This guide explains how to calculate the equilibrium composition of the dissociation reaction Cl2(g) → 2Cl(g). It details the initial conditions, equilibrium expressions, and calculations necessary to determine the moles and partial pressures of Cl2 and Cl at equilibrium. We consider the relationship between reactants and products, and use mole fractions and partial pressures to express the equilibrium constant (Kp). Additionally, the factors that influence phase stability of gases, liquids, and solids at various temperatures and pressures are discussed.
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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? • We need expressions for the partial pressures at equilibrium.
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
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.. • 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..
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 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? 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 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).
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