Chemical Energetics II

Energy cycle: MgCl₂(s) + aq → Mg²⁺(aq) + 2Cl⁻(aq) (ΔH_sol), with both sides formed from Mg(s) + Cl₂(g): −641 for MgCl₂(s), and ΔH_f = −467 + 2(−167) for the ions.[1]

By Hess' Law, ΔH_sol = 641 + (−467) + 2(−167) = −160 kJ mol⁻¹[1]

Since ΔH_sol is highly exothermic, MgCl₂ is very soluble in water.[1]

NoteThe magnitude of ΔS is often much smaller than that of ΔH. For most reactions, ΔS is less than 100 J K⁻¹ mol⁻¹. Hence when ΔH is very negative, ΔG is likely to be negative and the reaction is spontaneous.

Entropy is a measure of the randomness or disorder in a system, reflected in the number of ways that the energy of a system can be distributed through the motion of its particles.[1]

Entropy of the system increases due to mixing of gases. The volume available for each gas increases (to keep total pressure constant), hence there are more ways in which the gas particles and their energies can be distributed.[1]

Entropy of the system increases, as an increase in temperature causes the average kinetic energy of the gas particles to increase and the range of energies to increase. This leads to the broadening of the Maxwell–Boltzmann energy distribution, and hence there are more ways in which the energy can be distributed among the gas particles.[1]

Entropy of the system decreases. The number of gas particles decreases, since there is one gaseous reactant and no gaseous product. Hence the number of ways that the particles and the energy can be distributed decreases.[1]

Entropy of the system increases, as there is an increase in the number of gas particles, and thus the system becomes more disordered and there are more ways in which the particles and energy can be distributed.[1]

ΔH_soln[LiCl(s)] = −lattice energy + ΔH_hyd[Li⁺(g)] + ΔH_hyd[Cl⁻(g)]

= +843 + (−883) = −40 kJ mol⁻¹[1]

Heat absorbed = mcΔT = 50.0 × 4.20 × 3.3 = 693 J[1]

ΔH_soln[KCl(s)] = +693 ÷ 3.0074.6 = +17.2 kJ mol⁻¹ (3 s.f.)[1]

Since |LE| is inversely proportional to the interionic distance, the lattice energy of LiCl is slightly more exothermic than that of KCl.[1]

However, since hydration energy is proportional to charge density, Li⁺ will have a much more exothermic hydration enthalpy than K⁺. Therefore, the enthalpy change of solution of LiCl is more exothermic than that of potassium chloride.[1]

ΔG_{decomposition} = ΔH_{decomposition} − TΔS

= −1423 − [298 × (+208 ÷ 1000)] = −1485 kJ mol⁻¹[1]

Since ΔG is negative, the reaction is spontaneous at 298 K.[1]

The spontaneity is not affected by changes in temperature because ΔH_{decomposition} is negative, T is always positive and ΔS is positive (or −TΔS is always negative), i.e. ΔG = ΔH − TΔS = negative − [(positive) × (positive)] = negative.

Yes, the decomposition of nitroglycerin is spontaneous at all temperatures.[1]

ΔG^⦵ = ΔH^⦵ − TΔS^⦵. ΔG^⦵ (+172.6 kJ mol⁻¹) is positive at 298 K, hence reaction I is not spontaneous at room temperature.[1]

The high temperature in the car engine causes TΔS^⦵ to become more positive (or −TΔS^⦵ to become more negative). This leads to a more negative ΔG^⦵, and hence reaction I becomes spontaneous.[1]

The amount of gases decreases from 3 mol to 2 mol, hence there are fewer ways to arrange the gaseous particles and their energy in the system.[1]

ΔS^⦵ is negative.[1]

Since ΔH_hyd ∝ qr, and Mg²⁺ has a higher charge and smaller ionic size than Na⁺, the hydration energy of Mg²⁺ is more exothermic than that of Na⁺.[1]

ΔH_soln = −(lattice energy) + ΔH_hyd

For NaOH: −44 = 896 + (−390) + ΔH_hyd(OH⁻), so ΔH_hyd(OH⁻) = −550 kJ mol⁻¹[1]

For Mg(OH)₂: x = 2995 − 1890 + 2(−550) = +5.00 kJ mol⁻¹[1]

There is a decrease in disorderliness as H₂O molecules are attached to the metal ion and lose their degree of freedom. As more water molecules are attached to the Mg²⁺ ion on average, the entropy of the system decreases more (ΔS is more negative) than for NaOH.[1]

Mg(OH)₂ dissolves with the formation of more mobile particles (aqueous ions), so there are more ways in which the particles and energy can be distributed, which may cause entropy to increase (ΔS is positive).[1]