Preparing to study mixtures Imagine an indefinitely large volume of water When a further 1 mol of ho is added the volume increases by 18 cm3 The quantity 1 8 cm. mol Is the molar volume of pure water Now suppose that I mol of water is added to a large volume of pure ethanol the volume increases by only 14 cms Is found that It The quantity 14 cm3. mol-I is 4上一内容下一内容令回主目录 返回 2021/2/22
上一内容 下一内容 回主目录 返回 2021/2/22 Preparing to study mixtures: Imagine an indefinitely large volume of water. When a further 1 mol of H2O is added the volume increases by 18 cm3 . The quantity 18 cm3 ·mol-1 is the molar volume of pure water. Now suppose that 1 mol of water is added to a large volume of pure ethanol. It is found that the volume increases by only 14 cm3 . The quantity 14 cm3 ·mol-1 is
the partial molar volume of water in pure ethanol. The definition of partial molar volume has depended on the constancy of the original composition of the solution The system is taken to be so large that the addition of a does not change the mole fractions The same constancy can be assured if the sample is finite, but the addition of A is limited to an infinitesimal amount 4上一内容下一内容令回主目录 返回 2021/2/22
上一内容 下一内容 回主目录 返回 2021/2/22 the partial molar volume of water in pure ethanol. The definition of partial molar volume has depended on the constancy of the original composition of the solution. The system is taken to be so large that the addition of A does not change the mole fractions. The same constancy can be assured if the sample is finite, but the addition of A is limited to an infinitesimal amount
y is a state function that depends on the amounts of a and b present Therefore dv is an exact differential and can be written n,+ A B a/tP, nB B T, P,n4 The partial molar volumes may be identified with the partial derivatives pm=(OV/OnB)r p 4上一内容下一内容令回主目录 返回 2021/2/22
上一内容 下一内容 回主目录 返回 2021/2/22 V is a state function that depends on the amounts of A and B present. Therefore dV is an exact differential,and can be written B T P n B A T P n A dn n V dn n V dV B A , , , , + = The partial molar volumes may be identified with the partial derivatives: VB,m = B T P nA V n , , ( / )
Definition of partial molar quantities The concept of partial molar quantity can be extended to any of the extensive thermodynamic state functions-Z The partial molar quantity ofZ 2 def az B p,n2(c≠B) B 4上一内容下一内容◇回主目录 返回 2021/2/22
上一内容 下一内容 回主目录 返回 2021/2/22 Definition of partial molar quantities B , , (c B) B def ( )T p nc Z Z n The partial molar quantity of Z ： The concept of partial molar quantity can be extended to any of the extensive thermodynamic state functions – Z
Multi-component systems The state function z is a function of composition as well as pressure and temperature and should therefore be written Z=Z(7,p,n2n2…n) At const. t and p aZ On,,pn2“n dn,+(-) T,p,n1,n3…,k aZ aZ …+ on )T, p, m,, "nurk ∑() P,n2(c≠B) dr B 4上一内容下一内容令回主目录 返回 2021/2/22
上一内容 下一内容 回主目录 返回 2021/2/22 Multi-component systems The state function Z is a function of composition as well as pressure and temperature, and should therefore be written 1 2 k Z Z T p n n n = ( , , , , , ) At const. T and P ： 2 k 1 3 k 1 k-1 , , , , 1 , , , , , 2 1 2 , , , , k k d ( ) d ( ) d + ( ) d T p n n T p n n n T p n n Z Z n n n n Z n n Z = + + k , , ( B) B=1 B = ( )T p n c c Z n dnB