Problem 25 - General Chemistry

Question

The equation for the combustion of \(2 \mathrm{~mol}\) of butane can be written $$ 2 \mathrm{C}_{4} \mathrm{H}_{10}(g)+\mathrm{O}_{2}(g) \longrightarrow 8 \mathrm{CO}_{2}(g)+10 \mathrm{H}_{2} \mathrm{O}(g) ; \Delta H<\mathrm{O} $$ Which of the following produces the least heat? a. Burning 1 mol of butane. b. Reacting \(1 \mathrm{~mol}\) of oxygen with excess butane. c. Burning enough butane to produce \(1 \mathrm{~mol}\) of carbon dioxide. d. Burning enough butane to produce 1 mol of water. e. All of the above reactions \((a, b, c\), and \(d)\) produce the same amount of heat.

Step-by-Step Solution

Answer

Reacting 1 mol of oxygen with excess butane produces the least heat.

Step 1: Understand the Combustion Reaction

The combustion reaction given is for the complete burning of butane (C₄H₁₀). The balanced equation is: \[2 \mathrm{C}_{4} \mathrm{H}_{10}(g) + 13 \mathrm{O}_{2}(g) \rightarrow 8 \mathrm{CO}_{2}(g) + 10 \mathrm{H}_{2} \mathrm{O}(g)\]The change in enthalpy (\(\Delta H\)) indicates that the reaction is exothermic, meaning it releases heat.

Step 2: Calculate Heat Release per Mole

Since the combustion of 2 mol of butane releases a certain amount of heat (we'll assume \(-Q J\)), the heat released per mole of butane is \(-\frac{Q}{2} J\). Similarly, the heat released per mole of \( \mathrm{CO}_2 \) produced is \(-\frac{Q}{8} J\) and per mole of \( \mathrm{H}_2 \mathrm{O} \) is \(-\frac{Q}{10} J\).

Step 3: Evaluate Each Option

- **(a) Burning 1 mol of butane:** Releases \(-\frac{Q}{2} J\).- **(b) Reacting 1 mol of oxygen:** According to the stoichiometry, \(\frac{1}{13}\) of the reaction proceeds.This means \(-\frac{Q}{13} J\) of heat is released.- **(c) Producing 1 mol of \( \mathrm{CO}_2 \):** Releases \(-\frac{Q}{8} J\).- **(d) Producing 1 mol of \( \mathrm{H}_2 \mathrm{O}\):** Releases \(-\frac{Q}{10} J\).

Step 4: Determine the Least Heat Released

Compare all amounts:- \(-\frac{Q}{13} J\) (b) < \(-\frac{Q}{10} J\) (d) < \(-\frac{Q}{8} J\) (c) < \(-\frac{Q}{2} J\) (a).Hence, option (b), the reaction of 1 mol of oxygen, releases the least heat.

Key Concepts

Butane

Butane is a hydrocarbon, specifically an alkane, with the chemical formula \( ext{C}_4 ext{H}_{10} \). It is a colorless gas at room temperature and is commonly used as a fuel. Butane is known for being easily liquefied, which makes it useful for portable gas storage, such as in lighters and camping stoves.
However, in chemical terms, butane is significant because it undergoes combustion reactions to release energy. During combustion in the presence of sufficient oxygen, butane converts into carbon dioxide \( ext{CO}_2 \) and water \( ext{H}_2 ext{O} \) while releasing heat. This reaction is crucial in energy production for various applications, making butane a valuable resource in both industrial and everyday settings.

Enthalpy

Enthalpy is a concept in thermodynamics that represents the total heat content of a system. It is denoted by the symbol \( ext{H} \), and changes in enthalpy are used to quantify the heat absorbed or released during chemical reactions.
In the context of combustion reactions, like the burning of butane, the change in enthalpy \( \Delta ext{H} \) is negative, indicating that the reaction releases heat. This signifies an exothermic reaction. Understanding enthalpy changes helps predict the energy changes associated with chemical processes, which is essential for both practical applications and academic study.
When butane combusts, the energy needed to break chemical bonds is less than the energy released when new bonds form in the products \( ext{CO}_2 \) and \( ext{H}_2 ext{O} \). This net release of energy is reflected in the negative \( \Delta ext{H} \).

Exothermic Reaction

An exothermic reaction is a type of chemical reaction that releases energy in the form of heat, light, or sound. In these reactions, more energy is released from forming products than is consumed by breaking reactant bonds. The combustion of butane is a classic example of an exothermic reaction.

• Energy release in the form of heat is the hallmark of exothermic reactions.
• A negative enthalpy change \( \Delta ext{H} \) characterizes these reactions, as is the case with butane's combustion.

The heat generated in these reactions is harnessed for practical uses, such as heating houses or powering engines, highlighting their central role in energy production.

Stoichiometry

Stoichiometry is the area of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It ensures the laws of conservation of mass are fulfilled. In the combustion of butane, stoichiometry helps determine how much oxygen is needed to completely react with a given amount of butane to produce carbon dioxide and water.
Using the balanced chemical equation:

• 2 \( ext{C}_4 ext{H}_{10(g)} \) + 13 \( ext{O}_2{(g)} \) → 8 \( ext{CO}_2 ext{(g)} \) + 10 \( ext{H}_2 ext{O(g)} \)

We see that 2 mol of butane requires 13 mol of oxygen. This ratio is essential for calculating the heat released per mole of reactants or products, as seen in the exercise. Thus, stoichiometry enables us to quantify and compare the amount of heat released under different conditions successfully. This knowledge is crucial for designing efficient combustion systems and for optimizing the yield of desired products.