Unit 2.1 SOLUTION

LeC 4                          SOLUTIONS

Mostly of the reaction in laboratories are carried out in the form of solution so we have to study  solution. we will consider mostly liquid solutions and their formation. This will be followed by studying the properties of the solutions, like vapour pressure and colligative properties. We will begin with types of solutions and then various alternatives in which concentrations of a solute can be expressed in liquid solution.

Solutions are homogeneous mixtures of two or more than two components. By homogenous mixture we mean that its composition and properties are uniform throughout the mixture. Generally, the component that is present in the largest quantity is known as solvent. Solvent determines the physical state in which solution exists. One or more components present in the solution other than solvent are called solutes. In this section we shall consider only binary solutions i.e. solution of two componenets. 

Therefore, it is important to understand as how the amount of substance is expressed when it is present in the form of a solution. The concentration of a solution or the amount of substance present in its given volume can be expressed in any of the following ways.

1. Mass per cent or weight per cent (w/w %) or Volume Per cent (v/V%)

2. Mole fraction

3. Molarity

4. Molality

5. Part per Million

6. Normality

Let us now study four of them in detail, we will Normality study in  12^th standard.

1. Mass per cent or weight per cent (w/w %) or Volume Per cent (v/V%)

The mass percentage of a component of a solution is defined as:

For example, if a solution is described by 10% glucose in water by mass, it means that 10 g of glucose is dissolved in 90 g of water resulting in a 100 g solution

similarly we can define the Volume percent as

For example, 10% ethanol solution in water means that 10 mL of ethanol is dissolved in 90 mL water such that the total volume of the solution is 100 mL.

2. Mole fraction

Commonly used symbol for mole fraction is x and subscript used on the right hand side of x denotes the component. It is defined as:

For example, in a binary mixture, if the number of moles of A and B are nA and nB respectively, the mole fraction of A  & B will be

if there are i component in the solution then there is i mole fraction and sum of all mole fraction is unity.

3. Molarity

Molarity (M) is defined as number of moles of solute dissolved in one litre (or one cubic decimetre) of solution,

For example, 0.25 mol/L (or 0.25 M) solution of NaOH means that 0.25 mol of NaOH has been dissolved in one litre (or one cubic decimetre).

4. Molality

Molality (m) is defined as the number of moles of the solute per kilogram (kg) of the solvent and is expressed as:

For example, 1.00 mol/kg (or 1.00 m) solution of KCl means that 1 mole (74.5 g) of KCl is dissolved in 1 kg of water.

Each method of expressing concentration of the solutions has its own merits and demerits. Mass %, mole fraction and molality are independent of temperature, whereas Molarity is a function of temperature. This is because volume depends on temperature and the mass does not.

Problem: Calculate (a) molality (b) molarity and (c) mole fraction of KI if the density of 20% (mass/mass) aqueous KI is 1.202 g/mL.

5. Part per Million

Parts per million: When a solute is present in trace quantities, it is convenient to express concentration in parts per million (ppm) and is defined as:

As in the case of percentage, concentration in parts per million can also be expressed as mass to mass, volume to volume and mass to volume. A litre of sea water (which weighs 1030 g) contains about 6 × 10–3 g of dissolved oxygen (O2). Such a small concentration is also expressed as 5.8 g per 106 g (5.8 ppm) of sea water. The concentration of pollutants in water or atmosphere is often expressed in terms of μg/mL or ppm.

Solubility 

Solubility of a substance is its maximum amount that can be dissolved in a specified amount of solvent. It depends upon the nature of solute and solvent as well as temperature and pressure. this is the reason that we can mix a certain amount of sugar or salt in water, upto its solubility we cant mix more salt or sugar at that temperature and pressure. if we want to mix more amount of sugar then we have to change its temperature and pressure.

Let us discuss solution of solid in liquid, gas in liquid and liquid in liquid.

Solubility of a Solid in a Liquid

Every solid does not dissolve in all liquid,  a solute dissolves in a solvent if the intermolecular interactions are similar in the both solute and solvent.we may say like dissolves like .It is observed that polar solutes dissolve in polar solvents and non polar solutes in nonpolar solvents.

for example sodium chloride and sugar dissolve readily in water, naphthalene and anthracene do not. On the other hand, naphthalene and anthracene dissolve readily in benzene but sodium chloride and sugar do not. 

When a solid solute is added to the solvent, some solute dissolves and its concentration increases in solution. This process is known as dissolution. Some solute particles in solution collide with the solid solute particles and get separated out of solution. This process is known as crystallisation. 

A stage is reached when the two processes occur at the same rate. Under such conditions, number of solute particles going into solution will be equal to the solute particles separating out and a state of dynamic equilibrium is reached.At this stage the concentration of solute in solution will remain constant under the given conditions, i.e., temperature and pressure.

Solute + Solvent -------------> Solution + Heat

Similar process is followed when gases are dissolved in liquid solvents. Such a solution in which no more solute can be dissolved at the same temperature and pressure is called a saturated solution. An unsaturated solution is one in which more solute can be dissolved at the same temperature.

The solution which is in dynamic equilibrium with undissolved solute is the saturated solution and contains the maximum amount of solute dissolved in a given amount of solvent. Thus, the concentration of solute in such a solution is its solubility.

we have observed that solubility of one substance into another depends on the nature of the substances. In addition to these variables, two other parameters, i.e., temperature and pressure also control this phenomenon.

