Colligative Properties

What are colligative properties?

Properties that depend on the number of dissolved non-volatile solute species. Colligative properties include:

• Vapour pressure lowering

• Boiling point elevation

• Freezing point depression

• Osmotic pressure

Describe the effect of dissolving a solute in water on the entropy, enthalpy and free energy of the solution.

• Enthalpy increases

• Enthalpy remains constant

• Free energy decreases

The main difference is that enthalpy (S) increases in the solution, and the other effects can be explained by the equation ΔG = ΔH – TΔS

Describe the effect of adding a non-volatile solute to a solvent on the vapour pressure above the resulting solution, in terms of Gibbs free energy.

In this situation, only the solvent is able to evaporate, meanwhile the solute will only be in solution. This means that the solution contains both solute and solvent, while the vapour contains only the solvent.

Before adding the solute, the Gibbs free energy of the liquid must be higher than the vapour, as this allows the solvent to spontaneously evaporate.

When the solute is added, enthalpy of the solution increases, and therefore the Gibbs free energy decreases. This means that the difference between the free energies of the solution and the vapour is now smaller, or even reversed, meaning that less solvent evaporation is able to occur.

By this mechanism, the introduction of a non-volatile solute will decrease the vapour pressure above the solution.

What do positive, negative, and no change in Gibbs free energy (ΔG) mean?

• Negative ΔG: the process will occur spontaneously.

• Zero ΔG: the system is at equilibrium.

• Positive ΔG: the process requires additional energy input in order to occur.

Notice that we are referring to the change in Gibbs free energy when a reaction occurs (ΔG), not to the amount of free energy in one phase (G).

Why is vapour pressure lowering considered to be a colligative property?

When a solute is added to a solvent, this creates a solution with increased entropy. The more solute that is added, the greater the entropy will be.

In turn, when the increase in enthalpy is greater, the decrease in Gibbs free energy will also be greater. When the free energy of the liquid phase decreases, the vapour pressure also decreases. The more the free energy decreases, the lower the vapour pressure will become.

Therefore, the number of solute molecular species added is directly proportional to the reduction in vapour pressure, making this a colligative property.

What is Raoult’s law, and what does it mean?

There are two parts to Raoult’s law:

1. P1 = X1 𝜌1

• Raoult’s law states that the vapour pressure (P1) of a solvent over a dilute solution is equal to the vapour pressure of the pure solvent (𝜌1) multiplied by the mole fraction of solvent in the solution (X1).

• In other words, when a solute is added to the solvent, the mole fraction of solvent in the solution will decrease. This, in turn, will reduce the vapour pressure.

2. ΔP = X2 𝜌1

• The relative vapour pressure lowering (ΔP) depends only on the mole fraction of the solute (X2).

Why is elevation of boiling point considered a colligative property?

Elevation of boiling point is directly proportional to the lowering of vapour pressure when a non-volatile solute is added to a solvent. In turn, it is also directly proportional to the number of dissolved species, making it a colligative property.

What is the freezing point also known as?

Melting point.

Describe the effect of adding a solute to a solvent on the freezing point of the resulting solution, in terms of Gibbs free energy.

In this situation, only the solvent is able to freeze. This means that the solution contains both solute and solvent, while the solid contains only the solvent.

Before adding the solute, the Gibbs free energy of the liquid must be higher than the solid, as this allows the solvent to spontaneously freeze.

When the solute is added, enthalpy of the solution increases, and therefore the Gibbs free energy decreases. This means that the difference between the free energies of the solution and the solid is now smaller, or even reversed, meaning that less freezing is able to occur.

By this mechanism, the introduction of a solute will decrease the freezing point of the solution.

What is osmosis?

The process by which water diffuses across a semi-permeable membrane from areas of low solute concentration to areas of high solute concentration.

What is osmotic pressure?

The pressure which must be applied to a solution to prevent water from flowing in via a semi-permeable membrane.

Why is osmotic pressure considered a colligative property?

Osmotic pressure increases when the number of solute species on one side of the semi-permeable membrane increases. Therefore, the pressure that needs to be exerted on this side of the semi-permeable membrane to prevent osmosis will increase. Therefore, osmotic pressure is directly proportional to the number of solute species.

