Question

Differentiate between the enthalpy of formation of \(\mathrm{H}_{2} \mathrm{O}(1)\) and \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) .\) Why is it necessary to specify the physical state of water in the following thermochemical equation \(\mathrm{CH}_{4}(\mathrm{g})+2 \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{CO}_{2}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l} \text { or g })\) \(\Delta H=?\)

Short answer

The enthalpy of formation for liquid water, \(\Delta H_f^{\circ}\mathrm{(H_2O(l))}\), is approximately -285.8 kJ/mol, while the enthalpy of formation for gaseous water, \(\Delta H_f^{\circ}\mathrm{(H_2O(g))}\), is approximately -241.8 kJ/mol. These values are different because enthalpy depends on the physical state of the substances involved and the energy required for vaporization. In the given thermochemical equation, the enthalpy change, \(\Delta H\), will be different depending on whether water is in its liquid or gaseous state. Therefore, it is essential to specify the physical state of water in thermochemical equations to accurately account for the difference in enthalpy of formation and ensure precise calculations of enthalpy changes in a reaction.

Step-by-step solution

Define Enthalpy of Formation

Enthalpy of formation is the change in enthalpy during the formation of a compound from its constituent elements in their most stable form under standard conditions. It is denoted by \(\Delta H_f\).

Differentiate Between Enthaply of Formation for Liquid and Gaseous Water

Enthalpy of formation for liquid water, \(\Delta H_f^{\circ}\mathrm{(H_2O(l))}\), and gaseous water, \(\Delta H_f^{\circ}\mathrm{(H_2O(g))}\) are different because enthalpy depends on the physical state of the substances involved. The process of vaporization requires energy, and this energy difference is the reason for the difference in their enthalpy values.

Identify the Enthalpy of Formation for Water in its Liquid and Gaseous States

The standard enthalpy of formation for liquid water, \(\Delta H_f^{\circ}\mathrm{(H_2O(l))}\), is approximately -285.8 kJ/mol, while the standard enthalpy of formation for gaseous water, \(\Delta H_f^{\circ}\mathrm{(H_2O(g))}\), is approximately -241.8 kJ/mol.

Explain the Importance of Specifying the Physical State of Water in the Thermochemical Equation

In the given thermochemical equation: \[\mathrm{CH}_{4}(\mathrm{g})+2\mathrm{O}_{2}(\mathrm{g})\rightarrow \mathrm{CO}_{2}(\mathrm{g})+\mathrm{2H}_{2}\mathrm{O}(\mathrm{l} \text{ or g })\] The enthalpy change, \(\Delta H\), will be different depending on whether water is in its liquid or gaseous state. This is due to the energy required for vaporization. Failing to specify the physical state of water will lead to inaccurate calculations and results for enthalpy changes associated with the reaction. In conclusion, it is essential to specify the physical state of water in thermochemical equations to accurately account for the difference in enthalpy of formation and ensure precise calculations of enthalpy changes in a reaction.

Key concepts

Thermochemical Equation

A thermochemical equation is a balanced chemical equation that includes the enthalpy change of the reaction, usually represented as \( \Delta H \). Understanding thermochemical equations is crucial because they provide both the quantitative and qualitative aspects of a chemical reaction. These equations not only show the reactants and products involved but also the energy exchange that occurs during the reaction.

For instance, in the combustion reaction of methane, \( \mathrm{CH}_4(\mathrm{g}) + 2 \mathrm{O}_2(\mathrm{g}) \rightarrow \mathrm{CO}_2(\mathrm{g}) + 2 \mathrm{H}_2 \mathrm{O}(\mathrm{l} \text{ or } \mathrm{g}) \), the enthalpy change \( \Delta H \) must be specified. It illustrates how energy is absorbed or released depending on the state of products. Keeping track of these changes is critical for understanding reaction energetics. Also, the reaction conditions, such as temperature and pressure, can affect the \( \Delta H \), highlighting the need to specify the correct conditions within the thermochemical equation.

Some important elements to consider in thermochemical equations include:

• State symbols (\( (\mathrm{g}) \), \( (\mathrm{l}) \), \( (\mathrm{s}) \), \( (\mathrm{aq}) \))
• Enthalpy changes (exothermic \( \Delta H < 0 \) or endothermic \( \Delta H > 0 \))
• Energy units like kilojoules (kJ)

Physical State of Matter

The physical state of the matter involved in a chemical reaction influences the enthalpy change significantly. Each state of matter, whether solid (\( \mathrm{s} \)), liquid (\( \mathrm{l} \)), gas (\( \mathrm{g} \)), or aqueous (\( \mathrm{aq} \)), has specific enthalpy values.

In our example reaction, understanding the difference in enthalpy of formation between liquid and gaseous water is vital. Liquid water has an enthalpy of formation of approximately -285.8 kJ/mol, while gaseous water's is -241.8 kJ/mol. This variation is because additional energy is required to vaporize water from liquid to gas. This energy is crucially accounted for when specifying the state because it alters the \( \Delta H \) of the reaction.

Ignoring the physical state leads to incorrect predictions and miscalculations, especially in science and engineering contexts where precise transformation and energy balancing is needed. Hence, always specify the state in any thermochemical equations involving substances whose state contributes to their energy content.

When writing reactions, note the importance of:

• Specifying states to clarify enthalpy changes.
• Considering physical transitions (melting, boiling).
• Tracking energy changes due to state transitions in reactions.

Standard Conditions

Standard conditions refer to a set of physical conditions under which most thermodynamic data are reported. Typically, these conditions include a temperature of \( 298.15 \) K (\( 25^\circ \mathrm{C} \)), a pressure of 1 atmosphere, and concentrations of 1 molar for aqueous solutions.

Why are standard conditions so pivotal? They provide a reference point that allows scientists to compare the energies of reactions consistently. For example, the enthalpies of formation are usually measured under these conditions, making it easier to estimate or calculate the energy changes in chemical reactions.

In relation to the thermochemical equation involving methane, applying standard conditions simplifies calculating enthalpy since you reference the same baseline measures as those in tabulated data. This keeps interpretations and computations straightforward and comparable.

When working with standard conditions, remember:

• They help achieve consistency in reporting and using thermodynamic data.
• They are critical for achieving dependable comparisons across various reactions.
• Always ensure reaction contexts align with these conditions for accurate data application.