DILATOMETRY

For reaction where there is a decrease (or increase) in the number of molecules, there will a decrease (or increase) in volume as reaction proceed. This can also be made used of to monitor the reaction real−time. This is particular useful for polymerisation reactions.

Example:           n Styrene + initiator   →   Polystyrene.

The reaction normally proceeds at above 60�C. So the initiator (like benzoyl peroxide) and styrene is dissolved in a suitable solvent (like toluene) and placed into a dilatometer with the help of a long needle syringe. The dilatometer is then placed into a constant temperature bath and the height of the solution is watched until it reaches a maximum level (due to thermal expansion as the mixture heats up). This should normally take about 10 minutes. After that you should be able to see a gradual drop in the level of the mixture as the polymerisation proceed.

Let the total moles of styrene consumed when the reaction is complete be ΔM_f and the final drop in height is ΔH_f. If at time t the drop in height is ΔH_t, then;

On condition that the diameter of the glass tube for the dilatometer is uniform. The drop in height can be determine with great precision by the help of a travelling microscope (or cathetometer).

Extra precatuion must be taken to ensure that no gas bubble be present in the reaction mixture as it will expand with time thus giving serious errors to the reading of ΔH_t. Needless to say the reaction mixture must be well stirred. This technique is known as dilatometry.

OTHERS

Any change in measurable properties - pressure, conductivity, pH, etc, − can be exploited to monitor the progress of the reaction real time. Example if there is a gas released from the reaction then the number of mole of gas would be directly proportional to the change in pressure.

PSEUDO RATE LAW

"Pseudo" in Greek means imitation. So pseudo rate laws are not actual rate law but are rate laws which appears to conformed to the results of the experiments because we have performed tricks on it. This is done to simplify the experiments to be conducted.

Example:        d[M] / dt = − k [A]^a[M]

If we measured the rate of the early part of the reaction for varies [M]_os but at a fixed value of [A]_o (the subscript "o" denotes value at time zero), then for all intent and purpose the results measured will be for   d[M] / dt = − k'[M]; a pseudo first-order rate law.

We can then repeat the same series of [M]_i,os for a different value of [A]_o. By repeating this for different [A]_i,os we can collect sufficient data to plot (log k') against (log [A]_i,o). The gradient of the plot should give the value of "a". This technique is often referred to as the method of initial rates. In using this method it is important to remember that it is within 20% to 70% of reaction that the reaction is viewed to achieved a steady state where the rate of production and consumption of the intermediate species are equal. Below 20% reaction there must be a build up of intermediate species and above 70% there will be an increase in consumption, so the steady state approximation might not be applicable.

RELAXATION METHODS

This is a method used for the determination of the forward and reverse rates of reaction in an equilibrium reaction. The concept used here is to "shock" the equilibrium slightly by changing the condition of the equilibrium - like temperature, pressure, spicing with enzymes, catalysts, etc, very, very quickly. As long as the displacement from equilibrium is very small, the rate the restoration of equilibrium will always follow a first-order rate law. This technique requires very sensitive instruments to determine the time taken for it the reaction to come to equilibrium, known as the relaxation time (τ). No measurement of concentration is required.

Let us heat the above equilibrium reaction using microwave. Assuming that [H₂O] changes by   Φ   when the temperature is increased.

Since − k₁ [H₂O] + k_-1 [H⁺] [0H‾] = 0 and assuming   Φ�   to be negligible, then;

where 1/τ = k₁ + k_-1([H⁺] + [0H‾]); Φ_o is the amount of change in [H₂O] immediately after the temperature jump, and Φ the amount of change in [H₂O] under the final new equilibrium. Both in relation to the initial equilibrium.

Let the results be; it took 37 μs (37 x 10‾⁶ s) to reach the new equilibrium (pH = 7) at 298 K. What is the value of k₁ for the dissociation of water?