Physical Chemistr Solutions s Solution volume and partial molar volumes e The change in volume on mixing the solution from its pure components at constant T and P is given by the difference of (9.16)and(9.4) ∑nP,Ome- phase syst (9.16) V=nVm+n2Vm2+…+nVm=∑nVm AmisV=V-V=>n, ( Vi-Vm )const. T, P (9.17) Mean ∑x (9.16) molar volume n=∑n
Solution volume and partial molar volumes Solutions The change in volume on mixing the solution from its pure components at constant T and P is given by the difference of (9.16) and (9.4) = − i i i V n V one phase syst. (9.16)* = + + + = i V nVm n Vm nr Vm r ni Vm i * , * , * 2 ,2 * 1 ,1 * (9.4) V V V n V V const T P i m i i mix i ( ) . , * , * − = − (9.17) = i i Vm xi V (9.16)* i m n ni n V V , Mean molar volume Physical Chemistry
Physical Chemistry Solutions Measurement of partial molar volumes e Partial molar volumes can be measured in several ways One method is to measure the dependence of the volume on the composition and to fit the observed volume to a function of the mole fraction xa by using a computer curve-fitting problem (i. e, by finding the parameters that give a best fit of a particular function to the experimental data). Once the function has been found, its slope can be determined at any composition of interest by differentiation a+bx4+c(x4-1) With particular values of the parameters a, b, C, and with n=xn 6+2c A PT
Measurement of partial molar volumes Solutions Partial molar volumes can be measured in several ways. ( 1) 2 Vm = a + bxA + c xA − A A P T m A b cx x V V 2 , = + = With particular values of the parameters a, b, c, and with One method is to measure the dependence of the volume on the composition and to fit the observed volume to a function of the mole fraction xA by using a computer curve-fitting problem (i.e., by finding the parameters that give a best fit of a particular function to the experimental data). Once the function has been found, its slope can be determined at any composition of interest by differentiation. nA = xA n Physical Chemistry