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

The signs of q (heat) and w (work) for the combustion of gasoline into CO2 and H2O are both negative, as the reaction is exothermic ($q<0$) and the system does work on the surroundings by causing an expansion ($w<0$).

Step-by-step solution

Write down the balanced combustion equation for gasoline

We need to write the balanced combustion reaction for gasoline (C8H18) which reacts with oxygen (O2) to form carbon dioxide (CO2) and water (H2O) as products. The balanced equation is: $$C_8{H}_{18}(l)+\frac{25}{2}{O}_2(g)\to 8C{O}_2(g)+9H_{2}O(g)$$

Determine the sign of q (heat) for the combustion process

Combustion reactions are generally exothermic, meaning they release heat to the surroundings. In this case, the combustion of gasoline into CO2 and H2O is also an exothermic reaction. Since heat is being released to the surroundings, the sign of q (heat) will be negative. So, q < 0.

Determine the sign of w (work) for the combustion process

Since gasoline (C8H18) is combusted with oxygen (O2), the number of moles of gas in the products (8 moles of CO2 and 9 moles of H2O) is greater than the number of moles of gas in the reactants (12.5 moles of O2). When the number of moles of gaseous products is greater than the number of moles of gaseous reactants, the system does work on the surroundings, causing an expansion. In such cases, the work (w) done by the system is negative. So, w < 0. In conclusion:

Predict the signs of q and w for the combustion process

Based on the steps above, we can predict that the signs of q (heat) and w (work) for the combustion of gasoline into CO2 and H2O are both negative: q < 0 (Heat is released to the surroundings, exothermic reaction) w < 0 (Work is done by the system on the surroundings, expansion)

Key concepts

Combustion Reactions

Combustion reactions are chemical processes where a substance reacts rapidly with oxygen, often producing heat and light. A common example of a combustion reaction is the burning of gasoline, which consists mainly of octane, represented chemically as $C_8{H}_{18}(l)$. In a typical combustion reaction, $C_8{H}_{18}$ reacts with oxygen $O_2$ to produce carbon dioxide $C{O}_2$ and water $H_{2}O$. The balanced chemical equation for this reaction is:

• $C_8{H}_{18}(l)+\frac{25}{2}{O}_2(g)\to 8C{O}_2(g)+9H_{2}O(g)$

This equation signifies that eight moles of carbon dioxide and nine moles of water vapor are produced from each mole of octane combusted.
Combustion processes are key components of energy production in engines and power plants. Most combustion reactions are exothermic and involve hydrocarbons like gasoline. Understanding combustion is essential in fields such as energy management and environmental science, as it directly impacts carbon emissions.

Exothermic Processes

Exothermic processes are chemical reactions that release energy into their surroundings, usually in the form of heat or light. This release of energy is a defining characteristic of these processes. In the context of the combustion of gasoline, the reaction is clearly exothermic because it releases significant amounts of heat.
During the combustion of $C_8{H}_{18}(l)$, energy is given off which can be observed as heat and occasionally as flames. This released energy makes the sign of $q$ (heat) in thermodynamic terms negative, since energy is lost from the fuel to its surrounding.
Exothermic reactions are crucial in our daily lives, powering everything from car engines to home heating systems. A fundamental understanding of these reactions not only aids in efficient energy use but also allows for advancements in energy storage and generation technologies.

Gas Laws

Gas laws are fundamental principles that describe the behavior of gases and how they interact with parameters like temperature, volume, and pressure. When dealing with combustion reactions involving gases, understanding the gas laws is essential.
In the combustion of gasoline, as $C_8{H}_{18}$ reacts with $O_2$, the number of moles of gaseous products ($C{O}_2$ and $H_{2}O$) increases significantly. This expansion from fewer moles of reactants to more moles of products means that the gas volume increases if the reaction is occurring in a flexible container.

• According to the ideal gas law $PV=nRT$, if the amount of gas $n$ increases, assuming constant temperature $T$ and pressure $P$, the volume $V$ must also increase.

This increase in volume naturally results in work being done by the gas on its surroundings, thus bearing a negative sign for $w$ in thermodynamic terms.
Understanding gas laws is essential in predicting and manipulating the outcomes of chemical reactions, especially in industrial applications where gas flow and pressure changes are crucial.