Chemical Energetics

Gaseous State

(a) state the basic assumptions of the kinetic theory as applied to an ideal gas

- gas consists of particles or molecules of negligible size (or volume)
- gas particles have negligible intermolecular forces of attraction
- gas particles are in continuous random motion
- collisions between molecules are perfectly elastic, ie the gas molecules bounce apart on collision with no loss in kinetic energy; the molecules do not stick together

(bi) explain qualitatively in terms of intermolecular forces and molecular size: the conditions necessary for a gas to approach ideal behaviour

1. at low pressures
- gas molecules are widely spaced, and therefore have negligible size (vol occupied by the gas is very large compared to the gas molecule)
- forces of attraction between gas molecules are zero

2. at high temperatures
- there are negligible intermolecular attractions since the gas particles have sufficient kinetic energy to overcome it

(bii) explain qualitatively in terms of intermolecular forces and molecular size: the limitations of ideality at very high pressures and very low temperatures

1. at high pressures
- gas molecules are packed close together, and the size of a gas molecule cannot be assumed to be negligible
- shown by increase in pV/RT value

2. at low temperatures
- force of attraction between gas molecules are significant
- as shown by the fall in pV/RT value

Formula:

pV=nRT

where p = pressure in Pa
V = volume in m3
n = no. of moles in gas
R = gas constant (8.31 JK-1 mol -1)
T = temperature in K



The enthalpy change of a reaction, ▲H, is defined as the heat change (heat energy absorbed or evolved) when the reaction takes place between the masses of the reagents indicated by the stoichiometric equation for the reaction..

An exothermic reaction gives out heat to the surrounding, ie heat energy is evolved. Hence, the surrounding temperature rises as the heat content of the system falls.
▲H is negative (< 0) since heat content of products < heat content of reactants

An endothermic reaction absorbs heat from the surrounding. Hence, the surrounding temperature falls as the heat content of the system rises.
▲H is positive (> 0) since heat content of products > heat content of reactants


Types of Enthalpy change

1. The standard enthalpy change of formation, ΔHof of a compound is defined as the enthalpy change when one mole of the compound is formed from its elements under standard conditions (at 25°C, 1 atm).

e.g. H2(g) + ½ O2(g) à H2O (l) ΔHof (H2O (l)) = -286 kJmol-1

? ΔHof are usually calculated indirectly from other enthalpy changes of reaction.
? ΔHof elements in its standard state is zero. E.g. ΔHof ((N2(g))) = 0.
? ΔHof is often used to predict the stability of a compound relative to its constituent elements.


If ΔHof < 0, compound is energetically more stable than its constituent elements.


If ΔHof > 0, compound is energetically more stable than its constituent elements.


2. The standard enthalpy change of combustion, ΔHoc , is defined as the enthalpy change when one mole of a substance is completely burnt in oxygen under standard conditions (at 25°C, 1 atm).
e.g. S(s) + O2(g) à SO2(g) ΔHoc (S(s)) = -297 kJmol-1
? ΔHoc is always negative, as heat is always evolved in the combustion.
? ΔHoc can be used to give the energy values of fuels and foods.


3. The standard enthalpy change of hydration, DHөhyd, of an ion is defined as the enthalpy change when one mole of the gaseous ions is dissolved in a large amount of water under standard conditions (at 25°C, 1 atm).
e.g. Na+(g) + aq à Na+(aq) DHөhyd = -406 kJmol-1
? DHөhyd is always negative, as heat is produced when bonds are formed between the ions and the dipoles on the water molecules.
? The hydration energies of the ions depend on the charge and size of the ions
The higher the charge and the smaller the size of the ions, the greater (i.e. more exothermic) is the hydration energy.
4. The standard enthalpy change of solution, DHөsoln , is defined as the enthalpy change when one mole of a substance dissolves in such a large volume of solvent that addition of more solvent produces no further heat change under standard conditions (at 25°C, 1 atm).
e.g. NH3(g) + aq à NH3 (aq) DHөsoln = -35.2kJmol-1

? DHөsoln can be positive or negative.


If DHөsoln is very positive, compound is insoluble in water.

If DHөsoln is negative, compound is soluble in water.


