560 likes | 674 Views
Calculating Equilibrium Composition. Example Cl 2 (g) → 2Cl (g). Calculating Equilibrium Composition. Example: Cl 2 (g) → 2Cl (g) Initially, n 0 moles of Cl 2 gas is placed in a closed reaction vessel. The molecule partially dissociates into atoms.
E N D
Calculating Equilibrium Composition • Example • Cl2 (g) → 2Cl (g)
Calculating Equilibrium Composition • Example: • Cl2 (g) → 2Cl (g) • Initially, n0 moles of Cl2 gas is placed in a closed reaction vessel. • The molecule partially dissociates into atoms.
Calculating Equilibrium Composition • Example • Cl2 (g) → 2Cl (g) • Both are gasses, so use partial pressures rather than concentrations. • We know that at equilibrium we have a definite mixture (i.e., the composition of the mixture is not arbitrary), as the reactants and products are related.
Calculating Equilibrium Composition • What is the expression for the equilibrium quotient?
Calculating Equilibrium Composition • What is the expression for the equilibrium quotient? • We need expressions for the partial pressures at equilibrium.
Calculating Equilibrium Composition Initial No. of moles Cl2 = ?
Calculating Equilibrium Composition Initial No. of moles Cl2 = n0 2Cl = ?
Calculating Equilibrium Composition Initial No. of moles Cl2 = n0 2Cl = 0
Calculating Equilibrium Composition Initial No. of moles Cl2 = n0 2Cl = 0 No. of moles at eq. Cl2 = ?
Calculating Equilibrium Composition Initial No. of moles Cl2 = n0 2Cl = 0 No. of moles at eq. Cl2 = n0 – a
Calculating Equilibrium Composition Initial No. of moles Cl2 = n0 2Cl = 0 No. of moles at eq. Cl2 = n0 – a 2Cl = ?
Calculating Equilibrium Composition Initial No. of moles Cl2 = n0 2Cl = 0 No. of moles at eq. Cl2 = n0 – a 2Cl = 2a
Calculating Equilibrium Composition Initial No. of moles Cl2 = n0 2Cl = 0 No. of moles at eq. Cl2 = n0 – a 2Cl = 2a Mole fractions at eq. Cl2 = ?
Calculating Equilibrium Composition Initial No. of moles Cl2 = n0 2Cl = 0 No. of moles at eq. Cl2 = n0 – a 2Cl = 2a Mole fractions at eq. Cl2 = n0 – a/ n0+a 2 Cl = 2a/n0+a
Calculating Equilibrium Composition Initial No. of moles Cl2 = n0 2Cl = 0 No. of moles at eq. Cl2 = n0 – a 2Cl = 2a Mole fractions at eq. Cl2 = n0 – a/ n0+a 2 Cl = 2a/n0+a Partial pressures at eq. Cl2 = ?
Calculating Equilibrium Composition Initial No. of moles Cl2 = n0 2Cl = 0 No. of moles at eq. Cl2 = n0 – a 2Cl = 2a Mole fractions at eq. Cl2 = n0 – a/ n0+a 2 Cl = 2a/n0+a Partial pressures at eq. Cl2 = (n0 – a/ n0+a)p 2Cl = (2a/n0+a)p
Calculating Equilibrium Composition Initial No. of moles Cl2 = n0 2Cl = 0 No. of moles at eq. Cl2 = n0 – a 2Cl = 2a Mole fractions at eq. Cl2 = n0 – a/ n0+a 2 Cl = 2a/n0+a Partial pressures at eq. Cl2 = (n0 – a/ n0+a)p 2Cl = (2a/n0+a)p Now express Kp in terms of what we have.
Calculating Equilibrium Composition Partial pressures at eq. Cl2 = (n0 – a/ n0+a)p 2Cl = (2a/n0+a)p Now express Kp in terms of what we have. • In terms of partial pressures. Which, in terms of a and n0 is
Calculating Equilibrium Composition Partial pressures at eq. Cl2 = (n0 – a/ n0+a)p 2Cl = (2a/n0+a)p Now express Kp in terms of what we have. • Which in terms of a and the total pressure is
Calculating Equilibrium Composition Partial pressures at eq. Cl2 = (n0 – a/ n0+a)p 2Cl = (2a/n0+a)p Now express Kp in terms of what we have. This can now be expresses in terms of a and p only
Calculating Equilibrium Composition Thus, knowing Kp and the total pressure, we can calculate the equilibrium composition of the mixture.
