Chapter 7 One-component Phase Equilibrium
1 Chapter 7 One-component Phase Equilibrium
Physical Chemistry Chapter 7 The phase rule Phase: a state of matter that is uniform throughout in chemical composition and physical state. ( Gibbs) Number of phase(p) e Gas or gaseous mixture -single phase Liquid -one, two and three phases two tally miscible liquids- single phase a slurry of ice and water -two phases Solid -a crystal is a single phase an alloy of two metals-two phases(immiscible) one phase(miscible
2 The Phase Rule Phase: a state of matter that is uniform throughout in chemical composition and physical state. (Gibbs) Number of phase (p): Gas or gaseous mixture – single phase Liquid – one, two and three phases two tally miscible liquids – single phase a slurry of ice and water – two phases Solid – a crystal is a single phase an alloy of two metals – two phases (immiscible) - one phase (miscible) Physical Chemistry Chapter 7
Physical Chemistry Chapter 7 The phase rule The difference between(a)a single-phase solution, in which the composition is uniform on a microscopic scale, and(b)a dispersion, in which regions of one component are embedded in a matrix of a second component
3 The Phase Rule (a) (b) The difference between (a) a single-phase solution, in which the composition is uniform on a microscopic scale, and (b) a dispersion, in which regions of one component are embedded in a matrix of a second component. Physical Chemistry Chapter 7
Physical Chemistry Chapter 7 The phase rule The difference between(a) constituent and(b) component constituent: a chemical species(an ion or a molecule that is present in a system component: a chemically independent constituent of a system number of components(c: the minimum number of independent species necessary to define the composition of all the phase present in the system
4 The Phase Rule The difference between (a) constituent and (b) component constituent: a chemical species (an ion or a molecule) that is present in a system component: a chemically independent constituent of a system number of components (c): the minimum number of independent species necessary to define the composition of all the phase present in the system Physical Chemistry Chapter 7
Physical Chemistry Chapter 7 The phase rule When no reaction takes place, The number of constituent= the number of component Pure water: a one-component system water Mixture of ethanol and a two-component system water: ethanol water
5 The Phase Rule When no reaction takes place, The number of constituent = the number of component Pure water: a one-component system Mixture of ethanol and water: a two-component system water ethanol water Physical Chemistry Chapter 7
Physical Chemistry Chapter 7 The phase rule When a reaction takes place CaCO3(s)+ CaO(s)+ CO2( g) Phase 1 Phase 2 Phase 3 a two-component system Cao co CaO+CO2→CaCO3 The number of constituent* the number of component
6 The Phase Rule When a reaction takes place, CaCO3 (s) CaO(s) + CO2 (g) Phase 1 a two-component system CaO CO2 Phase 2 Phase 3 CaO + CO2 → CaCO3 Physical Chemistry Chapter 7 The number of constituent the number of component
Physical Chemistry Chapter 7 The phase rule ● Counting components How many components are present in a system in which ammonium chloride undergoes thermal decomposition? NH4CI(S+ NH3(8)+ HClg Phase 1 Phase 2 three constituents two-component a one-component system additional NHC1∠NH3 or hcl NH4CI→NH3+HC1
7 The Phase Rule Counting components NH4Cl(s) NH3 (g) + HCl(g) Phase 1 a one-component system NH4Cl Phase 2 NH4Cl → NH3 + HCl How many components are present in a system in which ammonium chloride undergoes thermal decomposition? three constituents additional NH3 or HCl two-component Physical Chemistry Chapter 7
Physical Chemistry Chapter 7 The phase rule Degree of freedom or Variance () the number of intensive variables that can be changed independently without disturbing the number of phases in a equilibrium The phase rule: a general relation among the variance f, the number of components c and the number of phases p at equilibrium for a system of any composition f=c-p+2 (7.7) no reactions
8 The Phase Rule Degree of freedom or Variance (f): the number of intensive variables that can be changed independently without disturbing the number of phases in equilibrium. The phase rule: a general relation among the variance f, the number of components c and the number of phases p at equilibrium for a system of any composition. f = c – p + 2 (7.7) no reactions Physical Chemistry Chapter 7
Physical Chemistry Chapter 7 The phase rule Two assumptions no chemical reactions occur (2)every chemical species is present in every phase Counting the total number of intensive variables .(properties that do not depend on the size of the system). The pressure P and temperature T count as 2 Specify the composition of a phase by giving the mole fractions of C-1 components( because x,+x2+... + c=1 and all mole fractions are known if all except one are specified. There are p phases, the total number of composition variables is plc-1). At this stage, the total number of intensive variables is p(c-1)+2
9 The Phase Rule Two assumptions: Counting the total number of intensive variables (properties that do not depend on the size of the system). The pressure P and temperature T count as 2. (1) no chemical reactions occur (2) every chemical species is present in every phase Specify the composition of a phase by giving the mole fractions of c-1 components (because x1+x2+…+xc=1, and all mole fractions are known if all except one are specified.) There are p phases, the total number of composition variables is p(c-1). At this stage, the total number of intensive variables is p(c-1)+2. Physical Chemistry Chapter 7
Physical Chemistry Chapter 7 The phase rule At equilibrium, the chemical potential of a component j must be the same in every phase Aa=B=… for p phase That is, there are p-1 equations to be satisfied for each component 1. as there are c components, the tota number of equations is c(p-1) e each equation reduces the freedom to vary one of the plc-1)+2 intensive variables. It follows that the total variance Is f=p(c-1)+2-c(p-1)=c-p+2 10
10 The Phase Rule At equilibrium, the chemical potential of a component j must be the same in every phase: That is, there are p-1 equations to be satisfied for each component j. as there are c components, the total number of equations is c(p-1). j, = j, =… for p phase Each equation reduces the freedom to vary one of the p(c-1)+2 intensive variables. It follows that the total variance is f = p(c-1) + 2 - c(p-1) = c – p + 2 Physical Chemistry Chapter 7