Problem 77 - Chemistry

Question

Predict the value of \(\Delta H_{\mathrm{f}}^{\circ}\) (greater than, less than, or equal to zero) for these elements at \(25^{\circ} \mathrm{C}:\) (a) \(\mathrm{Br}_{2}(g)\), \(\mathrm{Br}_{2}(l) ;(\mathrm{b}) \mathrm{I}_{2}(g), \mathrm{I}_{2}(s)\).

Step-by-Step Solution

Answer

\(\Delta H_{\mathrm{f}}^{\circ}\) is > 0 for \(\mathrm{Br}_{2}(g)\) and \(\mathrm{I}_{2}(g)\); it is 0 for \(\mathrm{Br}_{2}(l)\) and \(\mathrm{I}_{2}(s)\).

Step 1: Understanding Standard Enthalpy of Formation

The standard enthalpy of formation, \(\Delta H_{\mathrm{f}}^{\circ}\), is defined as the enthalpy change when one mole of a compound is formed from its elements in their standard states. For elements in their standard states, \(\Delta H_{\mathrm{f}}^{\circ}\) is defined as zero. Thus, we need to determine the standard state of each element at \(25^{\circ} \mathrm{C}\).

Step 2: Determine the Standard States of the Elements

At \(25^{\circ} \mathrm{C}\), the standard state of bromine is \(\mathrm{Br}_{2}(l)\), and the standard state of iodine is \(\mathrm{I}_{2}(s)\). This means that these forms are the most stable forms of bromine and iodine at room temperature and pressure.

Step 3: Predict the Enthalpy of Formation for Each Case

For \(\mathrm{Br}_{2}(g)\), since \(\mathrm{Br}_{2}(l)\) is the standard state, the conversion to gas would involve a positive \(\Delta H_{f}^{\circ}\). For \(\mathrm{Br}_{2}(l)\), being in its standard state, \(\Delta H_{f}^{\circ} = 0\). Similarly, for \(\mathrm{I}_{2}(g)\), \(\Delta H_{f}^{\circ}\) is positive because it is formed from \(\mathrm{I}_{2}(s)\) (its standard state). For \(\mathrm{I}_{2}(s)\), \(\Delta H_{f}^{\circ} = 0\) as it is in its standard state.

Key Concepts

Standard States of Elements

The standard state of an element refers to its most stable form at room temperature and atmospheric pressure (often approximated as 1 atmosphere). This is the form in which the element is most commonly found in nature under these conditions. For any chemical element in its standard state, the standard enthalpy of formation, denoted as \(\Delta H_{\mathrm{f}}^{\circ}\), is defined as zero. This principle helps in calculating enthalpy changes for reactions involving compounds made from these elements.

• At \(25^{\circ} \text{C}\), bromine is typically found as a liquid, denoted as \(\mathrm{Br}_2(l)\).
• Iodine, on the other hand, is commonly solidified, hence denoted as \(\mathrm{I}_2(s)\).

Understanding these standard states is crucial when calculating changes in enthalpy because any deviation from them involves an enthalpy change. Consequently, converting from the standard state to another state, such as from a liquid or solid to a gas, entails a positive enthalpy of formation.

Enthalpy Change

Enthalpy change is a thermodynamic concept that measures the energy absorbed or released during a chemical reaction or physical process at constant pressure. It is represented by \(\Delta H\), which indicates the difference in enthalpy between products and reactants. When a reaction releases energy, it is exothermic, causing \(\Delta H\) to be negative. Conversely, if a reaction absorbs energy, it is endothermic, with a positive \(\Delta H\).

• For elements in their standard states, \(\Delta H_{\mathrm{f}}^{\circ} = 0\), since no reaction is occurring to form the elements.
• When transitioning from a liquid to a gas, like \(\mathrm{Br}_2(l)\) to \(\mathrm{Br}_2(g)\), the process requires energy input, making \(\Delta H_{\mathrm{f}}^{\circ}\) positive.
• Similarly, going from \(\mathrm{I}_2(s)\) to \(\mathrm{I}_2(g)\) demands energy, so \(\Delta H_{\mathrm{f}}^{\circ}\) is positive.

In essence, calculating enthalpy changes allows one to determine the energy dynamics of chemical processes, an essential aspect of chemical thermodynamics.

Room Temperature and Pressure

Room temperature and pressure are standard conditions that simplify calculations and comparisons of thermodynamic data. Room temperature is typically taken to be about \(25^{\circ} \text{C}\) or \(298 \,\text{K}\), and standard pressure is usually \(1\,\text{atm}\). These conditions are critical when discussing standard states, as the stability of an element's phase can vary considerably with changes in temperature and pressure.

• At room temperature, bromine is liquid, hence \(\mathrm{Br}_2(l)\), while iodine is solid, \(\mathrm{I}_2(s)\).
• Standard conditions provide a baseline for reporting thermodynamic data such as \(\Delta H_{\mathrm{f}}^{\circ}\), ensuring consistency in scientific communication.

Utilizing room temperature and pressure as a reference point makes it easier to predict phase changes and enthalpy requirements for various chemical processes.

Chemical Thermodynamics

Chemical thermodynamics is the study of energy transformations in chemical reactions and physical changes of state. It covers concepts such as energy changes, enthalpy, and entropy, providing a framework for understanding how reactions occur and predicting their feasibility and extent.

• The concept of standard enthalpy of formation fits into chemical thermodynamics as it represents the energy change when forming a compound from its elemental constituents in their standard states.
• By examining \(\Delta H\), one can gauge whether a process is thermodynamically favorable under given conditions, such as room temperature and pressure.
• This field of study helps chemists understand and predict how substances interact over time and energy exchanges involved.

Thus, chemical thermodynamics is a key area of study that facilitates understanding and manipulation of chemical processes in both theoretical and practical domains.