Common experience: • Low T favours solids • High T favours gases • Similarly for high and low pressure. • Hear we study the conditions under which two (or even three) phases co-exist in equilibrium, at a given p and T.
Phases: Solid, liquid, gases. • Gases exist in only one phase..
Phases: Solid, liquid, gases. • Gases exist in only one phase.. • Liquids primarily also exist in only one phase..
Phases: Solid, liquid, gases. • Gases exist in only one phase.. • Liquids primarily also exist in only one phase.. • Exception: supercritical liquids
Phases: Solid, liquid, gases. • Gases exist in only one phase.. • Liquids primarily also exist in only one phase.. • Exception: supercritical liquids. • Solids: can exist in several phases. • E.g., crystal structures..
Water in a beaker, exists as a single phase. • Water and ice in a beaker = mixture of two distinct phases.
Conditions under which substances spontaneously form S, L, or G • Common experience • T reduces from 300 to 250 K. • Water (liquid) turns to ice (solid) • T increases from 300 to 400 K • Water turns to steam (gas)
Conditions under which substances spontaneously form S, L, or G • Solid CO2 at room temperature. • Sublimes: Turns from solid to gas, with out going through a liquid phase.
Conditions under which substances spontaneously form S, L, or G • What determines which phase is favoured (most thermodynamically stable) at a given p and T? • What is the criterion for stability?
Conditions under which substances spontaneously form S, L, or G • The minimising of the Gibb’s energy. For a pure substance, m = chemical potential, n = mole fraction,
Conditions under which substances spontaneously form S, L, or G • The minimising of the Gibb’s energy. For a pure substance,
Conditions under which substances spontaneously form S, L, or G • Asdm =dGm,
Conditions under which substances spontaneously form S, L, or G • Thus, the variation of m with p and T can be determined.
Conditions under which substances spontaneously form S, L, or G • Sm and Vm are always positive, thus; • m decreases as T increases, and • Increases with increasing p.
Conditions under which substances spontaneously form S, L, or G • The entropy varies slowly with T ( as ln T), • Thus, over a limited T range, • a plot of mv. T at const. p is a straight line of negative slope.
Conditions under which substances spontaneously form S, L, or G • We know from experience that melting and boiling are endothermic. • Thus, DS = DH/T is positive for both of these constant T processes. • We also know that Gasses, liquids and solids all have positive heat capacities.
Conditions under which substances spontaneously form S, L, or G • Therefore,
Conditions under which substances spontaneously form S, L, or G • The entropy of a phase is the magnitude of the slope of mversusT. • Recall
Conditions under which substances spontaneously form S, L, or G Thus, the functional relationship between m and T for solids, liquids, and gasses (at a given p) can be expressed graphically. The stable state at any given T is the phase with the lowest m.
Conditions under which substances spontaneously form S, L, or G Start in the solid phase and increase temperature. As T increases, m decreases with a certain slope.. Note the slopes for liquid and gas are greater. Therefore, they intersect. The points of intersection of the solid/liquid and the liquid/gas are the melting and boiling temperatures, respectively.
Conditions under which substances spontaneously form S, L, or G At the melting point (solid/liquid intersection) both phases exist in equilibrium. However, a further, but small increase in T results in complete melting. Why?
Conditions under which substances spontaneously form S, L, or G At the melting point (solid/liquid intersection) both phases exist in equilibrium. However, a further, but small increase in T results in complete melting. Why? The Liquid phase has a lower m at Tm + dT than the solid phase.
Conditions under which substances spontaneously form S, L, or G At the melting point (solid/liquid intersection) both phases exist in equilibrium. However, a further, but small increase in T results in complete melting. Why? The Liquid phase has a lower m at Tm + dT than the solid phase.
Conditions under which substances spontaneously form S, L, or G Similarly, at Tb both liquid and gas coexist at eq. The system is a gas at T > Tb.
Conditions under which substances spontaneously form S, L, or G Note: the progression from solid to liquid to gas cam be fully explained only by and
Conditions under which substances spontaneously form S, L, or G What is we increase the temperature fast (too fast)?.
Conditions under which substances spontaneously form S, L, or G What is we increase the temperature fast (too fast)?. At a phase change, the system does not reach equilibrium, leading to super heating.
Conditions under which substances spontaneously form S, L, or G What is we increase the temperature fast (too fast)?. At a phase change, the system does not reach equilibrium, leading to super heating (bumping). Similarly, rapid cooling leads to supercooling (e.g., glass formation).