Noura Dawass

5 96 P ROPERTIES OF U REA -C HOLINE C HLORIDE M IXTURES Similarly, to find g ωα ( r ), we apply the general expression for RDFs of two differ- ent molecules (Eq. (5.3) ) g ωα ( r ) = n ωα ( r ) N α c ( r ) (5.18) where n ωα ( r ) accounts for two contributions: n βα ( r ) and n γα ( r ). The probability that the central molecule is of type β is N β / N ω . Similarly, the probability that the central molecule is of type γ is N γ / N ω . As a result Eq. (5.18) can be rewritten as g ωα ( r ) = ³ N β N ω n βα ( r ) + N γ N ω n γα ( r ) ´ N α c ( r ) = N β N ω N α n βα ( r ) c ( r ) + N γ N ω N α n γα ( r ) c ( r ) (5.19) Using Eqs. (5.9) and (5.10) results in g ωα ( r ) = N β g βα ( r ) + N γ g γα ( r ) N ω (5.20) In the same way, Eqs. (5.17) and (5.20) can be generalized for the case of a system of component α and n indistinguishable components 1, 2, 3,... n denoted as ω . The RDFs of the pseudo-binary mixture composed of α and ω ( N ω = N 1 + N 2 + .... N n ) can be written as: g ωω ( r ) = n P i = 1 n P j = 1 N i N j g i j ( r ) µ n P i = 1 N i ¶ 2 (5.21) g ωα ( r ) = n P i = 1 N i g i α ( r ) n P i = 1 N i (5.22) In the case of an ideal gas, RDFs of the combined molecules g ωω ( r ) and g ωα ( r ) should converge to ( N ω − 1)/ N ω and 1, respectively. Considering an ideal gas mixture that consists of α and n indistinguishable components, we start with Eq. (5.21) and substitute the RDFs in the expressions with the ideal gas answer: g ii ( r ) = ( N i − 1)/ N i and g i j ( r ) = 1 (where i 6 = j ). This results in: