Question

Without referring to tables, predict which of the following has the higher enthalpy in each case: (a) \(1 \mathrm{~mol} \mathrm{CO}_{2}(\mathrm{~s})\) or \(1 \mathrm{~mol} \mathrm{CO}_{2}(\mathrm{~g})\) at the same temperature, (b) \(2 \mathrm{~mol}\) of hydrogen atoms or 1 mol of \(\mathrm{H}_{2}\), (c) \(1 \mathrm{~mol} \mathrm{H}_{2}(\mathrm{~g})\) and \(0.5 \mathrm{~mol}\) \(\mathrm{O}_{2}(g)\) at \(25^{\circ} \mathrm{C}\) or \(1 \mathrm{~mol} \mathrm{H}_{2} \mathrm{O}(g)\) at \(25^{\circ} \mathrm{C}\), (d) \(1 \mathrm{~mol} \mathrm{~N}_{2}(g)\) at \(100^{\circ} \mathrm{C}\) or \(1 \mathrm{~mol} \mathrm{~N}_{2}(g)\) at \(300^{\circ} \mathrm{C}\).

Short answer

In summary, the following substances have higher enthalpies in each case: (a) 1 mol \(\mathrm{CO}_{2}(\mathrm{g})\), (b) 2 mol hydrogen atoms, (c) 1 mol \(\mathrm{H}_{2}(\mathrm{~g})\) and \(0.5 \mathrm{~mol}\) \(\mathrm{O}_{2}(g)\) at \(25^{\circ} \mathrm{C}\), and (d) 1 mol \(\mathrm{N}_{2}(g)\) at \(300^{\circ} \mathrm{C}\).

Step-by-step solution

Case (a)

Comparing enthalpies of 1 mol \(\mathrm{CO}_{2}(\mathrm{s})\) and 1 mol \(\mathrm{CO}_{2}(\mathrm{g})\) at the same temperature: Since both solid \(\mathrm{CO}_{2}\) and gaseous \(\mathrm{CO}_{2}\) are at the same temperature, it should be noted that the enthalpy of a substance in the gaseous state is higher than that in the solid state. This is because, in the gaseous state, the molecules have more energy to move around, while in the solid state, they are restricted in a rigid structure. Therefore, 1 mol \(\mathrm{CO}_{2}(\mathrm{~g})\) has a higher enthalpy than 1 mol \(\mathrm{CO}_{2}(\mathrm{~s})\) at the same temperature.

Case (b)

Comparing enthalpies of 2 mol hydrogen atoms and 1 mol of \(\mathrm{H}_{2}\): In general, when bonds are formed, energy is released, and the enthalpy of the compound decreases. Here, we have 2 mol hydrogen atoms that can form 1 mol of the diatomic hydrogen molecule, \(\mathrm{H}_{2}\). Since the formation of the \(\mathrm{H}_{2}\) molecule involves the formation of a bond, the enthalpy of 1 mol \(\mathrm{H}_{2}\) is lower than that of 2 mol hydrogen atoms.

Case (c)

Comparing enthalpies of 1 mol \(\mathrm{H}_{2}(\mathrm{~g})\) and \(0.5 \mathrm{~mol}\) \(\mathrm{O}_{2}(g)\) at \(25^{\circ} \mathrm{C}\) with that of \(1 \mathrm{~mol} \mathrm{H}_{2} \mathrm{O}(g)\) at \(25^{\circ} \mathrm{C}\): Here, we need to compare the enthalpies of the reactants (1 mol \(\mathrm{H}_{2}(\mathrm{~g})\) and \(0.5 \mathrm{~mol}\) \(\mathrm{O}_{2}(g)\) at \(25^{\circ} \mathrm{C}\)) to the product (1 mol \(\mathrm{H}_{2} \mathrm{O}(g)\) at \(25^{\circ} \mathrm{C}\)). The reaction between \(\mathrm{H}_{2}\) and \(\mathrm{O}_{2}\) is exothermic, meaning that energy is released during the reaction, and the enthalpy of the product (\(1 \mathrm{~mol} \mathrm{H}_{2} \mathrm{O}(g)\)) is lower than that of the reactants (1 mol \(\mathrm{H}_{2}(\mathrm{~g})\) and \(0.5 \mathrm{~mol}\) \(\mathrm{O}_{2}(g)\)).

