SPONTANEOUS REACTIONS & ENTROPY

The spontaneity of a reaction merely describes it's tendancy to natuarlly occur in nature without any external influence or work to commence the reaction. A good example would be how a ball has a natural tendancy to roll down a gradient... but things that have no natural tendancy to occur would be considered non-spontaneous such as H₂O decomposing into hydrogen and oxygen. It is also nessasary to understand that it only describes the tendancy for a process to occur and therefore has no say on how quickly the process will happen (could be 1 second or 6 million years).

So what is it that drives Spontaneity?

Entropy is the supposed force responsible for spontaneous change. It measures the tendancy of energy and matter to become disordered. Lets look now at the 2^nd law of thermodynamics which states that the entropy of an isolated system increases for a irreversible reaction although it remains constant in a reversible reaction. i.e the entropy of an isolated system will never decrease. This now can help us see what entropy really is. Entropy is a measure of the distribution (dispersal) of the energy throughout a certain process conducted at a specific temperature.

This can expressed as a formula:

Change in entropy (S)=q_rev/T (q_rev= reversible heat transfer)

The equation is sufficant to solve simple problems of entropy, although if, for example, an ideal gas at a constant temperature begins to expand isothermally, the energy within the gas would be said to be equal to the sum of all the kinetics energies of all the molecules within the gas. If this is the case then the following formula would be more convienient to use:

dS=nRln(V_f/V_i) (where d= delta or differnce in)

And note that in this type of example the entropy of the so called perfect gas will increase logarithmically.

To measure the variation of entropy with the change in temperature then the formula is adapted from the rules of heat capacity at constant volume to give:

dS=C_vln(T_f/T_i)

Now lets consider how to calculate the entropy change associated wwhen a substance melts. We need to assume that at the melting point of the substance any heat energy is used by the system in order to melt the substance. We need to also insist that the procedure needs to be carried out at a constant pressure. Therefore the entropy of fusion is given by:

d_fusS=(d_fusH)/T

The vapourisation of a liquid incurs that the resulting gas will occupy a similar volume as any other liquid. Therefore it can be said that the entropies of vapourisation would be similar for all liquids at their boiling points. This is infact true and the quoted approximate of this value is d_vapS=85J K^-1mol^-1. Note that this is not true for any liquid that is hydrogen bonded. The same equation as the entropy of fusion can be used for vapourisation.

ENTROPY CHANGES IN THE SURROUNDINGS

Using the general definition of entropy, the entropy of the surroundings which is in contact with the system at temperature T is:

dS_surr=q_surr/T

Although now looking at the heat transfers with the system:

q_surr=-q

=> dS_surr=-q/T

=> dS_surr=-q/T=-nRln(V_i/V_f)

This shows that the change in entropy of the surroundings is exactly the opposite to the entropy of the system, implying the total entropy change to equal zero. In an isolated system it cannot be any less than 0 to complie with the second law

This now means that the third law of thermodynamics and absolute entropy can be defined. 'The entropy of a perfectly crystalline solid at a temperature of absolute zero is zero'.

One problem that excisted when finding the spontaneity of a reaction is that once the sum in entropy changes of the system and it's surroundings, what sign to give the resulting problem. This was rectified by a theoretician called Gibbs. Gibbs introduced a new relationship and introduced a term called Gibbs energy/function. This was the theory behind his new relationship:

If dS_tot=dS_sys+dS_surr and dS_surr=-dH_sys/T

Then we can substitute and simplify to -TdS_tot=dH-TdS_sys

If we now introduce Gibbs energy (G), then the expression at constant pressure and temperature:

dG=dH_sys-TdS_sys Note that this equation shows an obvious point that if for a spontaneous reaction the enropy change (dS) needs to be positive, then therefore the Gibbs energy will be negative for a spontaneous reaction. The value of delta G is also related to maximum amount of work for expansion dG=W_max

The formula of dG=dH_sys-TdS_sys use standard values of both the enthalpy and the entropy, if these values are not available however, the standard energies of formation may be used to calculate dG_f^o, within the following formula:

d_rG^o=[sum of]ndG_f(products)-[sum of]ndG_f(reactants). This outcome calculation of this formula will define if a substance is thermodynamically stable by the sign which the result takes... Negative values being stable and positive ones being unstable.

Gibbs energy relationships can be used in order to find out at what temperature a reaction becomes spontaneous. If we know that for a spontaneous reaction dG<0, then therefore it is possible to see that the minimum value that dG can take for spontaneity is 0. therefore:

0=dH-Tds which rearranges to dT=dH/dS.