Problem 85 - Chemistry The Science in Context

Question

Use the following standard heats of formation to calculate the molar enthalpy of vaporization of liquid hydrogen peroxide: \(\Delta H_{\mathrm{f}}^{\circ}\) of \(\mathrm{H}_{2} \mathrm{O}_{2}(\ell)\) is \(-188 \mathrm{kJ} / / \mathrm{mol}\) and \(\Delta H_{\mathrm{f}}^{\circ}\) of \(\mathrm{H}_{2} \mathrm{O}_{2}(g)\) is \(-136 \mathrm{kJ} / \mathrm{mol}\)

Step-by-Step Solution

Answer

Answer: The molar enthalpy of vaporization for hydrogen peroxide is 52 kJ/mol.

Step 1: Recall the definition of molar enthalpy of vaporization

The molar enthalpy of vaporization (\(\Delta H_{vap}\)) is the amount of energy required to transform one mole of a substance from its liquid state to its gaseous state at a constant temperature. Mathematically, it can be expressed as: $$\Delta H_{vap} = \Delta H_{f}^{\circ}(g) - \Delta H_{f}^{\circ}(l)$$ where \(\Delta H_{f}^{\circ}(g)\) is the standard heat of formation of the gaseous state, and \(\Delta H_{f}^{\circ}(l)\) is the standard heat of formation of the liquid state.

Step 2: Substitute the given values

We are given the standard heat of formation for liquid hydrogen peroxide (\(\Delta H_{f}^{\circ}(l) = -188 \,\text{kJ/mol}\)) and gaseous hydrogen peroxide (\(\Delta H_{f}^{\circ}(g) = -136 \,\text{kJ/mol}\)). Substituting the given values, we get: $$\Delta H_{vap} = (-136 \,\text{kJ/mol}) - (-188 \,\text{kJ/mol})$$

Step 3: Calculate the molar enthalpy of vaporization

Now, we can calculate the molar enthalpy of vaporization by solving the equation: $$\Delta H_{vap} = (-136 \,\text{kJ/mol}) + 188 \,\text{kJ/mol} = 52 \,\text{kJ/mol}$$ Hence, the molar enthalpy of vaporization for hydrogen peroxide is \(52 \,\text{kJ/mol}\).

Key Concepts

Standard Heat of Formation

The concept of standard heat of formation, represented as \(\Delta H_{\mathrm{f}}^{\circ}\), refers to the change in enthalpy when one mole of a compound is formed from its elements in their standard states. It's important because it serves as a fundamental benchmark for comparing the relative stability of compounds and their propensity to react. The standard states typically mean the most stable form of an element or compound at 1 atmosphere of pressure and a specified temperature, usually 25°C (298 K).

For instance, the standard heat of formation for liquid hydrogen peroxide (\(\mathrm{H}_{2}\mathrm{O}_{2}(\ell)\)) is given as \( -188 \mathrm{kJ/mol} \), which indicates the amount of energy released when one mole of liquid hydrogen peroxide forms from its elements, hydrogen and oxygen, under standard conditions. Similarly, the value for gaseous hydrogen peroxide (\(\mathrm{H}_{2}\mathrm{O}_{2}(g)\)) is \( -136 \mathrm{kJ/mol} \), with the phase change from liquid to gas factored into the energy calculation.

Enthalpy Change

Enthalpy change, denoted as \(\Delta H\), is a measure of the total heat content of a system and represents the heat absorbed or released during a chemical reaction or phase change at constant pressure. It's a key concept in thermodynamics and chemistry and provides insight into the energetics of reactions and physical processes.

Positive values of enthalpy change indicate an endothermic process, where the system absorbs heat from the surroundings. Conversely, negative values signify an exothermic process with heat being released to the surroundings. Calculating the enthalpy change, as shown in our earlier equation for the molar enthalpy of vaporization, allows us to assess the energy requirements for phase transitions, like turning a liquid into a gas, or the heat evolved or consumed during chemical reactions.

Vaporization

Vaporization is the physical process that converts a substance from a liquid to a gas phase. It requires energy, since molecules within the liquid must overcome intermolecular forces to transition into the gaseous state. This energy is known as the molar enthalpy of vaporization (\(\Delta H_{\mathrm{vap}}\)).

Understanding the concept of vaporization is critical as it explains not only everyday phenomena, such as water boiling on a stove, but also various industrial processes like distillation. The amount of heat required for vaporization is specific to each substance and signifies the strength of the molecular forces present; substances with strong intermolecular bonds typically require more energy to vaporize.

Hydrogen Peroxide

Hydrogen peroxide (\(\mathrm{H}_{2}\mathrm{O}_{2}\)) is a chemical compound commonly used for its bleaching and disinfectant properties, but it also has a host of industrial applications. It appears in both liquid and gaseous forms, with distinctive physical and chemical properties. The phase transition from liquid to gas, or vaporization, of hydrogen peroxide is particularly interest to chemists and chemical engineers, as it is accompanied by the release or absorption of energy—an aspect governed by its molar enthalpy of vaporization.

The liquid form (\(\mathrm{H}_{2}\mathrm{O}_{2}(\ell)\)) is more common and more stable than its gaseous counterpart. Understanding its properties, such as its standard heat of formation, is vital for those in fields such as environmental science, where the decomposition of hydrogen peroxide can be an important factor in remediation processes.