CRITERI
5. CONTEXT
5.2.4. Documents d’escola
Comparing the stabilities of Group 1 and Group 2 compounds:
o Group 1 compounds are more stable than group 2 compounds, particularly when group adjacent elements on the same period.
o The reason being the polarising effect of the group I cation M+, is much less than the polarising power of the smaller and more highly charged group II M2+ ion, particularly when comparing adjacent metals on the same period.
The group 2 cation is both smaller and more highly charged than the corresponding group 1 cation.
A thermodynamic discussion on the thermal stability of s–block compounds I'm referring to oxyanion compounds like carbonates, sulfates, hydroxides and sulfates
What ensues is a completely alternative explanation of the thermal stability trends of the oxyanion compounds of alkali metals and alkaline earth metals without any reference to the relative polarising effect of the cation.
It may seem curious at first sight, but large cations can stabilise large anions in a crystal lattice (and vice versa).
o The decomposition temperatures of thermally unstable compounds containing large anions e.g. carbonates, increases with cation radius.
o The stabilizing influence of a cation can be explained in terms of trends in lattice enthalpies (lattice energies).
o The arguments given below are purely in terms of the thermodynamics and explain the Group 2 carbonate stability trend without reference to the polarising power of the cation (which is the argument required by most UK GCE A level syllabuses).
An initial discussion of the Group II carbonate stability trend illustrates the points made above.
o A study of the thermal decomposition temperatures of the Group 2 Alkaline Earth carbonates proves most instructive.
o The general decomposition equation for group II carbonates to give the group II oxide is
MCO3(s) ==> MO(s) + CO2(g)
M = Be, Mg, Ca, Sr and Ba
Beryllium carbonate is not very stable (can be stabilised in an atmosphere of CO2) and radium carbonate would be rather too radioactive to study!
MCO3 and MO are sometimes referred to as the alkaline–earth carbonates and alkaline–earth oxides.
Most of the data tabulated below was obtained from 'Inorganic Chemistry' 2nd edition, by Shriver, Atkins and Langford and the Nuffield Science Book of Data (revised edition 1988) plus internet research for research papers quoting as upto date values as I could find.
Thermodynamic and decomposition temperature data for Group II carbonates of the periodic table.
the basis for the purely thermodynamic argument for the Group II carbonate thermal stability trend
Decomposition
data Be Mg Ca Sr Ba
ΔGØ (kJ mol–1) ? +48.3 +130.4 +183.8 +218.1
ΔHØ (kJ mol–1) ? +100.6 +178.3 +234.6 +269.3
ΔSØ (J K–1 mol–1) ? +175.0 +160.6 +171.0 +172.1
Tdecomp (oC, K)
theoretical ? 302, 575 837, 1110 1099, 1372 1292, 1565
Typical quoted decomposition temperatures
~100oC 400 oC 900 oC 1280 oC 1360oC
LEØMCO3 (kJ mol–1) ? 3180 2987 2720 2615
LEØMO (kJ mol–1) 4443 3960 3489 3248 3011
ΔLE(MO–MCO3) ? 780 502 528 396 M2+ radius in nm Be2+ = 0.034 Mg2+ = 0.078 Ca2+ = 0.100 Sr2+ = 0.127 Ba2+ = 0.143
other radii: oxide ion O2– = 0.140 nm, carbonate ion CO3
2– = 0.176 nm
ΔGØ = standard Gibbs free energy change for the thermal decomposition of the carbonate MCO3 (at 298K, 1
atm)ΔHØ = standard enthalpy change for the thermal decomposition of the carbonate MCO3 (at 298K, 1 atm)
ΔSØ = standard entropy change for the thermal decomposition of MCO3 (at 298K, 1 atm) o Note ΔSØ = ΔSØsystem and is NOT ΔSØsurroundings ...
o ... see theory of the method of calculating the decomposition temperature below.
