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Entropy change conclusions

1 Dissolving

When ionic solids dissolve in water two processes occur which both involve large energy changes. Energy must be first put in to separate the oppositely charged ions which attract each other strongly. This energy change is the reverse of the lattice energy. If this were the only process involved, ionic solids would never dissolve because so much energy is required. However, having separated the ions, the bare, charged ions will attract molecules of solvent towards them. This process releases energy as bonds are being formed. The process is called solvation, and is more significant if the solvent molecules are polar, like water.

If more energy is required to break the lattice apart than is released on solvation, the overall process will be endothermic. This is the case on dissolving ammonium nitrate crystals and with quite a few other ionic solids. This means that the entropy change of the surroundings is negative in this case. The driving force for the process is the large increase in entropy of the system on solution. The dissolved ions are far more disordered than the solid, ionic crystal from which they came (twice as many particles and in a more disordered state):

NH4NO3(s) + aq NH4+(aq) + NO3-(aq)

This increase in DSsystem more than compensates for the decrease in DSsurroundings when the temperature drops.


2 A neutralization reaction

Ammonium carbonate is used in smelling salts. You may have noticed a more complicated formula on the bottle. We shall stick with the simple formula that you would predict from ionic formulae. This gives the following equation:

(NH4)2CO3(s) + 2CH3COOH(l) 2CH3COONH4(aq) + H2O(l) + CO2(g)

This forms the salt ammonium ethanoate. There is a clear, positive entropy change in the system. First, there is a change from a solid to a gas and free moving ions. Secondly, there is an increase in the number of particles from two to six (remember that there are four free moving ions in 2CH3COONH4(aq)).

The reaction is endothermic, so there is a decrease in the entropy of the surroundings. However, the reaction is spontaneous, so there must be an increase in the total entropy change. This means that the decrease in the entropy of the surroundings must be outweighed by the increase in the entropy of the system.


3 A combustion reaction

This is a highly exothermic reaction. There is a clear drop in the entropy of the system (the chemicals) as a solid (magnesium) and a gas (oxygen) are converted to a solid (magnesium oxide). There is a decrease in the total number of particles, and a change from the very disordered gas state:

2Mg(s) + O2(g) 2MgO(s)

However, this decrease in the entropy of the system is more than compensated for by the large increase in the entropy of the surroundings when the temperature rises rapidly in the very exothermic reaction.


4 A redox reaction

NH4Cl(aq) + NaNO2(aq) NaCl(aq) + 2H2O(l) + N2(g)

There is a clear increase in the entropy change of the system. This can be seen from the equation. Four particles become five (don't forget that the aqueous ions are separate particles). More importantly, a very disordered gas is produced in this reaction.

The reaction is endothermic so the entropy change of the surroundings is negative. However, this reaction takes place slowly at room temperature. This means that it is spontaneous, and so the total entropy change must be positive. The negative entropy change of the surroundings is outweighed by the positive entropy change of the system.


5An acid-base reaction

In this reaction the temperature goes down, and so the entropy change of the surroundings decreases. The first change that is seen is the formation of a liquid when the two solids dissolve in the water of crystallization of the barium hydroxide:

Ba(OH)2.8H2O(s) + NH4Cl(s) Ba(OH)2(aq) + NH4Cl(aq) + 8H2O(l)

This is followed by an acid-base reaction in which the hydroxide ions from the barium hydroxide react with the hydrogen ions from the ammonium ions to form water. Ammonia gas is formed in this reaction and should have been smelt in the experiment.

NH4+(aq) + OH-(aq) NH3(g) + H2O(l)

Both these changes lead to an increase in the entropy of the system. In the first change two solids are converted to five aqueous ions and eight liquid water molecules. In the second there is no change in the number of particles, but a very disordered gas is produced. The positive entropy change of the system more than outweighs the negative entropy change of the surroundings.


6 A thermal decomposition

This reaction is endothermic (heat had to be supplied) so the entropy change of the surroundings is negative. When we write the equation for the reaction:

ZnCO3(s) ZnO(s) + CO2(g)

DS = + 174.8 J mol-1 K-1

we see that the entropy change of the system is positive. This is because one particle becomes two, and a very disordered gas is produced in the reaction. However, at room temperature the decrease in the entropy of the surroundings clearly outweighs the increase in that of the system. This means the total entropy change is negative, and so the reaction is not spontaneous.

If we raise the temperature, we find that the entropy change of the surroundings becomes less negative. If we also assume that the entropy change of the system is unaffected by the temperature change, there will come a point where the entropy change of the surroundings no longer outweighs the entropy change of the system. At this point, the reaction becomes spontaneous. We can calculate the temperature at which this will occur. You might like to run through the theory of entropy again.

DStotal = DSsystem- DH/T = 0 (when reaction just becomes spontaneous)

Rearranging this equation gives: T = DH/DSsystem

DH = + 71.0 kJ mol-1 = + 71000 J mol-1

T = 71000/174.8 = 406 K = 133 ºC


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