Question

Which of the following thermochemical equations can have \(\Delta H_{\mathrm{f}}^{\circ}\) for the heat of the reaction? If it cannot, then why not? (a) \(\mathrm{CO}\left(\mathrm{NH}_{2}\right)_{2}(a q) \longrightarrow \mathrm{CO}\left(\mathrm{NH}_{2}\right)_{2}(s)\) (b) \(\mathrm{C}+\mathrm{O}+2 \mathrm{~N}+4 \mathrm{H} \longrightarrow \mathrm{CO}\left(\mathrm{NH}_{2}\right)_{2}(a q)\) (c) \(\mathrm{C}(s,\) graphite \()+\frac{1}{2} \mathrm{O}_{2}(g)+\mathrm{N}_{2}(g)+4 \mathrm{H}_{2}(g) \longrightarrow\) \(\mathrm{CO}\left(\mathrm{NH}_{2}\right)_{2}(a q)\) (d) \(2 \mathrm{C}(s,\) graphite \()+\mathrm{O}_{2}(g)+2 \mathrm{~N}_{2}(g)+8 \mathrm{H}_{2}(g) \longrightarrow\) \(2 \mathrm{CO}\left(\mathrm{NH}_{2}\right)_{2}(a q)\)

Short answer

The correct thermochemical equation for assigning \(\Delta H_{\mathrm{f}}^{\circ}\) is equation (c), as it represents the formation of one mole of a compound directly from its constituent elements in their standard states.

Step-by-step solution

Understanding \(\Delta H_{\mathrm{f}}^{\circ}\) and Identifying the Formation Equation

The standard heat of formation, \(\Delta H_{\mathrm{f}}^{\circ}\), is defined as the heat change associated with the formation of one mole of a compound from its elements in their standard states. Hence, the correct thermochemical equation must represent the formation of one mole of a compound directly from its constituent elements in their standard states.

Analyzing Equation (a)

Equation (a) does not represent the formation of a compound from its elements; instead, it depicts a phase change from aqueous to solid state. Therefore, \(\Delta H_{\mathrm{f}}^{\circ}\) cannot be assigned to this reaction since no formation is occurring.

Analyzing Equation (b)

Equation (b) resembles a formation equation but does not use elements in their standard states. Moreover, the coefficients do not correspond to the formation of one mole of the compound. Thus, this equation cannot have \(\Delta H_{\mathrm{f}}^{\circ}\) assigned to it.

Analyzing Equation (c)

Equation (c) represents the formation of one mole of the compound \(\mathrm{CO}\left(\mathrm{NH}_{2}\right)_{2}(a q)\) from its elements in their standard states. This is a standard formation equation and can have \(\Delta H_{\mathrm{f}}^{\circ}\) assigned to it as the heat of reaction.

Analyzing Equation (d)

Equation (d) represents the formation of two moles of the compound, which does not fit the definition of \(\Delta H_{\mathrm{f}}^{\circ}\) because it should be for the formation of one mole of the compound from its elements. Therefore, this reaction cannot have \(\Delta H_{\mathrm{f}}^{\circ}\) for the heat of the reaction.

Key concepts

Thermochemical Equations

In the context of chemistry, a thermochemical equation is a chemical equation that includes the enthalpy change, denoted as \( \Delta H \), which expresses the amount of heat absorbed or released during a chemical reaction. This heat change is crucial as it helps determine whether a reaction is exothermic (releases heat) or endothermic (absorbs heat).

Each thermochemical equation is associated with specific conditions including pressure, temperature, and the physical states of the reactants and products. For example, \( \Delta H_{\mathrm{f}}^{\circ} \) in a thermochemical equation represents the standard heat of formation, which refers to the heat change when one mole of a compound is formed from its elements under standard conditions (1 atm pressure and 298.15 K temperature). It's important to remember that all substances in a thermochemical equation must be referenced to their standard states. This allows for the comparison of the amount of energy associated with different reactions and is foundational for calculations in thermochemistry.

Heat of Reaction

The heat of reaction, often referred to as the enthalpy change of a reaction, symbolized as \( \Delta H \), is the difference between the enthalpy of the products and the enthalpy of the reactants. If \( \Delta H \) is negative, the reaction is exothermic and releases heat into the surroundings. Conversely, if \( \Delta H \) is positive, the reaction is endothermic and absorbs heat from the surroundings.

The standard heat of formation, \( \Delta H_{\mathrm{f}}^{\circ} \) is a specific type of heat of reaction that occurs when one mole of a compound is created from its elements in their standard states. In a classroom setting, calculating \( \Delta H \) helps students understand the energy involved in chemical processes. Knowing the heat of reaction is not only pivotal for predicting reaction behavior but is also essential in industrial applications where energy management is crucial.

Chemical Compound Formation

Chemical compound formation is the process by which atoms of different elements combine in fixed ratios to form compounds. This occurs through chemical reactions where bonds are formed and broken, accompanied by energy changes. The stability of the resulting compound and the amount of energy released or required is a key focus in understanding chemical processes.

In standard heat of formation calculations, we consider the energy needed to form a compound from the most stable forms of its constituent elements, known as their standard states. These elements are often in their diatomic forms or, for carbon, as graphite. The rule for chemical compound formation in thermochemistry is that it must represent one mole of product formed from its elements, as any deviation from this would not accurately reflect the standard heat of formation. Understanding compound formation is critical in fields ranging from materials science to biochemistry, where the properties of a substance are directly linked to its formation process.