Chapter 4 Solution

Solid state solution Liquid state solution Gas state solution Normal solution Non-electrolyte solution Chapter 4 Solution

4 Solution 4.1 Introduction to solution 4.2 Expression solution composition 4.3 Partial molar quantity & Chem potential 4.4 Rault law and Henry law 4.5 Single chemical potential in mixing gases 4.6 Ideal solution 4.7 Chem. potential in dilute solution 4.8 Colligative properties in dilute solution 4.9 Duhem-Margules formula 4.10 Non-ideal solution 4.11Distribution law

4.1 Introduction to solution Generally speaking, the system which mix evenly by the ionic state of two and upwards substances is called solution.

4.1.1 Solution kinds Three kinds of solutions: gas state solution; solid state solution; and liquid state solution. According to the solute electric properties of the solution electrolyte solution non-electrolyte solution.

4.1.2 Solvent & solute If the substance which compose the solution has different states, the substance of liquid state is usually called solvent, the substance of gas or solid state is called solute. If all of the substance are liquid, therefore the more one is called solvent, the less one is called solute.

4.2 Expression of solution composition In non-electrolyte solution of liquid state, there are mainly four expressions of the concentration of solute B as following: 1. Mole fraction 2. Mass mole concentration 3. Amount-of-substance concentration 4. Mass fraction

mole fraction 4.2.1 Mole fraction The compare of mole of solute B and the total mole of the solution is called mole fraction of solute B, it is also called mole fraction, it has no unit.

4.2.2 Mass mole concentration molality The compare of the mole of solute B and the quantity of solvent A is called mass mole concentration of solute B, its unit is mol.kg-1 the advantage of its expression is that we can use the of weighing to confect solution, it does not affected by the temperature, it is used a great many in the electrochemistry.

4.2.3 Amount-of-substance concentration molality The compare of the mole of the solute B and the solution volume V is called the mole concentration of solute B, or it is called concentration of solute B, its unit is mol.m-3, but its unit in common use is mol.dm-3.

4.2.4 Mass fraction The compare of the mass of solute B and the total mass of solution is called the mass fraction of solute B, its units is 1. mass fraction

4.3 Partial molar quantity & chemical potential 1.Molar thermodynamic value in single component system 2.Partial value in multi-component system 3.Collective formula of partial molar quantity 4.Gibbs-Duhem formula 5.Definition of chemical potential 6.Basic formula in multi-component system 7.Relation between Chemical potential and Pressure 8.Relation between Chemical potential and Temperature

molar enthalpy molar entropy molar Helmholz free energy Molar volume molar Gibbs free energy Molar thermodynamic energy 4.3.1 Molar thermodynamic value in single component system

4.3.2 Partial value in multi-component system 4.3.2.1 Speciality of multi-component system

4.3.2.2 Definition of partial molar quantity In the multi-component system, every variable of thermodynamic function has not only two variables, it also has relationship with the mole of every substance which consists the system. Suppose Z stands for the extensive character of V, U, H, S, A, G and so on, therefore, for the multi-component system. Z=Z(T, p, n1, n2,…, nk)

4.3.2.2.2 Definition of partial molar quantity In the condition of isothermal and isobaric: ZB: partial molar quantity

4.3.2.3 Partial thermodynamic value in multi-component Pay attention to the followings when using partial mole: 1. The meaning of partial mole is that: in the condition which is isothermal, isobaric and the mole of all the composing except substance B unchangeable, or in

4.3.2.3 Partial thermodynamic value in multi-component the condition which is isothermal and isobaric, the change of the extensive character Z which is aroused by joining the unit substance mole B in the abundant fixed composing system.

4.3.2.3 Partial thermodynamic value in multi-component 2. Only extensive character has partial mole, however, partial mole is intensive character. 3. The partial mole of pure substance is its mole. 4. Every partial mole is the function which is composed by T, p and V.

4.3.3 Collective formula of partial molar quantity Keep the partial molar quantity unchangeable, get the formula above integral

4.3.3.2 Collective formula of partial molar quantity This is the collective formula of partial molar quantity, it shows that the total capacity character is equal to the summation of the partial molar quantity of every composing.

4.3.3.2 Collective formula of partial molar quantity For example: the system only has two composing, its mole and partial molar volume separately are n1,V1 and n2,V2, therefore the total system volume is: V= n1V1 + n2V2

4.3.3.3 Collective formula of partial molar quantity Written in the commonly form:

4.3.4 Gibbs-Duhem formula If append every composing in solution not in proportion, therefore the concentration of solution will change, at this moment, both the mole and partial mole of every substance will change.

