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Properties, whose values depend only on the concentration of solute particles in solution and not on the identity of the solute are called colligative properties.there may be change in number of moles of solute due to ionisation or association hence these properties are also affected.Number of moles of the product is related to degree of ionisation or association by van Hoff factor 'i' given by i=[1+(n-1)alpha] for dissociation where n is the number of products (ions or molecules ) obtained per mole of the reactant. & i=[1+(1/n-1)alpha] for association where n is number of reactant particles associated to give 1 mole product.A dilute solution contains 't' moles of solute X in 1 kg of solvent with molal elevation constant K_b.The solute dimerises in the solution according to the following equation.The degree of association is alpha. 2X hArr X_2 The equilibrium constant for the process can be expressed as |
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Answer» `K=(K_b t/(DeltaT_b))/(1-(K_bt)/(DeltaT_f))` Here`{:(2X,hArr,X_2),(t, , 0):}` `1-talpha(talpha)/2{(DeltaT_b,=(1-alpha//2)K_bt),(alpha,=alpha=(2(K_bt-DeltaT_b))/(K_bt)):}` `implies [X_2]=talpha//2` `[X]=t-talpha` `K=(talpha//2)/((t-talpha)^2)=1/(2t^2)xxalpha/((1-alpha)^2)=1/(2t)xxalpha/((1-alpha)^2)=1/(2t)XX((2(K_bt-DeltaT_b))/(K_bt))/(1-((2(K_bt-DeltaT_b))/(K_bt))^2)` Hence , `K=(K_b(K_bt-DeltaT_b))/((2DeltaT_b-K_bt)^2)` |
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