Isobaric potential of temperature dependent heat capacity

The isobaric potential of a reaction is a value whose change during a chemical reaction is equal to the change in the internal energy of the system. The isobaric potential shows how much of the total internal energy of the system can be used for chemical transformations. Thermal effect of reaction is enthalpy of the system. The heat capacity coefficients are tabular values for the reaction. They are used to express the dependence of heat capacity on temperature.

Notation:

1. \(T_\text{lab}\) (T_lab) is standard_laboratory_temperature.

Conditions:

1. We take into account the dependence of heat capacity on temperature according to the Temkin-Schwarzman formula.

2. The process is isobaric-isothermal.

molar_gibbs_energy_change

gibbs_energy change, or isobaric potential, per unit amount_of_substance.

Symbol:

Delta(G_m)

Latex:

\(\Delta G_\text{m}\)

Dimension:

energy/amount_of_substance

molar_enthalpy_change

enthalpy change, or thermal effect, per unit amount_of_substance.

Symbol:

Delta(H_m)

Latex:

\(\Delta H_\text{m}\)

Dimension:

energy/amount_of_substance

molar_entropy

entropy per unit amount_of_substance.

Symbol:

S_m

Latex:

\(S_\text{m}\)

Dimension:

energy/(amount_of_substance*temperature)

temperature

temperature.

Symbol:

T

Latex:

\(T\)

Dimension:

temperature

first_capacity_coefficient

First tabular coefficient of heat capacity.

Symbol:

a

Latex:

\(a\)

Dimension:

energy/(amount_of_substance*temperature)

second_capacity_coefficient

Second tabular coefficient of heat capacity.

Symbol:

b

Latex:

\(b\)

Dimension:

energy/(amount_of_substance*temperature**2)

third_capacity_coefficient

Third tabular coefficient of heat capacity.

Symbol:

c

Latex:

\(c\)

Dimension:

energy*temperature/amount_of_substance

law

Delta(G_m) = Delta(H_m) - T * S_m - T * (a * (log(T_lab / T) + T_lab / T - 1) + b * (T / 2 + T_lab^2 / (2 * T) - T_lab) + c * (1 / (T^2 * 2) - 1 / (T_lab * T) + 1 / (T_lab^2 * 2)))

Latex:

\[\Delta G_\text{m} = \Delta H_\text{m} - T S_\text{m} - T \left(a \left(\log \left( \frac{T_\text{lab}}{T} \right) + \frac{T_\text{lab}}{T} - 1\right) + b \left(\frac{T}{2} + \frac{T_\text{lab}^{2}}{2 T} - T_\text{lab}\right) + c \left(\frac{1}{T^{2} \cdot 2} - \frac{1}{T_\text{lab} T} + \frac{1}{T_\text{lab}^{2} \cdot 2}\right)\right)\]