What is the Van’t Hoff equation, and what types of solutions does it apply to?

πV = nRT, where:

• π is the osmotic pressure

• V is the volume of the solution

• n is the number of moles of solute

• R is the universal gas constant

• T is the absolute temperature (K)

The Van’t Hoff equation only strictly applies to dilute solutions, as there may be deviations when used for more concentrated solutions. However, the general concept remains the same.

What is another useful way that the Van’t Hoff can be expressed, other than πV = nRT?

π = cRT, where c is the concentration of the solute in moles/litre (molarity).

What is another equation that is used, and has been found to compare more closely with experimental findings, than the Van’t Hoff equation?

The Morse equation, which is expressed as π = mRT, where m is the molality of the solution.

What is molality?

Molality is the moles of solute per kilogram of solvent (mol/kg). This is different to molarity, which is the moles of solute per litres of solution. Therefore, molality is not affected by temperature, while molarity is. This makes molality more accurate to the experimental findings.

How is the Morse equation modified when the solute is an electrolyte that dissolves into two or more species?

π = imRT, where i is the number of ions formed when the solute dissolves in water.

When are two solutions considered isosmotic?

Two solutions are considered isosmotic when they each have equal concentrations of dissolved species. In other words, they contain equal osmols, and therefore have equal osmotic pressure.

What measurement is used for the number of dissolved species in a solution?

Osmol, which is the weight in grams of a solute that is osmotically equivalent to a mole of non-electrolyte. To calculate the Osmol/L of a solution:

Osmol/L = M (mol/L) x number of dissolved species

This means that for a non-electrolyte, 1mol = 1Osmol.

How many Osmols are produced when CaCl2 is dissolved in water?

3

What is the definition of osmolality?

The number of molals per litre of water (molal/L)

What is the definition of osmolarity?

The number of Osmols per litre of solution (Osm/L).

What is the key difference between the definitions of osmolality and osmolarity?

Osmolality refers to the mass of solute dissolved in 1kg of water, while osmolarity refers to the mass of solute dissolved in 1 litre of solution.

What is the equation that links the mass of a solute to the number of Osmols, its molecular weight, and the number of species it produces when dissolved in water?

Mass = (Osmol x MW) / (number of species)

What is the definition of an isotonic solution?

A solution which results in no net movement of water across a biological membrane.

What is the difference between isotonicity and isosmoticity?

Isosmoticity means that the solution will not cross a semi-permeable membrane, whereas isotonicity means that the solution will not cross a biological membrane.

Recall that a biological membrane is a type of imperfect semi-permeable membrane, which allows water as well as some types of solutes to pass through. Therefore, an isotonic solution needs to have equal osmolality to the body, and also needs to not contain any solutes that can cross the biological membrane.

What does paratonic mean?

A paratonic solution is one that is not isotonic. This means that it is either hypertonic or hypotonic.

What types of solutes are permeable through a biological membrane?

Urea, propylene glycol, ammonium chloride and glycerol are all permeable through a biological membrane. Some compounds are only permeable through certain biological membranes; for example, boric acid can permeate red blood cells, but not the mucus lining of the eye.

What happens to red blood cells if they are exposed to a hypotonic solution?

Swelling and lysis.

What happens to red blood cells if they are exposed to a hypertonic solution?

Shrinking and crenation.

Which type of paratonic solution is more damaging to red blood cells, and why?

Hypotonic solutions are more damaging as they cause swelling and lysis of red blood cells, which is irreversible. The crenation caused by hypertonic solutions is reversed when the solution is restored to isotonicity.

What are the consequences of injecting a hypotonic IV infusion?

This can result in haemolysis and water invasion into other body cells, which can lead to water intoxication. Symptoms of water intoxication include convulsions and oedema (pulmonary and cerebral). Renal failure may develop from haemoglobinaemia.

What are the considerations for a hypertonic IV infusion?

This can lead to crenation of red blood cells. This causes minimal problems for small infusion volumes injected slowly into a fast-flowing vein, but large volumes delivered too rapidly can cause osmotic diuresis and lead to dehydration. If delivered via a vein with slower circulation, hypertonic solutions can cause irritation to the blood vessel walls and cause them to collapse, resulting in occlusion.

