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Chemical Equilibrium, Law Of Mass-action : Equilibrium, Effect Of Temperature And Pressure |
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The dissociation of hydrogen iodide cannot be measured by the change of density, because the volume is unchanged. It is easily shown that the extent of dissociation of hydrogen iodide is unaffected by pressure. Let 2 gm mols. be heated in a volume V and let the degree of dissociation be γ. The numbers of gram molecules present in equilibrium are: 2HI(2-2γ) <=> H2(γ) + I2(γ), hence the concentrations are: [HI] = 2(1 - γ)/V; [H2]= γ/V; [I2] = γ/V K = [H2][I2]/[HI] = γ2/4(1 - γ)2, which is independent of the volume V, and therefore of the pressure This result is obtained in all cases where the total volume is unchanged by the reaction. If an increase of volume occurs, the extent of dissociation can be measured from the vapour density. This is the case with phosphorus pentachloride: PCl5 <=> PCl3 + Cl2. Let V be the volume and γ the extent of dissociation, then the concentrations are: [PCl5] = (I - γ)/V, [PCl3] = γ/V; [Cl2] = γ/V;  The extent of dissociation now depends on the volume, V, and therefore on the pressure. If V is increased (i.e., the pressure diminished), the denominator in the above expression for K becomes too large; the numerator and therefore γ, must also increase in order to maintain the value of the equilibrium constant. Hence the dissociation increases in this reaction when the pressure is reduced. The same effect is produced by adding an indifferent gas, which reduces the partial pressures. A change of volume or pressure influences the state of equilibrium only when the chemical reaction causes a change of volume (e.g., PCl5 (1 vol.) = PCl3 + Cl2 (2 vols.)). If no change of volume occurs (e.g., 2HI = H2 + I2) pressure has no influence on the equilibrium. If the pressure on a system in equilibrium is increased, that change occurs which leads to a diminution of volume, i.e., a decrease of pressure, and the equilibrium is correspondingly shifted. This is a special case of Le Chatelier's law of reaction: if a system in equilibrium is subjected to a constraint, a change occurs if possible of such a kind that the constraint is partially annulled. The effect of pressure on equilibrium is so regulated. Another aspect of this law is the effect of temperature on equilibrium. If the temperature of a system in equilibrium is raised (or lowered), that one of the two reversible reactions will occur which absorbs (or evolves) heat. Thus, the dissociation of PCl5 is increased by raising the temperature, because the reaction PCl5 = PCl3 + Cl2 occurs with absorption of heat. If Qv is the heat of reaction evolved at constant volume and K1, K2 are the equilibrium constants corresponding with the absolute temperatures T1 and T2, then it is shown by thermodynamics that if 1 gm. molecule of substance is taken: logK2 - logK1 =  .In this way the heat of reaction may be calculated. Example. 2.0 gm. of PCl5 are sealed in an evacuated bulb of 200 c.c. capacity, heated at 200°. Find the pressure developed if PCl5 is 48.5 per cent, dissociated under 1 atm. pressure at 200° C.
2.0 gm. of PCl5 = 2.0/208 = 0.0096 gm. mol. Let x = degree of dissociation under the conditions of experiment. Let the volumes be measured in litres; then [PCl5] = 0.0096(1-x)/0.2; [PCl3] = [Cl2] = 0.0096x/0.2; K = 0.0096x2/0.2(1-x) (i) At 200° under 1 atm. pressure PCl5 is 48.5 per cent, dissociated. The volume of 1 gm. mol. under these conditions is 22.4 x 1.485 x 473/273 = 57.6 litres. Hence K = (0.485)2/0.515 x 57.6 = 0.00793 (ii) From the two expressions for K we find, on solving the quadratic. equation, x = 0.332. There are thus 1.332 x 0.0096 gm. mols in 200 c.c., and the pressure is therefore 1.332 x 0.0096 x 22.4/0.2 x 473/273 = 2.48 atm. The degree of dissociation is reduced from 0.485 to 0.332 when the pressure is raised from 1 to 2.48 atm. |
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