Question

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

Short answer

In summary, the substances or states with higher enthalpy in each case are: a) 1 mol of gaseous iodine (I₂) has a higher enthalpy than 1 mol of solid iodine (I₂) at the same temperature. b) 2 mol of iodine atoms have a higher enthalpy compared to 1 mol of I₂. c) The reactants (1 mol of I₂ gas and 1 mol of H₂ gas) have a higher enthalpy compared to the products (2 mol of HI gas) at 25°C. d) 1 mol of H₂ gas at 300°C has a higher enthalpy compared to 1 mol of H₂ gas at 100°C.

Step-by-step solution

Compare the phases of iodine

Since we are comparing 1 mol of solid iodine (I2) and 1 mol of gaseous iodine (I2) at the same temperature, we must consider the enthalpy change required to turn the solid iodine into a gas, known as enthalpy of sublimation or the enthalpy of the phase transition.

Predict which state of iodine has a higher enthalpy

It requires energy to convert solid iodine to gaseous iodine. This energy input increases the enthalpy of the system. Therefore, we can predict that 1 mol of gaseous iodine (I2) will have a higher enthalpy compared to 1 mol of solid iodine (I2) at the same temperature. #b) Comparing enthalpy of 2 mol of iodine atoms and 1 mol of iodine molecules#

Consider the bond dissociation energy

In order to compare the enthalpy of 2 mol of iodine atoms and 1 mol of I2 molecules, we need to consider the bond dissociation energy. Breaking the bond between two iodine atoms in an I2 molecule requires energy, which increases the enthalpy of the system.

Predict which has a higher enthalpy

Since it requires energy to break the bond between two iodine atoms in an I2 molecule, we can predict that having 2 mol of iodine atoms will have a higher enthalpy compared to 1 mol of I2. #c) Comparing enthalpy of 1 mol of I2 gas, 1 mol of H2 gas, and 2 mol of HI gas at 25°C#

Compare enthalpy of formation

In this case, we need to compare the enthalpy of the reactants to the enthalpy of the products at the given temperature. The reaction we are considering is: \[\mathrm{I}_{2}(g) + \mathrm{H}_{2}(g) \rightarrow 2 \mathrm{HI}(g)\]

Predict which has a higher enthalpy

Since the formation of new bonds releases energy, the reactants must have a higher enthalpy than the products to provide energy for bond formation. We can predict that the reactants (1 mol of I2 gas and 1 mol of H2 gas) will have a higher enthalpy compared to the products (2 mol of HI gas) at 25°C. #d) Comparing enthalpy of 1 mol of H2 gas at 100°C and 1 mol of H2 gas at 300°C#

Understand the effect of temperature on enthalpy

Enthalpy is a state function and it increases with increasing temperature. In this case, we must compare the enthalpy of the same substance (H2 gas) at two different temperatures (100°C and 300°C).

Predict which has a higher enthalpy

Since enthalpy increases with increasing temperature, we can predict that 1 mol of H2 gas at 300°C will have a higher enthalpy compared to 1 mol of H2 gas at 100°C.

Key concepts

Phase Transition

When a substance changes its state, for instance, from solid to gas, it undergoes a phase transition. This transition involves the absorption or release of energy, and in the case of converting a solid into a gas, it is referred to as sublimation.
For iodine in our exercise, converting from solid (I_2 (s)) to gaseous form (I_2 (g)) requires energy. This energy input is required to overcome the forces holding the iodine molecules in solid form.
Consequently, gaseous iodine will possess a higher enthalpy than its solid counterpart at the same temperature, due to the energy absorbed during the phase transition. Understanding these energy changes helps predict enthalpy variations in different states.

Bond Dissociation Energy

The concept of bond dissociation energy revolves around the energy required to break the chemical bond between two atoms in a molecule.
In iodine's case, a molecule (I_2) contains two iodine atoms bonded together. Breaking this bond requires energy, referred to as bond dissociation energy.
The more energy used to break these bonds, the higher the enthalpy of the resulting atoms will be.
Therefore, 2 mol of individual iodine atoms will have a higher enthalpy than 1 mol of molecular iodine (I_2) since extra energy has been added to dissociate the bond.

Enthalpy of Formation

Enthalpy of formation refers to the change in enthalpy when one mole of a compound is formed from its constituent elements under standard conditions.
In a chemical reaction, like the formation of hydrogen iodide (2HI(g)) from hydrogen gas (H_2(g)) and iodine gas (I_2(g)) , new bonds are formed.
Forming these bonds releases energy, indicating the products have lower enthalpy compared to the reactants, which had to store energy initially for bond formation.
Therefore, the enthalpy of formation helps predict that the initial reactants, in this scenario, hold higher enthalpy than the resultant product.

State Function

Enthalpy is an example of a state function, meaning it depends only on the current state of the system and not on the path taken to achieve that state.
When comparing the same substance, such as hydrogen gas (H_2(g)) at different temperatures, it emphasizes that the increase in temperature corresponds directly to an increase in enthalpy.
At 300°C, the kinetic energy of the hydrogen molecules increases, leading to a higher enthalpy state than at 100°C.
Enthalpy as a state function allows us to compare energy changes involved easily under different conditions, crucial for predicting outcomes in reactions and transitions.