Physical Chemistry Crib Sheet: Principles of Thermodynamics and Ideal Gases, Summaries of Thermodynamics

Download Physical Chemistry Crib Sheet: Principles of Thermodynamics and Ideal Gases and more Summaries Thermodynamics in PDF only on Docsity! Physical Chemistry Crib Sheet The First Law of Thermodynamics The First Law may be written: ∆U = q + w where ∆U is the change in internal energy of the system, q is the heat given to the system, and w is the work done on the system. We adopt the convention that quantities with primes refer to the surroundings, so that, for example, q′ = −q is the heat given to the surroundings (lost by the system). Expansion work The work done in expansion by a volume dV against an external pressure p ex is given by dw = −p exdV For irreversible expansion, p ex is constant (as when a gas expands into the atmosphere) and by integration, w = −p ex∆V In particular, when the system expands into a vacuum, w = 0. For reversible expansion, the external pressure is controlled to be only infinites- imally smaller than the pressure of the system. For an ideal gas (pV = nRT ), work done as the system expands from volume Vi to Vf is: w = −nRT ln (Vf Vi ) Heating at constant volume At constant volume, dV = 0 and the First Law gives: ∆U = qV The heat capacity at constant volume is defined by: CV = (∂U ∂T ) V so dU = CV dT Heating at constant pressure The enthalpy, H , is defined by: H = U + pV so that the enthalpy change is equal to the heat transferred at constant pressure: ∆H = qp For an ideal gas, since pV = nRT , and gases have a much larger volume than solids and liquids, ∆H = ∆U + ∆ngRT Where ∆ng is the change in amount (number of moles) of gas in the process. The heat capacity at constant pressure is defined by: Cp = (∂H ∂T ) p so dH = Cp dT For an ideal gas, it can be shown that: Cp − CV = nR Reaction enthalpies From Hess’s law (since H is a state function), any reaction enthalpy change, ∆rH , may be expressed in terms of the enthalpies of formation of the products and reactants, ∆fH : ∆rH = ∑ products ν∆fH − ∑ reactants ν∆fH where ν are the stoichiometric coefficients. The temperature dependence of the enthalpy of reaction is given by Kirchoff’s Law : ∆rH (T2) = ∆rH (T1) + ∫ T2 T1 ∆rC p dT where ∆rC p = ∑ products νC p − ∑ reactants νC p Entropy and The Second Law The entropy of the universe never decreases in the course of all observed changes: ∆Suniv = ∆Ssys + ∆Ssurr ≥ 0 A thermodynamic definition of entropy in terms of the heat given reversibly to the system: dS = dqrev T The entropy change of a transition (e.g. vaporisation) at the transition temper- ature is: ∆trsS = ∆trsH Ttrs since the transition is an isothermal reversible process. The entropy change associated with the isothermal expansion of an ideal gas can be shown to be: ∆S = nR ln (Vf Vi )