Tdecomp = decomposition temperature in Celsius and Kelvin when the equilibrium pressure pCO2 = 1 atm
(101kPa)
LEØMCO3 = lattice enthalpy/lattice energy of the group 2 carbonate MCO3 (at 298K, 1 atm. pressure)
LEØMO = lattice enthalpy/lattice energy of the group 2 oxide MO (at 298K, 1 atm. pressure)
ΔLE(MO–MCO3) is the difference between the lattice enthalpies of the group 2 oxide and the corresponding group 2 carbonate
The decomposition temperature was calculated as follows ...
o (i) From the Gibbs free energy equation
ΔGØ = ΔHØ – TΔSØ (terms defined above)
The criteria for equilibrium is when ΔG = 0
therefore at equilibrium: ΔHØ – TΔSØ = 0, and rearranging terms and signs gives
TΔSØ = ΔHØ, therefore T = ΔHØ / ΔSØ
= decomposition temperature (K) to give an equilibrium pressure of 1 atm of carbon dioxide gas o (ii) From the total entropy change equation
This is if your course doesn't involve free energy, or just an alternative method depending on what data is given or available.
ΔSØtotal = ΔSØsystem + ΔSØsurroundings
The criteria for equilibrium is that ΔSØtotal = 0
therefore at equilibrium: 0 = ΔSØsystem + ΔSØsurroundings, rearranging so ...
at equilibrium: –ΔSØsurroundings = ΔSØsystem
since ΔSØsurroundings = –ΔHØ / T i.e. minus the enthalpy change divided by the absolute temperature
then: –(–ΔHØ / T) = ΔSØsystem
ΔHØ / T = ΔSØsystem, rearranging ...
gives: Tdecomposition = ΔHØ / ΔSØsystem
i.e. the identical expression derived from the Gibbs free energy expression.
o (iii) All you have to do now is substitute in the numerical values from the data table ...
... and note that ΔG and ΔH are usually in kJ BUT S or ΔS values are usually in J so don't forget to multiply the ΔG and ΔH values by 1000, therefore ...
Tdecomp(MgCO3) = 100600 / 175.0 = 575 K
Tdecomp(CaCO3) = 178300 / 160.6 = 1110 K
Tdecomp(SrCO3) = 234600 / 171.0 = 1372 K
Tdecomp(BaCO3) = 269300 / 172.1 = 1565 K o Assumptions and comments
The calculations have been based on the enthalpy, free energy and entropy value changes at 298K.
Enthalpy values (H) do vary with temperature and entropy values (S) increase with temperatures.
These factors have been ignored in the calculation BUT the values seem to be roughly born out by experiment as far as I can gather from the values quoted in the literature.
Note that the entropy change is almost constant because the increase in entropy is primarily due to the formation of 1 mole of carbon dioxide gas in each case.
Remember Sgas >> Sliquid > Ssolid
Giving a large increase in entropy, the formation of a gas is a powerful driving force to facilitate the decomposition of these essentially stable compounds BUT this factor applies almost equally to all the group 2 carbonates, therefore entropy cannot be used to explain the stability trend.
To explain the thermal stability trend thermodynamically, we must look at the enthalpy changes and the lattice enthalpies of the carbonate and the oxide residue.
The thermodynamic argument to explain the thermal stability trend of Group 2 carbonates.
o To follow the argument you need to x–reference with the numerical values in the data table above.
o Irrespective of the validity of the theoretical values calculated for the group 2 carbonate decomposition temperatures, what is clearly predicted is that they become more thermally stable down the group i.e.
with increase in atomic number of the metal.
o This increase in stability trend matches the experimental values which in turn are of the same order as those calculated theoretically despite the decrease in lattice enthalpy of the carbonate down the group!
o The first point to be made is that the endothermic enthalpy of reaction increases down the group.
o This is itself a clear indication that the decomposition is becoming much less energetically favourable down the group and remember the entropy change is almost constant down the group.
o The pivotal point in the argument–explanation rests on the differences between the lattice enthalpies (LEs) of the reacting carbonate and the oxide product as you descend the group.
o The difference in their LEs is primarily the reason for the rise in the endothermic enthalpy of reaction leading to the rising decomposition temperature.
o Down the group the lattice enthalpy of both the carbonate and the oxide decrease because the cation radius increases.
Lattice enthalpy is a function of two factors (other than the spatial positions of the ions)
(i) the charge on the positive and negative ions attracting each other, both constant in this case and ...
