Question

Assuming gasoline is pure \(\mathrm{C}_{8} \mathrm{H}_{18}(l),\) predict the signs of \(q\) and \(w\) for the process of combusting gasoline into \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(g)\)

Short answer

During the combustion of gasoline (C₈H₁₈) into CO₂(g) and H₂O(g), both q and w are negative. This means that heat is released to the surroundings (exothermic process) and the system does work against the surroundings due to the expansion of gases. Therefore, \(q < 0\) and \(w < 0\).

Step-by-step solution

1. Write the balanced chemical equation for the combustion of gasoline

For the combustion of C₈H₁₈, the balanced chemical equation is: \[C_{8}H_{18}(l) + 12.5O_{2}(g) \rightarrow 8CO_{2}(g) + 9H_{2}O(g)\]

2. Determine the signs of q

Combustion reactions are exothermic, meaning they release heat. As a result, the system loses heat to the surroundings, making the value of q negative. So, the sign of q is negative: \[q < 0\]

3. Determine the signs of w

To find the sign of the work (w) done during the combustion process, we need to consider the expansion of gases. In the balanced chemical equation, we see that 12.5 moles of O₂(g) are consumed and 17 moles of products (8 moles of CO₂ and 9 moles of H₂O) are formed, which means more gas molecules are produced. This results in an expansion of the gases, as more particles are created and occupy a larger volume. In an expansion, the system does work against the surroundings; thus, the sign of work is negative. So, the sign of w is negative: \[w < 0\]

4. Conclusion

During the combustion of gasoline (C₈H₁₈) into CO₂(g) and H₂O(g), both q and w are negative. This means that heat is released to the surroundings and the system does work against the surroundings in the expansion of gases. q is negative: \(q < 0\) w is negative: \(w < 0\)

Key concepts

Exothermic Reactions

Exothermic reactions are a key concept in understanding combustion. In an exothermic reaction, energy is released as heat during the transformation from reactants to products. This release of energy occurs because the energy required to break the bonds in the reactants is less than the energy released when new bonds form in the products.
For instance, when gasoline (\(\mathrm{C}_{8} \mathrm{H}_{18}(l)\) ) burns, it undergoes an exothermic reaction, releasing heat into the surroundings. This heat release is why the sign of \(q\) (heat) is negative during combustion, indicating that the system loses energy to its surroundings.
Exothermic reactions are prevalent in everyday life, not just in combustion. They include common processes like freezing water and rusting iron. Each time an exothermic reaction occurs, energy flows outward, which is fundamental to the reactions we observe, such as lighting a car engine with gasoline.

Chemical Equations

Chemical equations are a symbolic representation of a chemical reaction, illustrating how reactants transform into products. They are vital in predicting the outcomes of chemical processes.
In the combustion of gasoline, the balanced chemical equation is:\[C_{8}H_{18}(l) + 12.5O_{2}(g) \rightarrow 8CO_{2}(g) + 9H_{2}O(g)\]This equation shows us that one molecule of gasoline (\(\mathrm{C}_{8} \mathrm{H}_{18}\) ) reacts with 12.5 molecules of oxygen (\(\mathrm{O}_{2}\) ) to produce carbon dioxide (\(\mathrm{CO}_{2}\) ) and water vapor (\(\mathrm{H}_{2} \mathrm{O}\) ).
Writing balanced chemical equations is crucial as it ensures the conservation of mass and atoms, adhering to the law of conservation of matter. Understanding these equations enables us to analyze chemical reactions, predict products, and measure energy changes, such as heat released or absorbed.

Gas Expansion

Gas expansion occurs when the number of gas molecules increases during a reaction, often leading to a larger volume. In the context of combustion, understanding gas expansion helps explain why energy is expended by the system when gases evolve.
In the balanced equation for gasoline combustion, 12.5 moles of oxygen gas become 17 moles of total gas products. This net increase in the number of molecules means that the gases occupy more space, causing them to do work on their surroundings as they expand. This is why the sign of \(w\) (work) is negative in such reactions.
During gas expansion, the system performs work against external pressure. This work can be visualized as a balloon inflating, where the expanding gas inside pushes against the exterior pressure to expand. As gases spread out, they require energy to overcome surrounding forces, which is reflected in the negative sign of work during expansion.

Thermodynamics

Thermodynamics is the study of energy, heat, and their transformations. It provides a framework for understanding the energy exchanges in chemical reactions, including combustion.
In thermodynamics, we analyze two main factors in a reaction: heat transfer (\(q\)) and work done (\(w\)). Both are crucial in determining the energy change of a system. In the combustion of gasoline, as gasoline burns, it releases energy as heat (\(q < 0\)) and performs work through gas expansion (\(w < 0\)).
Thermodynamics involves understanding the laws governing energy changes:

• The First Law, which states that energy is conserved, it cannot be created or destroyed.
• The Second Law, which states that energy transfer will always result in increased entropy or disorder.

In a combustion reaction, the released energy primarily manifests as heat transferred to the surroundings, while work is done to accommodate gas expansion, both obeying these fundamental laws.