Problem 18 - Chemistry: Introducing Inorganic, Organic and Physical Chemistry

Question

The standard enthalpy change of combustion of heptane, \(\left.\mathrm{C}_{7} \mathrm{H}_{16}, \text { at } 298 \mathrm{K}, \text { is }-4817 \mathrm{kJmol}^{-1} \text {. (Section } 1.6\right)\) (a) Write a thermochemical equation for the complete combustion of heptane to carbon dioxide and water. (b) What is the enthalpy change when \(50 \mathrm{g}\) of heptane are bumed? (c) What mass of heptane would be needed to provide \(100 \mathrm{MJ}\) of energy?

Step-by-Step Solution

Answer

(a) Combustion equation: \(\mathrm{C}_7\mathrm{H}_{16} + 11\mathrm{O}_2 \rightarrow 7\mathrm{CO}_2 + 8\mathrm{H}_2\mathrm{O}\). (b) Enthalpy change for 50g: -2402 kJ. (c) 2081 g of heptane is needed for 100 MJ.

Step 1: Writing the balanced equation

Heptane (\(\mathrm{C}_7\mathrm{H}_{16}\)) reacts with oxygen to produce carbon dioxide \((\mathrm{CO}_2)\) and water \((\mathrm{H}_2\mathrm{O})\). The combustion reaction can be written as: \[\mathrm{C}_7\mathrm{H}_{16}(l) + 11\mathrm{O}_2(g) \rightarrow 7\mathrm{CO}_2(g) + 8\mathrm{H}_2\mathrm{O}(l)\]

Step 2: Calculate the moles of heptane in 50g

First, determine the molar mass of heptane, which is calculated as: \(7 \times 12.01 + 16 \times 1.01 = 100.23 \, \text{g/mol}\). Thus, the number of moles in 50 g is: \(\frac{50}{100.23} \approx 0.499 \, \text{moles}\).

Step 3: Calculate the enthalpy change for 50g of heptane

The enthalpy change for the combustion of 1 mole of heptane is \(-4817\, \text{kJ/mol}\). For 0.499 moles, the enthalpy change is: \(-4817\times 0.499 \approx -2402 \text{kJ}\).

Step 4: Calculate mass of heptane for 100 MJ

To find out how much heptane is needed to release 100 MJ (100000 kJ), set up the proportion: \(4817 \, \text{kJ/mol}\) is released by 1 mole. Therefore, to release 100000 kJ, \(\frac{100000}{4817}\approx 20.76 \text{moles}\) are needed. Convert this to grams: \(20.76 \times 100.23 \approx 2081 \, \text{g}\).

Key Concepts

Thermochemical Equation

A thermochemical equation is an essential tool in chemistry that not only shows the reactants and products in a chemical reaction but also provides information about the energy change during the reaction. For the combustion of heptane (\(\mathrm{C}_7\mathrm{H}_{16}\)), the balanced thermochemical equation is:
\[\mathrm{C}_7\mathrm{H}_{16}(l) + 11\mathrm{O}_2(g) \rightarrow 7\mathrm{CO}_2(g) + 8\mathrm{H}_2\mathrm{O}(l) \qquad \Delta H = -4817 \, \text{kJ/mol}\]Here, \(\Delta H = -4817 \, \text{kJ/mol}\) indicates the enthalpy change, signifying that 4817 kJ of energy is released when one mole of heptane undergoes complete combustion. This release of energy is often referred to as an exothermic process, where the system loses energy to the surroundings, typically seen as an increase in temperature.

Moles Calculation

Calculating moles is a fundamental part of stoichiometry, which is essential for understanding chemical reactions. To find out how many moles are in a given mass of a substance, use the formula:
\[moles = \frac{\text{mass of substance (g)}}{\text{molar mass (g/mol)}}\]For heptane, the molar mass is calculated by adding the atomic masses of its constituent elements: \(7 \, \text{C} \times 12.01 \, \text{g/mol} + 16 \, \text{H} \times 1.01 \, \text{g/mol} = 100.23 \, \text{g/mol}\).

• When you have 50 g of heptane, the moles are found using: \(\frac{50}{100.23} \approx 0.499 \, \text{moles}\).

Understanding this calculation helps you determine how much of a substance is present and participate accurately in the reaction dynamics.

Enthalpy Calculation

The enthalpy change of combustion provides insight into whether a reaction is releasing or absorbing energy. It is calculated as:
\[\Delta H = \Delta H_{\text{combustion per mole}} \times \text{moles of substance}\]In our example, the enthalpy change for burning 50 g of heptane involves:

• First, knowing the enthalpy for one mole is \(-4817 \, \text{kJ/mol}\).
• Then, multiplying this by the amount in moles: \(-4817 \times 0.499 \approx -2402 \, \text{kJ}\).

This calculation indicates that burning 50 g of heptane releases approximately 2402 kJ of energy, contributing to our understanding of the system's energy dynamics.

Combustion Reaction

Combustion reactions involve the burning of a substance in the presence of oxygen, leading to the formation of oxides like carbon dioxide and water. These reactions are a subset of chemical reactions that are exothermic, meaning they release heat. In the context of heptane:

• Heptane reacts with oxygen to produce carbon dioxide and water.
• This process not only releases energy but also translates into practical applications like generating heat or powering engines.

To find the mass of heptane needed for a specific energy output, such as 100 MJ, we follow these steps:
1. Calculate the moles needed for the desired energy: \(\frac{100,000}{4817} \approx 20.76 \, \text{moles}\).2. Convert moles to mass: \(20.76 \times 100.23 \approx 2081 \, \text{g}\).This example highlights how understanding the combustion reaction and its enthalpy allows us to gauge energy expenditure efficiently.