Case (d)

Comparing enthalpies of 1 mol \(\mathrm{N}_{2}(g)\) at \(100^{\circ} \mathrm{C}\) and 1 mol \(\mathrm{N}_{2}(g)\) at \(300^{\circ} \mathrm{C}\): Enthalpy is directly proportional to temperature. Therefore, as the temperature increases, the enthalpy of the substance also increases. In this case, since the temperature of 1 mol \(\mathrm{N}_{2}(g)\) at \(300^{\circ} \mathrm{C}\) is higher than that of 1 mol \(\mathrm{N}_{2}(g)\) at \(100^{\circ} \mathrm{C}\), the enthalpy of 1 mol \(\mathrm{N}_{2}(g)\) at \(300^{\circ} \mathrm{C}\) is higher than that of 1 mol \(\mathrm{~N}_{2}(g)\) at \(100^{\circ} \mathrm{C}\).

Key concepts

States of Matter

Understanding the states of matter is fundamental to grasping why enthalpy changes occur. Matter exists in three primary states: solid, liquid, and gas. These states differ in terms of particle arrangement and energy content.

In a solid, particles are tightly packed in a fixed arrangement, which limits their movement and potential for energy storage. Liquids have more freedom, allowing particles to slide past each other, resulting in higher enthalpy compared to solids. Gases, however, have particles that move freely and are spread far apart, possessing the highest kinetic energy of the three states. This freedom of movement in gases leads to their having a higher enthalpy compared to solids and liquids at the same temperature.

The transition between these states, such as solid to gas, requires energy input, known as enthalpy of sublimation, due to the need to overcome intermolecular forces.

Heat and Temperature

Heat and temperature are often confused, but they represent different concepts. Temperature is a measure of the average kinetic energy of particles in a substance, dictating how hot or cold a substance feels. Heat, on the other hand, is the transfer of thermal energy from a substance of higher temperature to one of lower temperature.

Enthalpy changes can occur due to heat transfer. When heat is added to or removed from a system, the overall energy of the system alters, affecting its enthalpy. For example, increasing the temperature of a gas like \(_2(g)\) from 100°C to 300°C raises its enthalpy because the addition of heat increases the kinetic energy of the gas particles.

• Heat causes substances to undergo phase changes, as seen when ice melts or water boils, reflecting changes in enthalpy.
• Enthalpy is a state function, so it depends only on the initial and final states, not the path taken.

Bond Formation and Breaking

Chemical reactions involve the making and breaking of bonds, which dramatically influence enthalpy. Bond forming releases energy, resulting in a decrease in enthalpy, whereas bond breaking requires energy, leading to an increase in enthalpy.

In a reaction where hydrogen atoms form \(_2\), the transition from unbonded atoms to a diatomic molecule releases energy, making the enthalpy of \(_2\) lower than that of individual hydrogen atoms.

Consider how this principle applies to energy requirements and releases in reactions:

• Exothermic reactions tend to have products with bonds that require less energy than those in the reactants, resulting in released energy and reduced enthalpy.
• Endothermic reactions absorb energy as bonds within reactants break, increasing enthalpy.

Exothermic and Endothermic Reactions

The terminology of exothermic and endothermic describes whether a reaction releases or absorbs energy respectively. This distinction correlates directly with changes in enthalpy.

Exothermic reactions, like the combustion of hydrogen with oxygen to form water, result in the formation of stronger, more stable bonds—which releases energy to the surroundings. This indicates a drop in enthalpy from reactants to products.

In contrast, endothermic reactions consume energy. Energy can be absorbed from the surroundings to break the stable bonds of reactants, resulting in products with higher enthalpy. Examples include photosynthesis and the melting of ice.

Understanding these concepts explains why reactions can feel hot (exothermic) or cold (endothermic) and provides insight into evaluating the enthalpic changes of chemical processes.