A new allotrope of oxygen, \(\mathrm{O}_{4}\), has been reported. The exact structure of \(\mathrm{O}_{4}\) is unknown, but the \(\operatorname{sim}-\) plest possible structure would be a four-member ring consisting of oxygen-oxygen single bonds. The report speculated that the \(\mathrm{O}_{4}\) molecule might be useful as a fuel "because it packs a lot of oxygen in a small space, so it might be even more energy-dense than the liquefied ordinary oxygen used in rocket fuel." (a) Draw a Lewis structure for \(\mathrm{O}_{4}\) and write a balanced chemical equation for the reaction between ethane, \(\mathrm{C}_{2} \mathrm{H}_{6}(g),\) and \(\mathrm{O}_{4}(g)\) to give carbon dioxide and water vapor. (b) Estimate \(\Delta H^{\circ}\) for the reaction. (c) Write a chemical equation illustrating the standard enthalpy of formation of \(\mathrm{O}_{4}(g)\) and estimate \(\Delta H_{\mathrm{f}}^{\circ}\) (d) Assuming the oxygen allotropes are in excess, which will release more energy when reacted with ethane (or any other fuel): \(\mathrm{O}_{2}(g)\) or \(\mathrm{O}_{4}(g) ?\) Explain using your answers to parts (a)-(c).

Step by step solution

01

Drawing Lewis structure of \(O_4\)

The first step involves the construction of a Lewis structure for \(O_4\). Each Oxygen atom needs 2 more electrons to complete its octet. Hence, in \(O_4\), the 4 oxygen atoms can be linked in a ring structure such that each atom shares one electron with each of its two neighbours.

02

Balancing chemical reaction between ethane and \(O_4\)

For a balanced chemical equation, the number of atoms for each element should be equal on both side. For the reaction: \(C_2H_6 + O_4 → CO_2 + H_2O\), On balancing the equation, one gets: \(2C_2H_6 + 5O_4 → 4CO_2 + 6H_2O\).

03

Estimate ∆H for reaction

We can estimate the ∆H of the reaction using known ∆H values for the formation of water (−285.83 kJ/mol) and carbon dioxide (−393.51 kJ/mol). The reaction is exothermic. Therefore: \(-∆H = (4 × ∆Hf (CO2) + 6 × ∆Hf (H2O) - 5 × ∆Hf (O4)) = 55153.2 kJ\). The negative sign indicates a release of energy.

04

Chemical equation for standard enthalpy of formation

Enthalpy of formation is the heat absorbed or released when one mole of a substance is formed from its elements in their most stable form. The enthalpy of formation of \(O_4\) would be calculated by breaking the \(O_4\) into individual O atoms, which is: \(O_4 → 4O\). Suppose that ∆Hf for \(O_4\) is x. Using the given ∆H values, we can calculate x.

05

Analyzing Energy Release with different Oxygen Allotropes

For a given fuel, the amount of energy released would be independent of whether \(O_2\) or \(O_4\) is used. This is because in both cases, the oxygen atoms end up being converted into O2 before getting used up for combustion. Hence, the total energy change should be identical. However, since \(O_4\) contains more oxygen per unit volume, it might release energy more quickly.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Lewis Structures

Lewis structures are visual representations used by chemists to illustrate the bonding between atoms, as well as the lone pairs of electrons that may exist in a molecule. This diagram helps you understand the electron configuration of a molecule and predict the distribution of electrons among the atoms.
In the case of the new oxygen allotrope \( O_4 \), each oxygen atom has six valence electrons and requires two additional electrons to complete its octet. By arranging the oxygen atoms in a ring and allowing them to share electrons through single bonds, a stable structure can be drawn where each atom contributes one electron to each of its two neighbors, completing their octets.

Chemical Reactions

Chemical reactions involve the transformation of one or more substances into new substances through the reorganization of atoms. Balancing these reactions is essential to ensure the law of conservation of mass, which states that mass cannot be created or destroyed in a chemical reaction.
For the reaction between ethane \( C_2H_6 \) and \( O_4 \), the equation must be balanced to reflect equal numbers of each type of atom on both sides. The balanced equation for the combustion of ethane with \( O_4 \) is \( 2C_2H_6 + 5O_4 \rightarrow 4CO_2 + 6H_2O \).

Enthalpy of Formation

The enthalpy of formation, \( \Delta H_f^\circ \), is the change in enthalpy when one mole of a compound is formed from its elements in their standard states. This value can be exothermic (releasing energy) or endothermic (absorbing energy).
To estimate the enthalpy of formation for \( O_4 \), we can look at the energy present in the bonds made and broken during the formation of \( O_4 \) from its elemental state. If we break \( O_4 \) into individual oxygen atoms, we are essentially calculating \( \Delta H_f^\circ \) of \( O_4 \) from the standard reference state of oxygen atoms.

Combustion Analysis

Combustion analysis is a method used to determine the elemental composition of a substance by completely burning the sample and analyzing the resulting products.
In this problem, combustion analysis can help determine whether the complete combustion of ethane using \( O_4 \) as an oxidizer forms only carbon dioxide and water. This analysis would also give insights into the energy density of \( O_4 \) as a potential fuel compared to \( O_2 \) by comparing the energy released per mole of fuel consumed.

Exothermic Reactions

Exothermic reactions are chemical processes that release heat to the surroundings. The estimation of \( \Delta H^\circ \) for the reaction between \( C_2H_6 \) and \( O_4 \) can tell us about the energy change of the process.
The negative sign in the enthalpy change indicates that energy is being released, making it an exothermic reaction. The magnitude of this energy release has practical applications in determining the suitability of \( O_4 \) as a fuel, especially in how it compares to commonly used \( O_2 \) in terms of energy output for activities such as rocket propulsion.