Question

Give the definition of the standard enthalpy of formation for a substance. Write separate reactions for the formation of \(\mathrm{NaCl}\) , \(\mathrm{H}_{2} \mathrm{O}, \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6},\) and \(\mathrm{PbSO}_{4}\) that have \(\Delta H^{\circ}\) values equal to \(\Delta H_{\mathrm{f}}^{\circ}\) for each compound.

Short answer

The standard enthalpy of formation (\( \Delta H_{\mathrm{f}}^{\circ} \)) is the change in enthalpy when one mole of a substance in its standard state is formed from its constituent elements in their standard states at a fixed temperature, usually 298.15 K. The formation reactions for the given substances are: 1. NaCl: \( \mathrm{Na} (s) + \frac{1}{2} \mathrm{Cl}_{2} (g) \rightarrow \mathrm{NaCl} (s) \) 2. H2O: \( \mathrm{H}_{2} (g) + \frac{1}{2} \mathrm{O}_{2} (g) \rightarrow \mathrm{H}_{2} \mathrm{O} (l) \) 3. C6H12O6: \( 6 \mathrm{C} (graphite) + 6 \mathrm{H}_{2} (g) + 3 \mathrm{O}_{2} (g) \rightarrow \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} (s) \) 4. PbSO4: \( \mathrm{Pb} (s) + \mathrm{S} (s) + 2 \mathrm{O}_{2} (g) \rightarrow \mathrm{PbSO}_{4} (s) \) The associated enthalpy changes, \(\Delta H^{\circ}\), for each of these reactions are equal to the standard enthalpy of formation, \(\Delta H_{\mathrm{f}}^{\circ} \), for the respective substances.

Step-by-step solution

Definition of Standard Enthalpy of Formation

The standard enthalpy of formation (\( \Delta H_{\mathrm{f}}^{\circ} \)) is defined as the change in enthalpy when one mole of a substance in its standard state is formed from its constituent elements in their standard states at a fixed temperature, usually 298.15 K.

Formation Reactions

Now, we will write the formation reactions for NaCl, H2O, C6H12O6, and PbSO4. It is essential to make sure that you have precisely one mole of the product in each formation reaction, and the reactants are in their standard states. 1. Formation of NaCl: In the standard state, sodium is a solid, and chlorine is a gas. Therefore, the formation reaction for NaCl would be: \[ \mathrm{Na} (s) + \frac{1}{2} \mathrm{Cl}_{2} (g) \rightarrow \mathrm{NaCl} (s) \] 2. Formation of H2O: In the standard state, hydrogen and oxygen are both gases. The formation reaction for H2O, considering it as a liquid, is: \[ \mathrm{H}_{2} (g) + \frac{1}{2} \mathrm{O}_{2} (g) \rightarrow \mathrm{H}_{2} \mathrm{O} (l) \] 3. Formation of C6H12O6 (glucose): In the standard state, carbon is a solid (graphite), hydrogen is a gas, and oxygen is a gas. The formation reaction for glucose, considering it as a solid, is: \[ 6 \mathrm{C} (graphite) + 6 \mathrm{H}_{2} (g) + 3 \mathrm{O}_{2} (g) \rightarrow \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} (s) \] 4. Formation of PbSO4: In the standard state, lead is a solid, sulfur is a solid, and oxygen is a gas. The formation reaction for PbSO4, considering it as a solid, is: \[ \mathrm{Pb} (s) + \mathrm{S} (s) + 2 \mathrm{O}_{2} (g) \rightarrow \mathrm{PbSO}_{4} (s) \] These reactions represent the formation of one mole of the compound in its standard state from its constituent elements in their standard states. The associated enthalpy changes, \(\Delta H^{\circ}\), for each of these reactions are equal to the standard enthalpy of formation, \(\Delta H_{\mathrm{f}}^{\circ} \), for the respective substances.

Key concepts

Thermodynamics

Thermodynamics is the branch of physics that deals with the relationships between heat, work, temperature, and energy. In the context of chemistry, it explains how these physical quantities influence chemical reactions and processes. The standard enthalpy of formation is a concept stemming from thermodynamics that helps us understand how much heat energy is absorbed or released when a compound is formed from its elements. Understanding thermodynamics is essential as it provides insights into whether a reaction will occur spontaneously, how much energy is needed or released, and the efficiency of energy conversion. This field revolves around several key laws, such as the first law of thermodynamics, which states that energy cannot be created or destroyed, only transferred or converted from one form to another. In practice, when calculating enthalpy changes (\(\Delta H\)), thermodynamics allows chemists to predict the energy balance of the reaction, helping design reactions that are energy-efficient and environmentally friendly.

Chemical Reactions

Chemical reactions are processes where reactants convert into products, involving the making and breaking of chemical bonds. During these reactions, energy is either absorbed or released, which relates directly to the concept of enthalpy change. In a chemical reaction, the enthalpy change (\(\Delta H\)) indicates the heat exchanged with the surroundings at constant pressure.The standard enthalpy of formation specifically deals with reactions leading to the formation of one mole of a compound from its elements in their standard states. This is a key part of chemical reactions' studies since it allows for the comparison of energies involved in forming different compounds. By writing balanced equations for each reaction, such as those for the formation of NaCl, \(\mathrm{H}_{2}\mathrm{O}\), \(\mathrm{C}_{6}\mathrm{H}_{12}\mathrm{O}_{6}\), and \(\mathrm{PbSO}_{4}\), we can derive important data about the energy requirements and feasibility of the reactions.

Standard State Conditions

Standard state conditions are a set of baseline parameters agreed upon so that enthalpy changes can be easily compared between different reactions. These conditions typically include a pressure of 1 bar, a temperature of 298.15 K (25°C), and substances in their most stable form at this temperature and pressure.Establishing standard state conditions is crucial because it ensures consistency in reporting and comparing thermodynamic data. Without these norms, it would be challenging to determine whether one reaction is more energetically favorable than another. For standard enthalpy of formation values (\(\Delta H^{\circ}_f\)), the reactants must be in their standard states. This means, for example, that sodium is taken as solid Na, chlorine as \(\mathrm{Cl}_{2}\) gas, carbon as graphite, and so on. This standardization simplifies calculations and allows chemists to use tabulated enthalpy values to evaluate reaction spontaneity and other thermodynamic properties.

Chemical Thermodynamics

Chemical thermodynamics merges concepts of both chemistry and physics to understand how energy transformations govern chemical processes. It looks at energy exchanges at a molecular level, applying thermodynamic principles to predict and explain reaction behaviors. Using the standard enthalpy of formation, chemists can predict which reactions will release energy and are thus potentially useful in energy generation, or which will require energy input and could be driven by external sources. This field employs various thermodynamic quantities such as Gibbs free energy, entropy, and enthalpy to paint a comprehensive picture of reaction spontaneity and equilibrium. A proper grasp of chemical thermodynamics can help in crafting reactions that minimize energy loss, enhancing both the sustainability and effectiveness of chemical manufacturing processes. Integrating these principles leads to solutions that may help tackle larger challenges like energy conservation and developing alternative green technologies.