What is the difference between the standard enthalpy of formation and the standard enthalpy of reaction?

Enthalpy of formation, often symbolized as \(\triangle H_f^{\text{°}}\), is a key concept in thermochemistry. It represents the change in enthalpy when one mole of a compound is formed from its constituent elements under standard conditions.
Standard conditions are defined as a temperature of 298 K (25°C) and a pressure of 1 atm.
For example, for water (\text{H}_2\text{O}), the standard enthalpy of formation would be determined by the energy change when hydrogen gas (\text{H}_2) and oxygen gas (\text{O}_2) react to form one mole of liquid water.
It's important to note that when elements are in their standard states, their enthalpy of formation is zero. This standardizes the formation enthalpies and makes calculations easier.

The enthalpy of reaction, symbolized as \(\triangle H_r^{\text{°}}\), refers to the change in enthalpy when a chemical reaction proceeds under standard conditions.
This is the total energy change for the reaction, which can involve the breaking and forming of chemical bonds. For instance, in the combustion of methane (CH_4) to form carbon dioxide (\text{CO}_2) and water (\text{H}_2\text{O}), the enthalpy change encompasses all the energy changes associated with breaking bonds in the reactants and forming new bonds in the products.
To find the enthalpy of reaction, we typically use the enthalpies of formation of the reactants and products. The general formula used is:
\[ \triangle H_r^{\text{°}} = \text{sum of enthalpies of formation of products} - \text{sum of enthalpies of formation of reactants} \]

Thermochemistry is the branch of chemistry that studies the heat evolved or absorbed in chemical reactions.
It involves understanding concepts like enthalpy changes, heat capacity, and standard states. With the knowledge of enthalpy changes, chemists can predict whether reactions will be exothermic (release heat) or endothermic (absorb heat).
Key tools in thermochemistry include calorimetry, which measures the amount of heat absorbed or released during a reaction, and Hess's Law, which states that the total enthalpy change for a reaction is the same, no matter how many steps the reaction is carried out in.

Standard conditions are the specific set of conditions under which thermodynamic measurements are made.
Typically defined as a temperature of 298 K (25°C) and a pressure of 1 atm. These conditions allow chemists to compare different reactions and substances under the same baseline.
When referring to enthalpies of formation or reaction using the symbols \(\triangle H_f^{\text{°}}\) or \(\triangle H_r^{\text{°}}\), it indicates that these values are determined under these standard conditions.
This standardization is crucial for consistency and helps avoid discrepancies when tabulating and comparing thermodynamic data.