Effect of Temperature & Pressure 

The solubility of a solid in a liquid is significantly affected by temperature changes and must follow Le Chateliers Principle. In general, if in a nearly saturated solution, the dissolution process is endothermic (Δsol H > 0), the solubility should increase with rise in temperature and if it is exothermic (Δsol H > 0) the solubility should decrease. These trends are also observed experimentally.

Pressure does not have any significant effect on solubility of solids in liquids. It is so because solids and liquids are highly incompressible and practically remain unaffected by changes in pressure

before discuss gas in liquid and liquid in liquid lets discuss vapour pressure.

vapour pressure

The vapor pressure of a liquid is the equilibrium pressure of a vapor above its liquid (or solid), that is, the pressure of the vapor resulting from evaporation of a liquid (or solid) above a sample of the liquid (or solid) in a closed container. The vapor pressure of a liquid varies with its temperature, As the temperature of a liquid or solid increases its vapor pressure also increases

Factors That Affect Vapor Pressure:

1) Surface Area: the surface area of the solid or liquid in contact with the gas has no effect on the vapor pressure.

2)Types of Molecules: the types of molecules that make up a solid or liquid determine its vapor pressure. If the intermolecular forces between molecules are relatively strong, the vapor pressure will be relatively low and if relatively weak, intermolecular forces between molecules are weak the vapor pressure will be relatively high.

3) Temperature: at a higher temperature, more molecules have enough energy to escape from the liquid or solid

Solubility of a Gas in a Liquid

Many gases dissolve in water. Oxygen dissolves only to a small extent in water. It is this dissolved oxygen which sustains all aquatic life. Solubility of gases in liquids is greatly affected by pressure and temperature. The solubility of gases increase with increase of pressure. For solution of gases in a solvent, consider a system as shown in Fig.. The lower part is solution and the upper part is gaseous system at pressure p and temperature T. Assume this system to be in a state of dynamic equilibrium, i.e., under these conditions rate of

gaseous particles entering and leaving the solution phase is the same. Now increase the pressure over the solution phase by compressing the gas to a smaller volume. 

This will increase the number of gaseous particles per unit volume over the solution and also the rate at which the gaseous particles are striking the surface of solution to enter it. The solubility of the gas will increase until a new equilibrium is reached resulting in an increase in the pressure of a gas above the solution and thus its solubility increases.

Henry was the first to give a quantitative relation between pressure and solubility of a gas in a solvent which is known as Henry’s law. The law states that at a constant temperature “the

partial pressure of the gas in vapour phase (p) is proportional to the mole fraction of the gas (x) in the solution” and is expressed as:

p = KH x

Here KH is the Henry’s law constant. If we draw a graph between partial pressure of the gas  HCl (in torr) versus mole fraction of the gas in solution, then we should get a plot of the type as shown in Fig. 

Different gases have different KH values at the same temperature. This suggests that KH is a function of the nature of the gas.

It is obvious from equation that higher the value of KH at a given pressure, the lower is the solubility of the gas in the liquid.

It can be seen that KH values for both N2 and O2 increase with increase of temperature indicating that the solubility of gases increases with decrease of temperature. It is due to this reason that aquatic species are more comfortable in cold waters rather than in warm waters.

we can see application of Henry's laws in soft drinks, scuba drivers, people living at high altitude.

Effect of Temperature:

When dissolved, the gas molecules are present in liquid phase and the process of dissolution can be considered similar to condensation and heat is evolved in this process. We have learnt in the last Section that dissolution process involves dynamic equilibrium and thus must follow Le Chatelier’s Principle. As dissolution is an exothermic process, the solubility should decrease with increase of temperature.

Liquid - Liquid Solution

Let us consider a binary solution of two volatile liquids and denote the two components as 1 and 2. When taken in a closed vessel, both the components would evaporate and eventually an equilibrium would be established between vapour phase and the liquid phase. Let the total vapour pressure at this stage be ptotal and p1 and p2 be the partial vapour pressures of the two components 1 and 2 respectively. These partial pressures are related to the mole fractions x1 and x2 of the two components 1 and 2 respectively.

The relationship is known as the Raoult’s law which states that for a solution of volatile liquids, the partial vapour pressure of each component in the solution is directly proportional to its mole fraction.

Thus, for component 1

Following conclusions can be drawn from equation:

(i) Total vapour pressure over the solution can be related to the mole fraction of any one component.

(ii) Total vapour pressure over the solution varies linearly with the mole fraction of component 2.

(iii) Depending on the vapour pressures of the pure components 1 and 2, total vapour pressure over the solution decreases or increases with the increase of the mole fraction of component 1.

A plot of p1 or p2 versus the mole fractions x1 and x2 for a solution gives a linear plot as shown in Fig. These lines (I and II) pass through the points and respectively when x1 and x2 equal

unity. Similarly the plot (line III) of ptotal versus x2 is also linear. 

The composition of vapour phase in equilibrium with the solution is determined by the partial pressures of the components. If y1 and y2 are the mole fractions of the components 1 and 2 respectively in the vapour phase then, using Dalton’s law of partial pressures