5. The standard enthalpy change of atomization, DHөatom, is defined as the enthalpy change when an element or a compound is converted into one mole of free gaseous atoms under standard conditions (at 25°C, 1 atm).
e.g. Na(s) à Na(g) DHөatom = +109 kJmol-1
? DHөatom is always positive, because energy must be absorbed to pull the atoms far apart and to break all the bonds between them/
? The enthalpy change of atomization is not the same as the enthalpy change of vapourisation.



6. The standard enthalpy change of neutralization, DHөneut , is defined as the enthalpy change when one mole of water is formed in the neutralization between an acid and an alkali, the reaction being carried out in aqueous solution under standard conditions (at 25°C, 1 atm).
e.g. HCl(aq) + NaOH(aq) à NaCl(s) + H2O(l) DHөneut = -57.1 kJmol-1
? DHөneut is always negative.
? For the neutralisation of strong acids with a strong base, the standard enthalpy of neutralisation is almost constant. (DHөneut = -57.3 kJmol-1 )
Ø Strong acids and strong bases are completely ionised in dilute solutions
HX(aq) à H+(aq) + X-(aq)
MOH(aq) à M+(aq) + OH-(aq)
Ø Thus, the reaction between any strong acid and any strong base involves simply the formation of water from H+ and OH- ions.
H+(aq) + OH-(aq) à H2O(l) (DHөneut = -57.3 kJmol-1 )
Ø Since the process is exactly the same for all, the enthalpy change of neutralisation must, therefore, be the same (and the value is -57.3 kJmol-1 )
? If a weak acid or weak base is used, or if both acid and base are weak, then the standard enthalpy of neutralisation differs significantly from -57.3 kJmol-1 .
CH3CO2H(aq) + NaOH (aq) à Ch3CO2Na(aq) + H2O(l) (DHөneut = -55.2 kJmol-1 )
Ø Weak acids and weak bases are only slightly ionised in aqueous solution.
Ø So, with weak acids or bases, neutralisation involves the enthalpy change due to the reaction
H+(aq) + OH-(aq) à H2O(l) (DH1 = -57.3 kJmol-1 )

(DH2 = ±)and an enthalpy change due to the unionised acid or base that has to be converted into ions (DH here may be positive or negative).
HA(aq) à H+(aq) + A-(aq)
BOH(aq) à B+(aq) +OH-(aq)
Ø Thus, the enthalpy change of neutralisation involving either weak acids or weak bases (DHөneut = DH1 + DH2)
? DHөneut can be determined by mixing solutions of acids and alkalis in a calorimeter, and measuring the rise in temperature.
Heat evolved
No. of moles of water formedDHөneut =
where m = mass of solution
c = specific heat capacity of solution
DT = change in temperature
Heat evolved = mc DT
and

7. Bond Dissociation Energy, B.E, is the energy required to break one mole of covalent bonds between 2 atoms in the gaseous state.
e.g. O=O(g) à 2O(g) B.E. = +497 kJmol-1
? Bond dissociation energy can be used to compare the strength of covalent bonds.
? The greater the bond energy, the stronger the bond.

8. Ionisation Energy, I.E. is the energy required to remove one mole of electron from one mole of atoms or ions in the gaseous state.
? First I.E. of an element is the energy required to remove one mole of electrons from one mole of atom of the element in gaseous state.
M(g) à M+(g) + e-
? Second I.E. of an element is the energy required to remove one mole of electron from one mole of singly-charged positive ion of the element in the gaseous state.
M+(g) à M2+ (g) + e-

9. Electron Affinity, E.A. is the enthalpy change when one mole of atom or negatively charged ion in gaseous state gains one mole of electron.
? First E.A. of an element is the energy required for one mole of gaseous atom acquires one mole of electron to form one mole of singly-charged negative ion.
A(g) + e à A-(g)


10. Lattice Energy is the enthalpy change when 1 mole of an ionic compound is formed from its gaseous ions under standard conditions of 1atm and 298K.
q+ q-

r+ + r-M+(g) + A-(g) à MA (s)
? Magnitude of lattice energy
Where q+ : charge of cation & q- : charge of anion
r+ : radius of cation & r- : radius of anion
? Lattice energy cannot be measured directly. However, it can be determined using Hess’ Law
11. Hess’ Law states that the enthalpy change for a chemical reaction is the same, regardless of the route taken, provided that the initial states of the reactants and the final states of the products are the same.
Hess’s Law is used to determine enthalpy changes that cannot be found by direct experiments, through the construction of an energy cycle or an energy level diagram





(g)Entropy: ▲ (S) The measure of the disorder/ randomness in a system.

