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

In the combustion of gasoline (C8H18) into CO2 and H2O, the process is exothermic, releasing heat to the surroundings, making q < 0. As the volume increases during combustion, the system performs work on the surroundings, resulting in w < 0. Thus, the signs of q and w are both negative.

Step-by-step solution

Determine the balanced equation for the combustion of gasoline

First, we need to find the balanced chemical equation for the combustion of gasoline. The general equation for the combustion of a hydrocarbon is: \( \mathrm{C}_{n} \mathrm{H}_{m}(l) + \left(n + \frac{m}{4}\right) \mathrm{O}_{2}(g) \to n \mathrm{CO}_{2}(g) + \frac{m}{2} \mathrm{H}_{2} \mathrm{O}(g) \) For gasoline, the hydrocarbon involved is octane (C8H18), so we can write the balanced equation as: \( \mathrm{C}_{8} \mathrm{H}_{18}(l) + \left(8 + \frac{18}{4}\right) \mathrm{O}_{2}(g) \to 8 \mathrm{CO}_{2}(g) + 9 \mathrm{H}_{2} \mathrm{O}(g) \) Alternatively, substitute 8 for n and 18 for m in the general combustion equation.

Determine the sign of heat (q)

Since combustion is an exothermic process, it releases heat to the surroundings. Therefore, the sign of q is negative: q < 0

Determine the sign of work (w)

In the combustion process, the volume of the system increases as gasoline (liquid) is converted into gaseous products (CO2 and H2O). The system does work on the surroundings as it expands to accommodate the higher volume of gases. Therefore, the sign of w is also negative: w < 0

Conclusion

In the process of combusting gasoline (C8H18) into CO2 and H2O, both heat (q) and work (w) have negative signs, indicating the release of heat to the surroundings and the system doing work on the surroundings.

Key concepts

Chemical Equation for Combustion

Understanding the chemical equation for the combustion of gasoline is crucial for grasping the process of converting fuel into energy. Gasoline, often approximated as octane \textbf{(C8H18)}), undergoes a complex reaction with oxygen \textbf{(O2)} from the air when ignited in an engine. The balanced chemical equation representing this combustion is written as:
$\backslash [\; \backslash mathrm\{C\}\_\{8\}\; \backslash mathrm\{H\}\_\{18\}(l)\; +\; 12.5\; \backslash ,\; \backslash mathrm\{O\}\_\{2\}(g)\; \backslash rightarrow\; 8\; \backslash ,\; \backslash mathrm\{CO\}\_\{2\}(g)\; +\; 9\; \backslash ,\; \backslash mathrm\{H\}\_\{2\}\; \backslash mathrm\{O\}(g)\; \backslash ]$
In this equation, the coefficients indicate the number of moles of each substance that are involved. For every mole of octane burned, 12.5 moles of oxygen are required to produce 8 moles of carbon dioxide \textbf{(CO2)} and 9 moles of water \textbf{(H2O)}, both in gaseous form. It's paramount for students to note that balancing this chemical equation is a key step in understanding the stoichiometry of the combustion reaction – a concept that involves the quantitative relationships between the amounts of reactants used and products formed in a chemical reaction.

Exothermic Process

An exothermic process is characterized by the release of energy to the environment, which usually occurs in the form of heat. The combustion of gasoline is a classic example of an exothermic reaction. During this process, the chemical energy stored in the fuel is released when the carbon and hydrogen atoms in octane bond with oxygen to form carbon dioxide and water. This energy release is perceived as heat and, to a lesser extent, light.

Significance in Combustion

In the context of the combustion of gasoline, the release of energy explains why engines get hot and why heat is felt when touching the hood of a car after it has been running. The negative sign of heat (q) in thermochemical equations symbolizes this energy going out of the system, hence q < 0. For students, it's important to associate the exothermic nature of combustion with the practical outcomes, such as the warming of the engine and the exhaust gases that heat up the surroundings.

Thermochemistry

The branch of chemistry that deals with the energy changes accompanying chemical reactions is called thermochemistry. In the case of gasoline combustion, thermochemistry focuses on the quantities of heat (q) and work (w) involved in the reaction. The signs of these quantities can tell us a lot about the processes occurring.
Since the reaction is exothermic, the heat term (q) is negative, indicating that energy is released into the surroundings as heat. Simultaneously, as gaseous products are formed, the system expands and performs work on the surroundings, represented by a negative sign for work (w), so w < 0.

• Heat Release (q): Negative because energy is released
• Work Done (w): Negative because the system expands against the surroundings

A thorough understanding of these concepts helps students predict physical changes and energy flows in various chemical processes so that they can apply this knowledge to real-world applications, such as how a vehicle's engine harnesses the energy from fuel.