What is an example of a hypertonic, large volume IV infusion, and where is it administered?

Total Parenteral Nutrition (TPN) is administered slowly via the central vein, which is a fast-flowing vein.

What are the consequences of injecting a paratonic intrathecal solution?

Disrupts the osmotic pressure, resulting in headache, vomiting and more serious neurological consequences such as seizures. All intrathecal injections must be strictly isotonic.

What are the tonicity considerations for intramuscular injections?

If the solution is slightly hypertonic, this can encourage dilution by the tissue fluids and result in faster drug absorption.

Why are nasal preparations usually isotonic?

Paratonic solutions in the nasal cavity can irritate the mucosa and interfere with cilial action.

Why are ophthalmic preparations usually isotonic?

Paratonic solutions in the eye can irritate the mucosa, and can flush out the drug and reduce retention time due to tear formation.

What are the tonicity considerations for enteral delivery?

• Enteral feeding solutions are hyperosmotic, but if excessive, this can result in osmotic diarrhoea and mucosal damage.

• In premature infants, high tonicity of enteral feeds is associated with necrotising enterocolitis.

• Oral liquid medications are often highly hyperosmotic; when given to premature infants, this can cause pneumatosis intestinalis.

How can the tonicity of a hypertonic solution be reduced?

Dilution.

Aqueous solutions with the same freezing point are:

Isosmotic

What is the freezing point of biological fluids, including blood plasma and lachrymal fluid?

-0.52C

What is the freezing point depression of biological fluids, including blood plasma and lachrymal fluid?

0.52C

An aqueous solution with a freezing point higher than -0.52C will be:

Hypotonic

An aqueous solution with a freezing point lower than -0.52C will be:

Hypertonic

What solutes can be used to adjust the tonicity of parenteral solutions?

Sodium chloride or dextrose.

What solutes can be used to adjust the tonicity of ophthalmic solutions?

Sodium chloride, boric acid, or occasionally dextrose.

Can boric acid be used to adjust the tonicity of parenteral solutions?

No, because it can permeate through the biological membrane of red blood vessels.

What is the concentration of sodium chloride in aqueous solution that is isotonic to biological fluids?

0.9% w/v

What is the concentration of dextrose that in aqueous solution that is isotonic to biological fluids?

5% w/v

What is the general formula for calculating the amount of adjusting substance required to make a solution isotonic?

w = (0.52 - a) / b

• w: % w/v of adjusting substance

• a: ∆Tf of unadjusted solution (in other words, the total freezing point depression from all solute species in the unadjusted solution)

• b: FD1% of adjusting substance

Regardless of the number of solute species, we need to be able to calculate the value of a. A reformulated equation with this in mind is:

w = [0.52 - (% w/v x FD1%) - (% w/v x FD1%) …] / b

Therefore, to calculate the total freezing point depression of the solution, we need to calculate the percentage concentration of each solute species and multiply by the FD1% of that species.

How do we approach isotonicity calculations using the FD1% method if we need to produce an isotonic solution after dilution?

We need to calculate the percentage concentration of each solute species in the final, diluted solution. This means that any original percentage concentrations may no longer be useful for this calculation.

This also means that all the species, including the adjusting substance, will be hypertonic in the undiluted solution. This is fine!

What does the FD1% mean?

The freezing point depression exerted by a 1% aqueous solution of a solute species.

What does the SCE mean?

The mass (in grams) of sodium chloride that will produce the same osmotic effect as 1 gram of the solute species.

What is the equation used for the sodium chloride equivalence method for isotonicity calculations?

%NaCl = 0.9 - (SCE x %w/v of each solute)

If we are using any adjusting substance other than sodium chloride, we need to divide the final answer by the SCE of that adjusting substance.

What does the superscript “a” mean in the APF table for FD1% or SCE values?

This indicates that these solutes can pass through red blood cell walls. A solution containing these solutes that has a freezing point of -0.52C will be isosmotic with the plasma, but will not be isotonic.

What do we do if a parenteral solution contains a solute that can pass through the membrane of red blood cells?

Leave these substances out of the tonicity calculation, as they will equilibrate on both sides of the membrane.