Question

Given that: $$ \mathrm{H}(g)+\mathrm{H}(g) \longrightarrow \mathrm{H}_{2}(g) \quad \Delta H^{\circ}=-436.4 \mathrm{~kJ} / \mathrm{mol} $$ calculate the change in mass (in \(\mathrm{kg}\) ) per mole of \(\mathrm{H}_{2}\) formed.

Short answer

The mass change is approximately \( -4.85 \times 10^{-12} \, \mathrm{kg/mol} \).

Step-by-step solution

Understand the Reaction

We are given the reaction where two hydrogen atoms combine to form a hydrogen molecule: \( \mathrm{H}(g) + \mathrm{H}(g) \rightarrow \mathrm{H}_{2}(g) \). The enthalpy change (\( \Delta H^{\circ} \)) for this reaction is \(-436.4 \, \mathrm{kJ/mol}\), which means energy is released when \(1\) mole of \(\mathrm{H}_{2}\) is formed.

Calculate Energy-Mass Equivalence

Use the mass-energy equivalence principle: \( E = mc^2 \). Here, \(E\) is the energy change which is \( -436.4 \, \mathrm{kJ} \), and \( c \) is the speed of light \( 3 \times 10^8 \, \mathrm{m/s} \). Convert \( E \) to \( \mathrm{J} \) (since \(1 \, \mathrm{kJ} = 1000 \, \mathrm{J}\)): \[ E = -436.4 \, \mathrm{kJ/mol} \times 1000 \, \frac{\mathrm{J}}{\mathrm{kJ}} \] \[ E = -436400 \, \mathrm{J/mol} \]

Solve for Change in Mass

Rearrange the mass-energy equivalence equation \( E = mc^2 \) to solve for \( m \): \[ m = \frac{E}{c^2} \]Substitute \( E = -436400 \, \mathrm{J/mol} \) and \( c = 3 \times 10^8 \, \mathrm{m/s} \) into the equation:\[ m = \frac{-436400}{(3 \times 10^8)^2} \]Calculate \( m \):\[ m \approx -4.85 \times 10^{-12} \, \mathrm{kg/mol} \]

Interpret the Result

The negative sign indicates a loss in mass consistent with the exothermic nature of the reaction. Per mole of \( \mathrm{H}_{2} \) formed, the mass decreases by approximately \( 4.85 \times 10^{-12} \, \mathrm{kg} \).

Key concepts

Enthalpy Change

Enthalpy change is a crucial concept in chemistry, representing the total heat content of a system. It is often denoted by the symbol \( \Delta H \), which signifies the difference between the enthalpy of the products and the reactants. When dealing with chemical reactions, understanding whether \( \Delta H \) is positive or negative can tell us about the energy changes taking place.

In the given reaction, where hydrogen atoms form a diatomic hydrogen molecule, the enthalpy change \( \Delta H^{\circ} \) is \(-436.4 \, \mathrm{kJ/mol}\). This indicates that the process is exothermic, meaning energy is released into the surroundings. Such reactions often proceed spontaneity because they lower the potential energy of the system, making the products more stable.

• \( \Delta H > 0 \): Endothermic, energy is absorbed.
• \( \Delta H < 0 \): Exothermic, energy is released.

Remember: the magnitude of the enthalpy change gives us insight into the strength of chemical bonds being formed or broken during a reaction.

Hydrogen Bonding

Hydrogen bonding is a special type of attractive force that exists between molecules. Although not explicitly mentioned in the original exercise, understanding hydrogen bonding can provide a richer context for discussions about hydrogen molecules. These bonds occur when a hydrogen atom is covalently bonded to highly electronegative elements like oxygen, nitrogen, or fluorine.

While in the diatomic hydrogen molecule (\( \mathrm{H}_2 \)), hydrogen bonding isn't present, it's important to understand its implications when hydrogen atoms interact with other elements. This attraction significantly impacts the physical properties of substances, such as water's high boiling point. In chemical terms, hydrogen bonds are relatively weak compared to covalent bonds, but they play a critical role in determining the structure and interactions of molecules.

• Strength: Weaker than covalent or ionic bonds.
• Influence on boiling/melting points.
• Key in biological molecules (e.g., DNA's double helix).

Reaction Enthalpy

Reaction enthalpy refers to the change in enthalpy during a chemical reaction. It is an essential indicator of how energy is exchanged between a chemical system and its surroundings. In reactions, like the formation of \( \mathrm{H}_2 \), it helps determine if energy is absorbed or released.

For calculations involving reaction enthalpy, it's vital to consider the stoichiometry of the reaction to ensure accurate measurements of \( \Delta H \). In our reaction, the enthalpy indicates that forming one mole of \( \mathrm{H}_2(g) \) releases \(-436.4 \, \mathrm{kJ/mol}\). This value can be utilized in further calculations to predict energy changes in larger-scale reactions.

• Determines heat exchange.
• Assists with equilibrium conditions.
• Aids in predicting phase transitions.

Knowing the enthalpy of reaction frames our understanding of the driving forces behind chemical changes.

Exothermic Reaction

Exothermic reactions are processes that release energy into their surroundings, commonly in the form of heat. The negation in the enthalpy change value \( \Delta H^{\circ} = -436.4 \, \mathrm{kJ/mol} \) for this hydrogen formation reaction nicely illustrates such a reaction.

These reactions are characterized by a decrease in temperature within the reacting body but an increase in the ambient environment. This is in contrast to endothermic reactions, which absorb energy.

• Examples: Combustion, respiration.
• Creates more stable products.
• Often favored in spontaneous reactions.

Exothermic processes are integral to a variety of industries, from energy production to materials manufacturing, emphasizing the practical importance of understanding such chemical processes.