Question

Write equations to define the processes to which \(\Delta_{\mathrm{a}} H^{\mathrm{o}}(298 \mathrm{K})\) refers for each of the following elements: (a) \(\mathrm{F} ;\) (b) \(\mathrm{Rb} ;(\mathrm{c}) \mathrm{Br}\) \(\mathrm{r} ;(\mathrm{d}) \mathrm{V} ;(\mathrm{e}) \mathrm{Si}\)

Short answer

(a) \( \mathrm{F_2(g)} \rightarrow 2 \mathrm{F(g)} \), (b) \( \mathrm{Rb(s)} \rightarrow \mathrm{Rb(g)} \), (c) \( \mathrm{Br_2(l)} \rightarrow 2 \mathrm{Br(g)} \), (d) \( \mathrm{V(s)} \rightarrow \mathrm{V(g)} \), (e) \( \mathrm{Si(s)} \rightarrow \mathrm{Si(g)} \)

Step-by-step solution

Understanding the Problem

The symbol \( \Delta_{\mathrm{a}} H^{\mathrm{o}}(298 \mathrm{K}) \) refers to the standard enthalpy change when one mole of an element is converted from its most stable form to gaseous atoms. We will write the appropriate chemical equations for each element mentioned in the exercise.

Writing the Equation for Fluorine (F)

For solid fluorine \( \mathrm{F}_2(g) \), the change refers to breaking the diatomic molecule into atoms. So the equation is: \[ \mathrm{F_2(g)} \rightarrow 2 \mathrm{F(g)} \] The enthalpy change is for forming 2 moles of gaseous fluorine atoms from 1 mole of \( \mathrm{F_2} \).

Writing the Equation for Rubidium (Rb)

Rubidium is a solid metal in its standard state, so the equation for forming gaseous atoms is:\[ \mathrm{Rb(s)} \rightarrow \mathrm{Rb(g)} \] This equation represents the enthalpy change when one mole of solid rubidium is converted to gaseous rubidium atoms.

Writing the Equation for Bromine (Br)

Bromine exists naturally as \( \mathrm{Br_2(l)} \), so the equation for forming gaseous bromine atoms is: \[ \mathrm{Br_2(l)} \rightarrow 2 \mathrm{Br(g)} \] This represents the enthalpy change when converting 1 mole of \( \mathrm{Br_2} \) to 2 moles of gaseous bromine atoms.

Writing the Equation for Vanadium (V)

Vanadium is a solid metal under standard conditions, and its conversion to gaseous atoms is shown as: \[ \mathrm{V(s)} \rightarrow \mathrm{V(g)} \] This describes the enthalpy change when solid vanadium is turned into gaseous vanadium.

Writing the Equation for Silicon (Si)

Silicon is also a solid in its standard form. The equation for gaseous atoms is:\[ \mathrm{Si(s)} \rightarrow \mathrm{Si(g)} \] This represents the enthalpy change when converting solid silicon to gaseous atoms.

Key concepts

Standard Enthalpy

When studying chemical reactions, understanding standard enthalpy change is crucial. This involves the change in heat content during a process when substances are converted from their standard states to another state.
Standard states at 298 K make it possible to compare reactions under similar conditions.

• For each element, this means shifting from its most stable form to isolated gaseous atoms.
• Standard enthalpy is often symbolized as \( \Delta H^\circ \), where the superscript \( \circ \) signifies "standard conditions."

Whether understanding energy changes in forming bonds or breaking them, \( \Delta H^\circ \) provides a consistent measure. This is specifically helpful when analyzing reactions involving elements like fluorine, rubidium, bromine, vanadium, and silicon.

Chemical Equations

Chemical equations are like recipes that tell us about the substances involved in a reaction, their states, and the changes that occur.
Writing an equation correctly ensures precise communication of chemical processes, which can be better understood in terms of enthalpy and other thermodynamic properties.

• A balanced equation shows the conservation of mass by having equal numbers of each type of atom on both sides.
• The states of the substances (solid, liquid, gas) are critically marked to clarify the conditions under which the reaction occurs.

Whether for diatomic molecules like \( \mathrm{F}_2(g) \) or metals like \( \mathrm{Rb(s)} \), constructing a proper equation is critical for understanding the enthalpy change in elemental conversion to gases.

Gaseous Atoms

Converting elements to their gaseous atoms is a common theme when looking at enthalpy changes.
Gaseous atoms represent a specific state where each atom is isolated from others, free from intermolecular forces beyond basic atomic structure.

• For diatomic molecules like fluorine and bromine, this involves breaking bonds to yield free atoms.
• Solid metals such as rubidium and silicon must overcome strong atomic interactions to exist as individual gaseous atoms.

This transformation offers insightful data on the energy required and plays a fundamental role in thermodynamic studies of elements.

Elemental Conversion

Elemental conversion refers to the transformation of elements from their natural state to gaseous atoms.
This process is vital to understanding energy requirements and the behavior of elements under various conditions.

• Fluorine, bromine, and oxygen naturally exist as diatomic molecules, necessitating bond dissociation to achieve gaseous elemental atoms.
• Metals like vanadium and silicon must transition from a solid lattice to individual gaseous atoms.

Understanding elemental conversion is essential for grasping the kinds of reactions elements can undergo and the enthalpy changes involved. This knowledge aids in predicting behavior, reactivity, and energy changes across different chemical scenarios.