- Entropy, S, is a measure of 'disorder' of a system
- Entropy is a measure to the extent to which energy is dispersed.
- Substances with high entropy are nearly alike than those with low entropy.
- Entropy tends to increase in natural processes.
- disorder tends to increase
- energy tends to become more dispersed
- things that are different tend to become less distinguishable
- It is a thermochemical quantity that makes it possible to decide whether or not a reaction is spontaneous.
- A system becomes energetically stable when it becomes more disordered.
- Ludwig Boltzmann derived the formula S = k ln W
Entropy, Different States
- Solids have relatively low values for standard molar entropies. The atoms/molecules are fixated in place.
- In diamond, carbon atoms are held in place by strong directional covalent bonds. Lead has a higher value for standard molar entropy, because metallic bonds are not directional . The heavier and larger lead atoms, can vibrate more freely and share out energy in more ways that diamond.
- Liquids have higher standard molar entropies than solids because the atoms/molecules are free to move. There are many more ways in distributing the particles and energy.
- Standard molar entropy of mercury is greater than lead. Molecules with more atoms have higher standard entropies because they can vibrate, rotate and share out energy in more ways.
- Gases have higher standard molar entropies than liquids, the atoms/molecules not only are free to move, but are widely spaced. There are even more ways of distributing the particles energy.
- Entropy of argon is even higher than mercury. As with liquids, molecules with more atoms can rotate, vibrate and arrange themselves in more ways.
Entropy, Calculations I
Entropy change of the system
ΔS system = ΣΔS products - ΣΔS reactants
- If ΔS system is positive, there is an increase in disorder.
- If ΔS system is negative, there is a decrease in disorder.
- Example: Calculate the entropy change of ΔS system, for the reaction:
2Mg (s) + O2 (g) → 2MgO (s) [MgO = 26.9], [O2 = 102.5], [Mg = 32.7]
ΔS system = ΣΔS products - ΣΔS reactants
ΔS system = [2(26.9)] - [2(32.7) + 102.5]
= - 114.1 JK-1mol-1
- This shows that entropy of system decreases when nitrogen and hydrogen react to form ammonia. Half the no. of gas molecules in the products than in reactants.
- This is expected since, the no. of possible arrangements of molecules has reduced.
Entropy, Calculations II
Entropy change of surroundings
ΔSsurroundings = -ΔH/T NOTE: T in kelvin and ΔH is in joules
- The minus sign is included, as the entropy charge is larger as more heat is released in surroundings. For an exothermic reaction ΔH is negative and so -ΔH is positive.
- For any value of heat energy, the increase in entropy in the surrounding is greater when surroundings are cool, than when they are hot.
- There's greater effect on the no. of ways of distributing energy when adding heat to atoms in cold system, than adding same amount of heat energy to a already hot system.
- Example: Consider the reaction, under standard conditions
2Mg (s) + O2 (g) → 2MgO (s) ΔH= - 1204 KJmol-1
ΔSsurroundings = -ΔH/T = -(-1204000)/298
=+ 4040 JK-1mol-1
Entropy, Calculations III
Total entropy change
ΔStotal = ΔS system + ΔS surroundings
- For changes that happen spontaneously, ΔS must be positive. Changes that tend to proceed naturally are called spontaneous changes, they can be quite slow.
- Example: Calculate total entropy change of:
2Mg (s) + O2 (g) → 2MgO (s) ΔS sys= - 114.1JK-1mol-1 , ΔS sur = +4040JK-1mol-1
ΔStotal = ΔS system + ΔS surroundings = [-114.1] + [+4040] = 3925.9
= 3930 JK-1mol-1 (3 s.f.)
- Most exothermic reactions tend to go as room temperature because the value -ΔH/T is much larger and more positive than ΔS system, which means ΔStotal is positive
- An endothermic reaction can be spontaneous if ΔS system >ΔS surroundings.
- A reaction that tends not to go a room temperature may become spontaneous as the temperature rises because ΔS surroundings decreases as T increases.
Lattice Enthalpy, Theoretical Lattice
- Theoretical lattice can be calculated from the expression that relates the force of attraction F, between the ions to the size and charge of ions:
Z+ = no. of charge on cation
Z- = n. of charge on anion
r+ = radius of cation
r- = radius of anion
Lattice Enthalpy, Ionic Lattices
- Stronger the electrostatic attraction between oppositely charged ions the more exothermic.
- Small ions pack together closely in an ionic lattice and attract each other strongly.
- Larger the size, the further apart in the ionic lattice and the electrostatic forces of attraction are weaker.
Lattice Enthalpy, Ionic Lattices II
- As the size of the charge on the ions increases, the lattice enthalpy becomes more exothermic, as there is a stronger electrostatic force attraction between the ions.
- Compounds with the most negative lattice enthalpies are those that have small, highly charged ions.
(insert - hmmm)
- As charge increases, the ions decreases in ionic radius produce a greater attraction between these positive and negative ions.
- Decrease in ionic radius brings the ions in lattice closer together, producing stonger electrostatic attraction.
Lattice Enthalpy, Theoretical Values
- Experimental lattice enthalpies are the value s of lattice enthalp calculated from Born-Harber cycles.
- Theoretical values are calculated on the basis of a purely ionic model - 100% ionic character exists in the compound or ions are perfectly spherical.
- If there is good agreement between the theoretical values and experimental value, then the pure ionic model of the bonding compound is an accurate one.
- However, if there is poor agreement between these two values, then the compound has a slightly covalent character, in addition to ionic bonding present.
- Example: Silver cholride, Experimental = -890 KJmol-1 , Theoretical = -769 KJmol-1
Insert Immm 2nd
- Small highly polarising Ag+ distorts the electron cloud of Cl-, thereby introducing covalent character into the bond
- The experimental lattice enthalpy above is -121 KJmol-1 more exothermic than theoretical value. It shows the lattice has been strengthened by a degree of covalency in the bonding.
Lattice Enthalpy, Fajans' rules
- Extent of polarisation of the negative ion by the positive ion is described by Fajan's rule.
- There is a tendancy towards increasing covalent character in an ionic compound when:
- the positive ion is small
- the posiive ion has multiple positive charges
- the negative ion is large
- the negative ion has multiple negative charges
insert hmmm 3rd
- Calculated valuesof standard enthalpy change can be used to predict the stoichiometry of an ionic compound.
Group 2, Metals I
- It is seen that 1st IE decreases down group 2 (2nd IE follows trend)
- i.e. It is becoming progressively easier to remove outer electrons
- The atomic radius increases down the group as more shells are added.
- atomic number increases down the group
- Ionisation energy decreases because ...
- ...although nuclear charge increases, shielding from increasing number of e- shells down the group cancels out the additional problems.
- ...as atomic radius increases, the outer e- is becoming further away from the nucleus, experiences a weaker force of attraction.
- ...thus means that the outer e-s becomes progressively easier to remove, therefore IE decreases down the group.
Group 2, Metals II
- Solubility increases down the group
- pH of solution increases down a group
Carbonates + Nitrates
- MgCO2 Mg(NO3)2
- CaCO2 Ca(NO3)2
- SrCO2 Sr(NO3)2
- BaCO2 Ba(NO3)2
- Decreasing ease of thermol decomposition down a group
Group 2, Metals III
Summary reactions of Group 2
insert image .....