Any system in random motion tends to become more “mixed up” or disorderly as time passes. In an isolated environment, nature tends towards maximum entropy.

(h)Change in Temperature: Entropy increases as temperature increases.

E.g: H2O (l) at 25˚c à H2O (l) at 35˚c

Temperature increases from 25 - 35˚c.
K.E of particles increases resulting in higher movement rate of particles.
System becomes more disordered. ▲ (S) increases

As temperature increases, the molecules or ions undergo greater vibration in solid) and more rapid motion (in liquids and gases) and this reduces their orderliness.

(h)Change in Phase: Gas >> liquid >> solid

E.g: H2O (s) at 0˚c à H2O (l) at 0˚c

Change in phase
Crystalline structure of solid is broken, thus H20 molecules now more around freely in liquid state.
System becomes more disordered. ▲ (S) increases

A solid has low entropy due to its crystalline structure which is highly ordered and regular.
The entropy of a liquid is greater than that of a solid as molecules or ions in liquid state display less order than in solid state. Because particles/ions in liquid state move around more freely.
Entropy of gas is much greater than liquid because gases has a higher disorder due to the particles of gas having free movement and are not constrained to be adjacent to each other. Entropy of gas is far greater than that of solid.

(h)Change in number of particles: Entropy increases as the no. of particles increases.

E.g: CL2 (g)à 2CL(g)

Increase in number of particles
1mol of CL2 changes to 2mols of CL which contains more particles.
More ways to arrange CL particles
System becomes more disordered. ▲ (S) Increases.

Entropy increases as the no. of particles increases and the system becomes less orderly.


(h)Mixing of particles: Mixing process leads to disorder and so entropy increases.

E.g: NaCl (s) à Na (aq) + 2CL (aq)

Mixing of particles
Change in phase solid to liquid
Change in no. of particles

Entropy increases when two pure gases are mixed and allowed to diffuse into each other. Their orderliness is reduced as the molecules become randomly mixed
Entropy increases when a solid dissolves into a liquid. The resulting solution has less order than the original crystal because the particles are scattered throughout the solution and mix homogeneously with the solvent.

(i)The change in entropy (S) is given by the expression: ▲S = S(final) – S(initial)

▲S is positive when the system becomes less orderly S(final) > S(initial). This occurs when there is a change of state, or when a gas is produced by the decomposition of a liquid or solid.
▲S is negative when the system becomes more orderly S(final) < S(initial).

E.g: Ar at 2 atm à Ar at 1 atm .

▲S is positive because when pressure is decreased, Ar atoms are free to move in a larger volume and the system becomes less orderly.

(J)Every chemical reaction is accompanied by a heat (or energy) change ▲H, and a redistribution of matter, ▲S. The combined effects of these two factors are expressed by the quantity free energy, G.

Standard Gibbs free energy, ▲G is a state function of a system and is defined by means of the equation ▲G = ▲H - ▲S where T = temperature in K.
The sign of ▲G may be used to deduce whether a reaction or process will be spontaneous.

(K)
· If ▲G is negative (▲G < 0) the reaction is feasible and could take place spontaneously. The reaction is said to be exergonic or energy-giving.
· If ▲G is positive (▲G >0) the reaction is said to be not feasible and cannot take place spontaneously. The reaction is said to be endergonic or energy-giving.
· If ▲G is zero (▲G =0) the reaction is at equilibrium.

(L) When ▲G is positive, the reaction is non-spontaneous at r.t.p.
When ▲G is negative, the reaction is spontaneous at r.t.p.

(M)From the equation ▲G = H - T▲S the value of ▲G is dependent on temperature.

Hence ▲G may be negative when:
▲H - , ▲S+
Exothermic reaction, increase in entropy. Spontaneous at all temperatures.
▲H-, ▲S- :
Exothermic reaction, decrease in entropy as long as ▲H > T▲S. spontaneous at low temperatures.
▲H +, ▲S+:
Endothermic reaction, large increase in entropy where T▲S > ▲H. spontaneous only at high temperature.
▲H=0, ▲S+:
Reduction in Gibbs free energy arises completely from the increase in entropy.

▲G is positive when ▲H >0 (endothermic) and ▲S < 0 (decrease in entropy), the reaction is non-spontaneous at all temperature and has to be driven.