Problem 99 - General Chemistry: Principles and Modern Applications

Question

A handbook lists two different values for the heat of combustion of hydrogen: \(33.88 \mathrm{kcal} / \mathrm{g} \mathrm{H}_{2}\) if \(\mathrm{H}_{2} \mathrm{O}(\mathrm{l})\) is formed, and \(28.67 \mathrm{kcal} / \mathrm{g} \mathrm{H}_{2}\) if \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) is formed. Explain why these two values are different, and indicate what property this difference represents. Devise a means of verifying your conclusions.

Step-by-Step Solution

Answer

The values for heat of combustion of hydrogen differ based on whether liquid water or water vapor is formed due to the energy involved in the phase change, represented by the heat (enthalpy) of vaporization. Verification of this conclusion can be performed by conducting a controlled combustion of hydrogen and measuring the heat released when each state of water is formed.

Step 1: Understanding the Problem and Concepts

The heat of combustion refers to the amount of heat released during a combustion reaction. In this scenario, hydrogen is the substance combusting and forming water. The difference in heat of combustion when water is formed as a liquid versus when it is formed as a gas can be primarily attributed to the heat of vaporization: the energy required to change water from a liquid to a gas (or, conversely, the energy released when changing from gas to liquid).

Step 2: Identify the Property

The property representing this difference is known as enthalpy (Heat) of vaporization (ΔHvap), which is the energy required for the phase change from a liquid to vapor, and this energy is additional to the enthalpy of formation since more energy is required to form water vapor rather than liquid water.

Step 3: Devise a Verification Method

To validate this conclusion, an experiment may be performed where hydrogen is combusted under controlled conditions to form both water liquid (under one set of conditions) and water vapor (under another set of conditions). By carefully measuring the heat released in each case, the difference in values related to the heat of combustion based on the state of water formed can be observed, confirming that the difference corresponds to the heat of vaporization.

Key Concepts

Enthalpy of Vaporization

The concept of enthalpy of vaporization plays a crucial role in understanding the difference in heat of combustion of hydrogen when forming liquid water versus gaseous water. When a substance goes from a liquid to a gas, it requires a certain amount of energy, known as the enthalpy of vaporization, denoted as \(\Delta H_{vap}\). This is because molecules in a gaseous state have much more energy compared to a liquid state due to their high kinetic energy, which requires breaking intermolecular forces.

This energy input is not part of the chemical reaction itself but is essential for changing the state of the substance. So, when hydrogen combusts to form water vapor, less heat is released compared to when it forms liquid water since some of the energy will have been used to vaporize the water.

• Think of it as the energy "cost" for changing from a liquid to gas.
• The additional energy required results in a lower heat of combustion when forming \(\mathrm{H}_{2} \mathrm{O} (g)\) compared to \(\mathrm{H}_{2} \mathrm{O} (l)\).
• It highlights the unique requirement of phase transitions in thermodynamics.

By understanding this concept, it's clear why there are two different values listed for the heat of combustion in the exercise.

Combustion Reaction

When we talk about a combustion reaction, we are referring to a chemical process where a substance reacts with oxygen to release energy in the form of heat and light. In the mentioned exercise, hydrogen combusts with oxygen to form water, either in its gas or liquid form.

A simple representation of this reaction is:\[ \mathrm{2H}_{2(g)} + \mathrm{O}_{2(g)} \rightarrow 2 \mathrm{H}_{2} \mathrm{O} \] The phase of \(\mathrm{H}_{2}\mathrm{O}\) that is produced (either liquid or gas) heavily influences the total energy change, hence affecting the heat of combustion.

• Exothermic nature: Combustion reactions are exothermic, meaning they release heat energy.
• Energy comparison: This released energy is what is being quantified as the heat of combustion.
• Influence of form: When the result is water vapor, more energy is retained in the system compared to when liquid water forms, due to the energy consumed in changing phases.

By considering these aspects of combustion reactions, it becomes clear why different conditions of the output affect the observed heat values.

Enthalpy of Formation

Enthalpy of formation is another key concept closely related to heat of combustion. It refers to the change in enthalpy when one mole of a substance is formed from its constituent elements under standard conditions.

In our scenario, this is particularly about forming \(\mathrm{H}_{2}\mathrm{O}\):\[ \mathrm{H}_{2(g)} + \frac{1}{2} \mathrm{O}_{2(g)} \rightarrow \mathrm{H}_{2} \mathrm{O (l/g)} \] The enthalpy of formation varies based on whether the water is formed as a liquid or gas. This is because the energy required to form the substance is compounded by any additional energy changes from phase shifts.

• Larger energy requirement: To form water vapor rather than liquid, more energy must be accounted for, attributed to the vaporization process.
• Direct observation: The differing heat of formation values can directly show us the additional enthalpy due to state changes.
• Standard conditions: Under standard conditions, these values are used to predict the feasibility and energy efficiency of reactions.

Understanding enthalpy of formation helps in predicting the total energy outcomes in reactions, particularly those involving combustion like this hydrogen and oxygen scenario.