A dilute solution contains m mol of solute A in 1 kg of a solvent with molal elevation constant K_(b). The solute dimerises in solution as 2AhArrA_(2) Select the correct exprression of equilibrium constant 'K' for the dimer formation. (assume molarity = molality)

A dilute solution contains m mol of solute A in 1 kg of a solvent with

1.	A dilute solution contains m mol of solute A in 1 kg of a solvent with molal elevation constant K_(b). The solute dimerises in solution as 2AhArrA_(2) Select the correct exprression of equilibrium constant 'K' for the dimer formation. (assume molarity = molality)
Answer» `K=(K_(b)(K_(b)m-DeltaT_(b)))/((K_(b)m+2DeltaT_(b))^(2))` `K=(alpha)/(2m(1-alpha)^(2))` `K=(K_(b)(K_(b)m-DeltaT_(b)))/((2DeltaT_(b)-K_(b)m)^(2))` `K=(2(K_(b)m-DeltaT_(b)))/(K_(b)m)` Solution : `2A HARR A_(2)` moles at `t=0, m, 0` moles at `t_(eq), m-malpha, (malpha)/2` Total moles `=m-(m alpha)/2=m(1-(alpha)/2)` `DeltaT_(b)=iK_(b)m=K_(b)m(1-(alpha)/2)` `1-(alpha)/2=(DeltaT_(b))/(K_(b)m)` `alpha=(2(K_(b)m-DeltaT_(b)))/(K_(b)m)` Equilibrium constant `K` for the dime FORMATION is `K=([A_(2)])/([A]^(2))=(malpha)/(2[m(1-alpha)]^(2))` `K=(alpha)/(2m(1-alpha)^(2))` `K=(2(K_(b)m-DeltaT_(b)))/(K_(b)m)//2m[1-(2(K_(b)m-DeltaT_(b)))/(K_(b)m)]^(2) ` `K=(K_(b)(K_(b)m-DeltaT_(b)))/((K_(b)m-2K_(b)m+2DeltaT_(b))^(2))` `K=(K_(b)(K_(b)m-DeltaT_(b)))/((2DeltaT_(b)-K_(b)m)^(2))`