(ii) the radius of the ions. Here the carbonate ion and the oxide ion radii are constant, but the cation radius is increasing with atomic number of the group 2 metal. This increase the nuclear (+) ... (–) ion distance, reducing the force of attraction and hence reducing the lattice enthalpy.
o However, generally speaking (3/4 values!), as you go down the group the lattice enthalpy of the oxide decreases more rapidly than the lattice enthalpy of the carbonate.
o This means the difference between the two enthalpies becomes less and less down the group making the enthalpy more and more positive/endothermic and resulting in an increasingly higher temperature to effect the thermal decomposition (to the extent of producing an equilibrium partial pressure of 1 atmosphere of carbon dioxide gas).
Breaking up the M2+CO3
2– lattice is endothermic, but the formation of the M2+O2– lattice is exothermic and numerically greater than for MCO3 and particularly the lower the atomic number of the metal (i.e.) higher up the group).
o Note that, although I do not have the comparable data for beryllium, the quoted lattice energy for beryllium oxide (BeO) is very high due to the very small beryllium cation Be2+, and therefore extrapolating up the group, you would expect beryllium carbonate to have a much lower decomposition temperature.
This is usually quoted as ~100oC and completely fits in with both the theoretical thermal stability trend and the experimental thermal decomposition values quoted in the literature–textbooks.
Further extension of the ideas – looking at other thermal stability trends
o The anhydrous Group 2 sulphates show a similar thermal stability trend to the carbonates...
i.e. for the reaction: MSO4(s) ==> MO(s) + SO3(g)
the Tdecomp is in the order BaSO4 > SrSO4 > CaSO4 > MgSO4
–
o The effect of the cation radius also shows up when comparing the thermal stability of Group 1 carbonates and Group 2 carbonates.
Comparing the two thermal decomposition reactions ...
Because of the greater charge on the Group 2 cation (M2+) compared to the Group 1 cation (M+) the lattice enthalpy of the Group 2 oxide is much greater than for the Group 1 oxide.
So, for the s–block metals on the same period, for Tdecomp the trend is M2CO3 > MCO3
The lattice enthalpies are ...
2478 kJ mol–1 for Na2O (1239 kJ per mol Na)
and 3960 kJ mol–1 for MgO (3960 kJ per mol Mg)
The very high lattice enthalpy of MgO compared to that the LE for Na2O contributes to a much less endothermic enthalpy of decomposition for the Group 2 carbonate compared to the Group 1 carbonate and hence a lower decomposition temperature for the MCO3.
–
o The stability trend for Group 1 alkali metal carbonates is similar to that of the Group 2 carbonates ...
i.e. for Tdecomp the trend is K2CO3 > Na2CO3 > Li2CO3 etc. ...
... for exactly the same reasons argued above for MCO3 stability.
o Comparing the thermal stability of Group 1 nitrates [nitrate(V)] and Group 2 nitrates [nitrate(V)].
In group 1, only lithium nitrate readily decomposes to the oxide ...
4LiNO3(s) ==> 2Li2O(s) + 2NO2(g) + O2(g)
whereas all the other nitrates initially give the thermally stable nitrite [nitrate(III)] ...
2MNO3(s) ==> 2MNO2(s) + O2(g) (M = Na, K, Rb, Cs)
The relatively much smaller size of the lithium cation (Li+) produces a particularly high lattice enthalpy for lithium oxide compared to the other group 1 oxides, hence the direct formation of the oxide.
However, due to the much higher MO lattice enthalpies, the oxide is formed directly in each case for the group 2 nitrates ...
2M(NO3)2(s) ==> 2MO(s) + 4NO2(g) + O2(g) (M = Mg, Ca, Sr and Ba)
and the thermal stability trend will be Ba(NO3)2 > Sr(NO3)2 > Ca(NO3)2 > Mg(NO3)2
as in the case of the group 2 carbonates and sulfates etc.
o –
7.12. some examples of the uses of Group 1 and 2 Metals and their Compounds.
MCl & MCl2 The Group 1 and Group 2 chlorides are used as sources of metal extraction by electrolysis.
Na & Mg Sodium and magnesium are then used to extract titanium from its chloride by displacement.
Na Sodium vapour is used in the yellow–orange street lamps.
NaCl Sodium chloride 'common salt' is used as a food flavouring and preservative, source of chlorine, hydrogen, sodium metal and sodium hydroxide via electrolytic processes.
NaHCO3 is used in baking powders – heat or a weak organic acid (e.g. citric acid) is used in baking powders to form carbon dioxide gas to produce the 'rising' action in baking.