Determination Of Relative Formula Masses.

number of methods are used depending on the physical states or whether it is in solution.

Colligative Method.

It’s used to determine the RFM on non-volatile solutes in solution.

Colligative properties of a solution.

Colligative property is a physical property of a dilute solution which depends on the concentration or number of particles of a non-volatile solute dissolved in a solvent and not on the nature of the particles.

Examples;

• Osmotic pressure of the solution.
• Lowering of vapour pressure of the solvent.
• Depression of freezing point of the solvent.
• Elevation of boiling point of the pure solvent.

Depression of freezing point of the solvent (cryoscopic method).

Depression of freezing point is reduction of the freezing point of the solvent when a solute is dissolved in it.

It’s a colligative property because the lowering of the freezing point of the solvent is proportional to the number of dissolved particles and doesn’t depend on their nature.

Cryoscopic constant (freezing point lowering constant-Kf)

This is the amount by which the freezing point of a solvent is lowered when one mole of a solute is dissolved in 1kg of a solvent.

The units are degrees/moles/kg.

This constant is a characteristic of each solvent.

Knowing the value of Kf, the RFM of the solute can be worked out.

Determination Of Freezing Point Depression And Hence RFM.

Beckmann’s Apparatus.

Diagram.

The depression of freezing point is small.ie. Less than 1 degree celsius therefore a sensitive thermometer is used to record it.

A glass tube A contains a known weight of solvent, in which the bulb of the Beckmann’s thermometer is immersed. This tube is fitted with a stirrer and has a side arm through which the solid can be introduced. The tube is surrounded by a wider tube which is an air-jacket that ensures uniform cooling. The freezing agent consists of a mixture of ice and salt and is kept stirred by the stirrer.

A weighed amount of solvent is placed in A and both solvent and freezing agent are kept well stirred. Almost invariably super cooling occurs, the temperature of the solvent falling below the true freezing point before solidification starts. The solid solvent begins to separate and the first crystals appear. Temperature T is recorded.

The air jacket is removed and the solvent (freezing mixture) is allowed to gain heat from the room then it melts. Temperature T2 at which the last crystals just disappear is recorded.

A weighed amount of the substance under investigation is introduced in pellet form through the side-arm and stirred until completely dissolved. The air jacket is again placed in the freezing mixture and the mixture stirred and cooled. The temperature T3 at which crystals of solid solvent appear is recorded. It should be noted that when the solution freezes the pure solvent alone separates out. The air jacket is removed from the freezing mixture and the solid solvent is allowed to melt, temperature T4 at which the last crystals disappear is recorded.

The depression of freezing point for a known weight of solute in a known weight of solvent has now been found. Further determinations can be made by adding further weighed quantities of solute, thus discovering the depression of freezing point at different concentrations. In each case the molecular weight is calculated and the average of the results taken.

The depression of the freezing point is also given by T-T3 or T2-T4. ideally these two temperature differences T-T3 and T2-T4 should be identical but in practice they will be different because firstly, a cooled liquid even if stirred doesn’t usually commence to solidify when freezing point is reached but continues to cool in liquid state for several degrees.

This is known as super cooling. Eventually a crystal nucleolus is formed and sudden crystallisation occurs accompanied by a rise in temperature owing to the liberation of the latent heat of solidification.

If the liquid is pure, the temperature finally attained is the freezing point of the quantity of solid solvent separates when freezing occurs after super cooling because the temperature has fallen several degrees below the true freezing point. This is the most convenient method for determining the molecular weight of a substance in solution and it’s employed whenever possible.

For successful application of this method;

• A solvent must be chosen which forms a solution of type in which pure solvent alone separates at the freezing point.
• The solution must be dilute.
• The solute must not change its molecular constitution when entering into solution.

Relationship Between Freezing Point And Vapour Pressure.

The vapour pressure of a pure liquid changes with temperature as shown in the figure below.

Graph.

At the freezing point of the pure liquid T, there is a sharp change in the curve, the vapour pressure, temperature curve, below T1 being that of a solid.

If a non-volatile solid is dissolved in the liquid, the vapour pressure will be lowered and the vapour pressure temperature curve will be shown above.

The freezing point of solution 1 will be T1.

dissolving a non-volatile solute in a liquid causes a lowering of the freezing point. Addition of more solute to form solution 2 causes a further lowering of vapour pressure and the freezing point falls to T2.

For dilute solutions, the areas abe and abc are approximately similar triangles so that ad//eb.ie. the lowering of the freezing point of dilute solution is proportional to the lowering of the vapour pressure of the same solution. This will only apply to a solution which on freezing deposits pure solid solvents. The above method of determination of RFM will only give correct values if;

• The solute used is non-volatile.
• The solute does not dissociate or associate in the solvent.eg. ethanoic acid in benzene can associate to form a dimer.

Structure.

• Dilute solutions are used.
• There is no chemical reaction between solute and solvent.
• The solution on freezing deposits pure solid solvent.

Lowering vapour pressure of solvent.

The reduction in the saturated vapour pressure of a pure liquid/solvent when a solid is introduced, it’s called the lowering of vapour pressure of the solvent.

It’s a colligative property because if a solute is a solid of low vapour pressure (non-volatile), the decrease in the vapour pressure of the liquid will be proportional to the concentration or number of dissolved particles of the solute.

Equilibrium between a liquid and its vapour.

Graph

At any given temperature and pressure a liquid is always in equilibrium with its own vapour. A vapour pressure is established above the liquid and this vapour pressure corresponds to the number of vapour molecules.

Only pure liquid molecules are at the surface and due to surface tension, the surface molecules have an inward pull on them. The vapour above them sets up a vapour pressure of the liquid and this vapour pressure approaches atmospheric pressure towards the boiling point of the liquid hence a liquid boils when its vapour pressure is equal to external pressure.