4.3.4 Gibbs-Duhem formula According to the collective formula Get Z differential coefficient In the condition of isothermal and isobaric, the complete differential coefficient of the capacity character of certain equal phase system is:

4.3.4.2 Gibbs-Duhem formula Compare with (1) (2),. We can get: That is This is called Gibbs-Duhem formula, it shows that there is certain relationship of partial mole. The change of the other partials can be get from the change of certain partial mole., Example A

4.3.5 Definition of chemical potential Narrow definition: Keep the temperature, pressure and the other composing except B unchangeable, the change rate of the system Gibbs free energy is called chemistry potential.

4.3.5 Definition of chemical potential Therefore, the chemistry potential is the partial molar Gibbs free energy Chemical force has important effect in judging the phase change, the way of the chemical change and the limit aspect.

4.3.5 Definition of chemical potential Generalized definition: Keep the character variable and the other composing except B unchangeable, the change rate of the certain thermodynamic function following the mole nB is called chemical force.

4.3.6 Basic formula in multi-component system In the multi-component system, the value of the thermodynamic function not only has relation with its variable. But also the mole of the composing which consist the system. For example: thermodynamic energy

4.3.6 Basic formula in multi-component system That is: • Its complete differential coefficient The same reason

4.3.7 Relation between Chemical potential and Pressure For pure component system, according

4.3.7 Relation between Chemical potential and Pressure to the basic formula, we have: For the multi-component system, turn Gm into µB , therefore the mole volume become partial mole volume VB

4.3.8 Relation between Chemical potential and Temperature According to the basic formula of pure component system,

， 4.3.8 Relation between Chemical potential and Temperature Replace Gm by µB , therefore the mole volume Sm becomes partial mole volume SB.

4.4 Raoult law and Herry law 4.4.1 Raoult’s Law In 1887, france chemist Raoult concluded an experience law from the experiment: under the fixed temperature, in the dilute solution, the vapor pressure of the solvent p*A is equal to the value vapor pressure of pure solvent multiplies the mole fraction XAof the solvent.

4.4.1.2 Raoult law We use formula to figure it out: If there is only two composing the solution, therefore

4.4.1.3 Raoult law Raoult’s Law is also can be expressed: the compare of the decrease value of the vapor pressure of solution and the vapor pressure of pure solution is equal to the mole fraction of solute.

4.4.2 Herry law In 1803, Britain chemist Henry concluded another experience law according to the experiment: under certain temperature and equilibrium state, the compare of gas solubility in the solution and the gas equilibrium partial pressure is direct ratio.

or 4.4.2.2 Herry law We use formula to figure it out: P=kxx kx is called Henry law constant, its value has relationship with temperature, pressure, solvent and the properties of the solute. If the expressions are different, their value are different too, that is:

4.4.2.3 Herry law Pay attention to Henry Law: (1) P in the formula must be the gas partial pressure. For the mix gas, when the total pressure is not large, Henry Law is separately the same with every kind of gas. (2) the molecule state of solute in gas phase or solution must be the same. Such as HCl, in gas phase it is molecule HCl, in solution it is H+ and Cl- .

4.4.2.4 Herry law Therefore, Henry Law is not applicable. (3) the more dilute the solution is, the better accord with Henry Law. For the gas solute, increase the temperature or decrease the pressure, it reduce the solubility, it obeys Henry Law better.

4.5 Single chemical potential in mixing gases Chemical potential of ideal gas Chemical potential of mixing gases *Chemical potential of non-ideal gas

4.5.1 Chemical potential of ideal gas Only one kind of ideal gas,

4.5.1.1 Chemical potential of ideal gas This is the expression of the ideal gas. Chemical potential is the function of T, P.μ$(T,p$)Is the chemical potential of ideal gas when the temperature is T, the pressure is standard one, this state is gas standard state.

4.5.2 chemical potential of mixing gases Chemical potential of certain gas B of the mixing gases This formula is also can be considered to be the definition of ideal mixing gases. Put the Dalton partial pressure law pB= pxB into the previous formula, we can get:

4.5.2 chemical potential of mixing gases μB*(T,p) is the chemical potential of pure gas B when T, p are appointed, obviously, this is not standard state.

4.6 Ideal solution Previous, mixing solution was called ideal solution. Definition of mixing solution: not disparting the solvent and the solute, any composing in all the concentration area accord with Raoult Law; seen from the molecule model, every composing molecule similar with each other, there is no thermal effect and volume when mixing, this kind of solution is called mixing solution.

(4) (1) (2) (3) 4.6 Ideal solution Photics isomer, isotope and mixing solid isomer belong to this kind. General characters of mixing solution: (5) there is no difference between Raoult Law and Henry Law

(1) or (2) 4.6.1 Ideal solution Chemical potential of every composing in the mixing solution In formula (1), μB*(T,p) is not standard state chemical potential, but the one when the total pressure above the solution is P and the temperature is T.

4.6.1 Ideal solution Considering the affect which effect chemical potential by pressure, use formula (2) to denote it, μB$(T) in the formula (2) is the standard state chemical potential. Because of the affect which effect the solution volume by pressure not so large, integral item can be ignored usually,

Chapter 4 Solution