ΔHsys / T (at constant temperature and pressure) |

Gibbs Free Energy(G) | A thermodynamic state function related to enthalpy and entropy by the equation G = H - T*S... where H is enthalpy,T is the temp. in kelvins, and S is the entropy. Chemical systems tend towards lower Gibbs free energy, also called the chemical potential |

1. Change in Gibbs Free Energy(ΔG) | ΔG = ΔH - T*ΔS. If we combine Gibbs Free Energy equation with the change Gibbs free energy equation, we get the equation... ΔG = -T*ΔSuniv |

2, Change in Gibbs Free Energy(ΔG) | The change in Gibbs free energy for a process occurring at constant temperature and pressure is proportional to the negative of Δuniv. |

Summarizing Gibbs Free Energy(at Constant Temperature and Pressure) | 1. ΔG is proportional to the negative of ΔSuniv.. 2. A decrease in Gibbs free energy(ΔG < 0) corresponds to a spontaneous process.. 3. An increase in Gibbs free energy(ΔG > 0) corresponds to a nonspontaneous process |

Gibbs Free Energy and Chemical Potential | Gibbs free energy is also called chemical potential because it determines the direction of spontaneous change for chemical systems |

The Effect of ΔH, ΔS, and T on Spontaneity Case 1 | ΔH negative and ΔS positive. If a reaction is exothermic(ΔH>0), and if the change in entropy for the reaction is positive(ΔS>0), then the change in free energy will be negative at all temperatures and the reaction will be spontaneous at all temperatures |

The Effect of ΔH, ΔS, and T on Spontaneity Case 1 Equation | ΔG(negative at all temperatures) = ΔH(negative) - TΔS(positive) |

The Effect of ΔH, ΔS, and T on Spontaneity Case 2 | ΔH positive and ΔS negative. If a reaction is endothermic(ΔH>0), and if the change in entropy for the reaction is negative(ΔS<0), then the change in free energy will be positive and spontaneous at all temperatures |

The Effect of ΔH, ΔS, and T on Spontaneity Case 2 Equation | ΔG(positive at all temperatures) = ΔH(positive) - TΔS(negative) |

The Effect of ΔH, ΔS, and T on Spontaneity Case 3 | ΔH negative and ΔS negative. If reaction is exothermic(ΔH<0), and if change in entropy for reaction is negative(ΔS<0), then change in free energy will depend on temperature. Will be spontaneous at low temperature, but nonspontaneous at high temperature |

The Effect of ΔH, ΔS, and T on Spontaneity Case 3 Equation | ΔG(negative at low temperatures)(positive at high temperatures) = ΔH(negative) - TΔS(negative) |

The Effect of ΔH, ΔS, and T on Spontaneity Case 4 | ΔH positive and ΔS positive. If reaction is endothermic(ΔH>0), and if change in entropy for reaction is positive(ΔS>0), then change in free energy will depend on temperature. Will be nonspontaneous at low temperature but spontaneous at high temperature |

The Effect of ΔH, ΔS, and T on Spontaneity Case 4 Equation | ΔG(positive at low temperatures)(negative at high temperatures) = ΔH(positive) - TΔS(positive) |

Standard State For a Gas | The standard state for a gas is the pure gas at a pressure of exactly 1 atm |

Standard State For a Liquid or Solid | The standard state for a liquid or solid is the pure substance in its most stable form at a pressure of 1 atm and at the temperature of interest(often taken to be 25 degrees Celcius) |

Standard State for a Substance in Solution | The standard stat for a substance in solution is a concentration of 1 M |

Standard Entropy Change for a Reaction(ΔS°rxn) | The change in entropy for a process in which all reactants and products are in their standard states |

Standard Entropy Change Equation | ΔS°rxn = S°products - S°reactants |

Standard Molar Entropy(S°) | A measure of the energy dispersed into one mole of a substance at a particular temperature |

Third Law of Thermodynamics | The entropy of a perfect crystal at absolute zero (0 K) is zero |

Calculating the Standard Entropy Change(ΔS°rxn) for a Reaction | To calculate ΔS°rxn, subtract standard entropies of the reactants multiplied by their stoichiometric coefficients from standard entropies of the products multiplied by their stoichiometric coefficients.. ΔS°rxn = Σ[np*S°(products)] - Σ[nr*S°(reactants)] |

Standard Change in Free Energy(ΔG°rxn) | The change in free energy for a process when all reactants and products are in their standard states |

Free Energy of Formation(ΔG°f) | The free energy of formation(ΔG°f) is the change in free energy when 1 mol of a compound forms from its constituent elements in their standard states. The free energy of formation of pure elements in their standards state is zero |

Standard Change in Free Energy(ΔG°rxn) Equation | ΔG°rxn = Σ[np*ΔG°f(products)] - Σ[nr*ΔG°f(reactants)] |

Reversible Reaction | A reaction that achieves the theoretical limit with respect to free energy and will change direction upon an infinitesimally small change in a variable(such as temperature and pressure) related to the reaction |

Irreversible Reaction | A reaction that does not achieve the theoretical limit of available free energy. All real reaction are irreversible |

Calculating Free Energy Change of a Reaction Under Nonstandard Conditions | We can calculate the free energy change of a reaction under nonstandard conditions(ΔGrxn) from ΔG°rxn using relationship... ΔGrxn = ΔG°rxn + R*T*ln(Q)... where Q is reaction quotient, T is temperature in Kelvins, and R is the gas constant(8.314 J/mol*K) |

Relation for Free Energy(ΔG°rxn) and the Equilibrium Constant(K) | ΔG°rxn = -R*T*ln(K) |

1. Observing The Relationship Between ΔG°rxn and K by Considering the Foloowing Ranges of Values for K | 1. When K<1, ln(K) is negative and ΔG°rxn is positive. At standard conditions(Q=1) reaction spontaneous in reverse direction.. 2. When K>1, ln(K) is positive and ΔG°rxn is negative. At standard conditions(Q=1) reaction spontaneous in forward direction |

2. Observing The Relationship Between ΔG°rxn and K by Considering the Foloowing Ranges of Values for K | 3. When K=1, ln(K) is zero and ΔG°rxn is zero. The reaction happens to be at equilibrium under standard conditions |

Equation for Temperature Dependence of the Equilibrium Constant | ln(K) = (-ΔH°rxn / R)(1/T) + (ΔS°rxn / R)... is in the form y = mx +b. A plot of natural log of equilibrium constant(ln(K)) versus inverse of temperature in kelvins(1/T) yields a straight line with slope of -ΔH°rxn/R and a y-intercept of ΔS°rxn/R |

Equation for Finding ΔH°rxn From a Measurement of Equilibrium Constant at Two Different Temperatures | ln(K2/K1) = (-ΔH°rxn / R)*((1/T2) - (1/T1))... Used to find ΔH°rxn from measured equilibrium constant at two different temperatures, or to find equilibrium at some other temperature if you know equlibrium constant at a given temperature and and ΔH°rxn |