Topic: The elements of chemical thermodynamics and bioenergetics Termochemistry

 

The heat effects of chemical reactions are connected with a change of the internal energy of the system during the transformation of reactants (U₁) into products (U₂)

                                Δ U = U₂ – U₁

The change of internal energy depends only on the initial and final states of the system and not on how the change is accomplished. Initial and final states are determined only by pressure (P), volume (V) and temperature (T):

                                Q =Δ U + A (The first law of thermodynamics)

ΔU = Q – A, U₂ – U₁ = Q –A,                          

where Q –heat, A –work of expansion. At the constant pressure A equals:

                                          P∙∆V = P∙(V₂ – V₁),                                             

 where V₁ and V₂ – the volume of the system in initial (V₁) and final (V₂) states.

Therefore:

Q_p = (U₂- U₁) + P∙(V₂ – V₁) = (U₂ + P∙V₁) – (U₁ + P∙V₁).

The sum U + P∙V is called enthalpy H:

                                 Δ H =Δ U + P∙ΔV

The heat effect of reaction (if the pressure is constant) Q_p equals the change of enthalpy ∆H:

                                  Q_p = H₂ – H₁ = ∆H.

For the constant pressure: ∆H = ∑H_final - ∑H_initial.

If the volume is constant, heat effect of reaction Q_v equals the change of the internal energy of the system: Q_v = U₂ – U₁ = ∆U.

For the constant volume:

                                   ∆U = ∑U_final - ∑U_initial.

Thermochemical calculations are based on the Hess’s law and on the consequences of this law. For the reaction A → D, proceeding with intermediate stages, ∆H are: 

A → B, ∆H₁

B → C, ∆H₂

 C → D, ∆H₃

According to the Hess’s law: ∆H= ∆H₁ + ∆H₂ + ∆H₃ or the polygon of Hess (look at the Fig.) shows: the heat effects of direct convert or through the intermediate stages are equal to: ∆H= ∆H₁ + ∆H₂ + ∆H₃

                                                            ∆H          

                                                 A                         D

 

                                           ∆H₁                               ∆H₃

                                  

                                                 B                             C

                                                             ∆H₂

The Hess’s law is applied not only for chemical reactions, but for the all processes with the heat effects: phase conversions, dissolving, crystallization, evaporation., and so on.

According to the consequences of Hess’s law:

                                 aA + bB = cC + dD

∆H_{of reaction} = ∑∆H_f (prod.) - ∑∆H_f (reactants) =

= [c∙∆H_f(C) + d∙∆H_f(D)] - [a∙∆H_f(A) + b∙∆H_f(B)]

∆H_{of reaction} = ∑∆H_combustion (of react.) - ∑∆H_combustion (product) =

= [a∙∆H_com(A) + b∙∆H_com(B)] - [c∙∆H_com(C) + d∙∆H_com(D)]

If the enthalpy of the reaction decreases the reaction is named exothermic (∆H<0), but if the enthalpy increases, this reaction is endothermic (∆H>0).

The direction of spontaneous proceeding of the reaction is determined by the simultaneous actions of two factors:

a) enthalpy, ∆H<0

b) entropy, ∆S<0 (or T∙∆S).

To calculate the change of entropy of the chemical reaction, the first consequence of Hess’s law is applied:

∆S _reaction = ∑∆S_f (prod.) - ∑∆S_f (react.)

The change of volume of the system changes the entropy

1) ∆S>0, if V₂ > V₁; because V₂ – V₁ = ∆V, ∆V>0

2) ∆S<0, if V₂ < V₁; because V₂ – V₁ = ∆V, ∆V<0.

The process will be spontaneous in its nature if its ∆G<0 at P=const, T =const

(∆G = G₂ –G₁).

The spontaneous transfering of the system from initial state(G₁) to the final state (G₂) is possible if G₁>G₂ (∆G<0). If G₂=G₁ (∆G=0), the system exists in equilibrium.

The Gibbs’s free energy is connected with enthalpy and entropy:

                                     ∆G = ∆H - T∙∆S   ,

                       the second law of termodynamics.

The calculations of ∆G, ∆H, ∆S are done under the standard conditions:

                                 P = 101,3 kPa; T = 298⁰K.

 Ability of the substances to react with each other or chemical affinity is defined by the change of Gibb’s energy. The more negative value of ∆G is the higher the reaction ability of the substance will be.

The analysis of the relationship ∆G = ∆H - T∙∆S shows:

1) if ∆H <0 and ∆S >0, ∆G <0 at any temperatures

2) if ∆H <0 and ∆S <0, ∆G <0 at temperatures low enough, i.e. │∆H│>│ T∙∆S │

3) if ∆H >0 and ∆S >0, ∆G <0 at temperatures high enough, i.e. │ T∙∆S │>│∆H│;

4) if ∆H >0 and ∆S <0, ∆G >0 at any temperatures.