What happens to the boiling point of the liquid when the atmospheric pressure is lowered?

Fewer vapour molecules will now be needed to make up a vapour pressure equal to the reduced atmospheric pressure less energy (heat) and hence a lower temperature is required for the liquid to boil.

Dissolution of a non-volatile solute in a solvent.

In a solution, there will be even distribution of solid particles throughout the solution. The surface tension of the solution is lower than that of the solvent. Such that fewer solvent molecules escape into the vapour state than for the pure solvent at the same temperature.

There are both solvent and solute particles at the surface and since the solute is non-volatile. The number of solvent particles going into the vapour state at given temperature is reduced.

As a result, vapour pressure lowering and boiling point elevation occur. More heat is required to vaporise more solvent molecules to make up the atmospheric pressure relative formula masses of solutes can be determined by direct observation of vapour pressure changes.

The experimental law governing vapour pressures of dilute solutions of non-volatile solutes, non-electrolytes was formulated by Raoult.

Raoult’s law.

It states that the relative lowering of the vapour pressure of a solvent in a solution containing a non-volatile solute is equal to the mole fraction of the solute in the solution.ie.

Equations.

Examples.

Experiment to measure lowering of vapour pressure.

Diagram.

In the static method, the vapour pressure of the solvent is determined in the usual manner by the barometric technique and then the lowering of vapour pressure is measured directly with the help of a differential manometer.

One arm of the manometer is connected to the solution and the other to the pure solvent. Some non-volatile liquid of low density is used as the manometer indicator and the difference in level of the liquid in the two arms.

Relationship between boiling point and vapour pressure.

The vapour pressure of a pure solvent rises with increasing temperature as shown below. When the vapour pressure reaches external atmospheric pressure, the solvent boils so that the boiling point of the pure solvent is T. a solute dissolved in the solvent gives solution 1 with lower vapour pressure, which will increase with the rise of temperature as the vapour pressure of the pure solvent does. The boiling point of the solution will be T1 which is higher than the boiling point of the pure solvent. Therefore dissolving a non-volatile solid solute in a liquid solvent causes an elevation of boiling point of the solvent. Addition of more solute to form solution 2 will still give a further lowering of vapour pressure and rising of boiling point of solution T2.

Graph.

In the figure above, if dilute solutions are used, the areas ABD and ADE are approximately similar triangles and AB//AE. I.e. Equation.

Therefore the elevation of boiling point of a dilute solution is proportional to the lowering of vapour pressure in the same solution.

Experiment to measure boiling point elevation of a pure solvent due to addition of non-volatilesolute and hence RFM of a non-volatile solute.

The landsberger method.

Vapours of pure solvent are passed through the solution to heat it to boiling point. When the vapours condense, latent heat is given up and the latent heat of condensation raises the temperature of solution to boiling point.

Heating through vapours is done to avoid the danger of superheating. The flask A containing the pure solvent and is connected through a delivery tube to a tube B graduated towards the top of the tube, there’s a hole which permits communication with the outer vessel C.

A condenser which condenses the vapours is attached to D. a thermometer is also fitted through tube B. the thermometer is lowered in the solvent and a stream of vapours of the solvent from A is passed into it until the liquid begins to boil.

When the temperature measured by the thermometer is constant, it is recorded. This is the boiling point of the pure solvent. A weighed quantity of the solute under investigation is then put into the tube B and passage of vapours is continued until the temperature is constant. This is the boiling point of the solution.

The volume of the solution in B is noted. If the density of the solvent is known, the mass of the solvent present in the solution can be easily found. It is assumed that the solute does not occupy any volume. The difference in the two readings gives the boiling point elevation of the solution.

Examples.

Osmotic pressure of solution.

Osmosis is the movement of solvent molecules through a semi-permeable membrane from a dilute solution into a more concentrated solution OR from a solvent into a solution.

Osmotic pressure is one that is required to stop osmosis when the solution is separated from the solvent by the semi-permeable membrane.

It depends only on concentration or number of particles in solution and not on their nature. I.e. it is a colligative property. The laws governing osmotic pressure are the same as those governing gases (gas laws).

Effect of concentration and temperature on osmotic pressure.

Concentration; at a given temperature in dilute solution and so long as the solute is neither dissociated nor associated. The osmotic pressure of a solution is directly proportional to its concentration.

Temperature; under the same conditions for concentration above, no association or dissociation occurs and for a given concentration, the osmotic pressure of a solution is proportional to its absolute temperature.

Relationship with gas laws.

The concentration and temperature have the same effect on the pressure of a gas as for the osmotic pressure of a solution. Hence, for a solution of n moles in a volume V, at a thermodynamic temperature T1 , the osmotic pressure is given by ( equation) where R is the universal gas constant.

Osmotic pressure measurements are used in finding calculation of RFM of compounds particular by macromolecules. A device used to measure osmotic pressure is called osmometer.

Examples.

Measurement of osmotic pressure.

Berkeley and Hartley method.

The solvent is placed in the horizontal tube A, on the sides of which a thin layer of copper Ferro cyanide is deposited. This tube is placed by means of watertight joints into a metal jacket B which contains the solution and carries an attachment C through which pressure can be applied. A is first filled with the solvent through D up to a definite point in the capillary E. as a result of osmosis, the level of liquid in the capillary will fall but by applying pressure through C, it is restored to its initial value. This pressure is taken as the osmotic pressure of the solution.

Diagram.

Vapour density.

It’s the mass of the gas or vapour with mass of an equal volume of hydrogen gas at constant temperature and pressure.

It can be determined experimentally because it involves weighing equal volumes of hydrogen and that of the vapour/gas.

Vapour density can be used to determine RFM of gases and volatile liquids from the relationship RFM= 2 * vapour density.