Enthalpy of reaction Knowledge-Based Study

Study notes

1. What is Enthalpy?

   Enthalpy, denoted by the symbol H, is a thermodynamic state function defined as the sum of a system's internal energy (U) and the product of its pressure (P) and volume (V):

   $H = U + PV$

   Because internal energy, pressure, and volume depend solely on the current state of the system, enthalpy is also a state function. In laboratory chemistry, most chemical processes occur in open containers at constant atmospheric pressure. Under constant pressure conditions, the change in enthalpy ($\Delta H$) equals the heat exchanged by the system ($q_p$):

   $\Delta H = q_p$

   Enthalpy of Reaction ($\Delta H_{\text{rxn}}$)

   The enthalpy of reaction (also called the heat of reaction) represents the difference between the total enthalpy of the products and the total enthalpy of the reactants for a given chemical process:

   $\Delta H_{\text{rxn}} = \sum H_{\text{products}} - \sum H_{\text{reactants}}$

   Because absolute enthalpies cannot be measured directly, chemists measure the enthalpy change, $\Delta H$, which is typically expressed in units of kilojoules per mole (kJ/mol).

   Classification Based on Enthalpy Change

   Chemical reactions either release heat to their surroundings or absorb heat from them, depending on the relative enthalpies of the reactants and products.

   1. Exothermic Reactions ($\Delta H < 0$)

   • Heat flow: Thermal energy is released by the reacting system into the surroundings.
   • Energy relationship: The products have lower enthalpy than the reactants ($H_{\text{products}} < H_{\text{reactants}}$).
   • Observable effect: The temperature of the reaction mixture and surroundings rises.
   • Example: Combustion of methane:
     $\text{CH}_4(g) + 2\text{O}_2(g) \rightarrow \text{CO}_2(g) + 2\text{H}_2\text{O}(l) \quad \Delta H = -890.4\text{ kJ/mol}$

   2. Endothermic Reactions ($\Delta H > 0$)

   • Heat flow: Thermal energy is absorbed by the reacting system from the surroundings.
   • Energy relationship: The products have higher enthalpy than the reactants ($H_{\text{products}} > H_{\text{reactants}}$).
   • Observable effect: The temperature of the surroundings drops unless continuous heat is supplied.
   • Example: Thermal decomposition of calcium carbonate:
     $\text{CaCO}_3(s) \rightarrow \text{CaO}(s) + \text{CO}_2(g) \quad \Delta H = +178.3\text{ kJ/mol}$

   Working with Thermochemical Equations

   A thermochemical equation includes both the balanced chemical reaction and the corresponding value of $\Delta H$. When interpreting and manipulating thermochemical equations, several key rules apply:

   1. Physical States Matter

   Enthalpy values depend strongly on the physical states of all reactants and products. For instance, condensing water vapor into liquid water releases heat; therefore, reactions forming $\text{H}_2\text{O}(l)$ have a more negative $\Delta H$ than those producing $\text{H}_2\text{O}(g)$.

   2. Proportionality to Stoichiometric Coefficients

   Enthalpy is an extensive property. If the coefficients of a balanced equation are multiplied by a factor n, the enthalpy change must also be multiplied by n:

   $\text{H}_2(g) + \frac{1}{2}\text{O}_2(g) \rightarrow \text{H}_2\text{O}(l) \quad \Delta H = -285.8\text{ kJ}$

   $2\text{H}_2(g) + \text{O}_2(g) \rightarrow 2\text{H}_2\text{O}(l) \quad \Delta H = 2 \times (-285.8\text{ kJ}) = -571.6\text{ kJ}$

   3. Reversing a Reaction Inverts the Sign

   When a reaction is written in reverse, the numerical value of $\Delta H$ remains identical, but the algebraic sign changes from positive to negative or vice versa:

   $2\text{H}_2\text{O}(l) \rightarrow 2\text{H}_2(g) + \text{O}_2(g) \quad \Delta H = +571.6\text{ kJ}$

   Calculating $\Delta H^\circ_{\text{rxn}}$ from Standard Enthalpies of Formation

   The standard enthalpy of reaction ($\Delta H^\circ_{\text{rxn}}$) is the enthalpy change when all reactants and products are in their standard states (typically 1 bar of pressure and a specified temperature, commonly 25 °C or 298.15 K).

   Standard Enthalpy of Formation ($\Delta H^\circ_f$)

   The standard enthalpy of formation is the enthalpy change for the formation of one mole of a compound from its constituent elements in their most stable reference states at 1 bar. By definition, the standard enthalpy of formation of any pure element in its most stable allotropic form is zero:

   $\Delta H^\circ_f[\text{O}_2(g)] = 0\text{ kJ/mol}, \quad \Delta H^\circ_f[\text{C}(s, \text{ graphite})] = 0\text{ kJ/mol}$

   The Summation Formula

   Hess's law allows the calculation of $\Delta H^\circ_{\text{rxn}}$ directly from formation enthalpies:

   $$\Delta H^\circ_{\text{rxn}} = \sum n\,\Delta H^\circ_f(\text{products}) - \sum m\,\Delta H^\circ_f(\text{reactants})$$

   where n and m are the stoichiometric coefficients from the balanced equation.

   Worked Example

   Calculate $\Delta H^\circ_{\text{rxn}}$ for: $2\text{CO}(g) + \text{O}_2(g) \rightarrow 2\text{CO}_2(g)$
   Given: $\Delta H^\circ_f[\text{CO}(g)] = -110.5\text{ kJ/mol}$ and $\Delta H^\circ_f[\text{CO}_2(g)] = -393.5\text{ kJ/mol}$.

   $\Delta H^\circ_{\text{rxn}} = [2(-393.5)] - [2(-110.5) + 1(0)]$
   $\Delta H^\circ_{\text{rxn}} = -787.0 - (-221.0) = -566.0\text{ kJ}$