Problem 114 - Chemistry The Central Science In Si Units

Question

Three hydrocarbons that contain four carbons are listed here, along with their standard enthalpies of formation: \begin{tabular}{llc} \hline Hydrocarbon & Formula & \(\Delta H_{i}^{2}(\mathrm{k} \mathrm{U} / \mathrm{mol})\) \\ \hline Butane & \(\mathrm{C}_{4} \mathrm{H}_{10}(\mathrm{~s})\) & -125 \\ 1-Butene & \(\mathrm{C}_{4} \mathrm{H}_{8}(g)\) & -1 \\ 1-Butyne & \(\mathrm{C}_{4} \mathrm{H}_{6}(\boldsymbol{g})\) & 165 \\ \hline \end{tabular} (a) For each of these substances, calculate the molar enthalpy of combustion to \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(l) .\) (b) Calculate the fuel value, in \(\mathrm{kJ} / \mathrm{g}\), for each of these compounds. (c) For each hydrocarbon, determine the percentage of hydrogen by mass. (d) By comparing your answers for parts (b) and (c), propose a relationship between hydrogen content and fuel value in hydrocarbons.

Step-by-Step Solution

Answer

Butane has the highest fuel value (49.6 kJ/g) and hydrogen percentage (17.2%), suggesting more hydrogen increases a hydrocarbon's fuel value.

Step 1: Combustion Reaction for Hydrocarbons

For each hydrocarbon, write down its balanced combustion reaction. - **Butane (C4H10):**\[ \mathrm{C}_4\mathrm{H}_{10} + \frac{13}{2}\mathrm{O}_2 \rightarrow 4\mathrm{CO}_2 + 5\mathrm{H}_2\mathrm{O} \]- **1-Butene (C4H8):**\[ \mathrm{C}_4\mathrm{H}_8 + 6\mathrm{O}_2 \rightarrow 4\mathrm{CO}_2 + 4\mathrm{H}_2\mathrm{O} \]- **1-Butyne (C4H6):**\[ \mathrm{C}_4\mathrm{H}_6 + \frac{11}{2}\mathrm{O}_2 \rightarrow 4\mathrm{CO}_2 + 3\mathrm{H}_2\mathrm{O} \]

Step 2: Calculate Enthalpy of Combustion

Using the standard enthalpy of formation, calculate the enthalpy of combustion for each compound using: \[ \Delta H_{rxn} = \sum \Delta H_f^{\circ} (\text{products}) - \sum \Delta H_f^{\circ} (\text{reactants}) \] - **For Butane:**\[ \Delta H_{rxn} = [4(-393.5) + 5(-285.8)] - [-125 + 0] \approx -2877 \text{ kJ/mol} \]- **For 1-Butene:**\[ \Delta H_{rxn} = [4(-393.5) + 4(-285.8)] - [-1 + 0] \approx -2710 \text{ kJ/mol} \]- **For 1-Butyne:**\[ \Delta H_{rxn} = [4(-393.5) + 3(-285.8)] - [165 + 0] \approx -2484 \text{ kJ/mol} \]

Step 3: Calculate Fuel Value (kJ/g)

Convert the enthalpy of combustion from \(\text{kJ/mol}\) to \(\text{kJ/g}\): - **Butane (C4H10):** \[ \text{Molar mass = } 58 \text{ g/mol} \rightarrow \frac{-2877}{58} \approx -49.6 \text{ kJ/g} \]- **1-Butene (C4H8):** \[ \text{Molar mass = } 56 \text{ g/mol} \rightarrow \frac{-2710}{56} \approx -48.4 \text{ kJ/g} \]- **1-Butyne (C4H6):** \[ \text{Molar mass = } 54 \text{ g/mol} \rightarrow \frac{-2484}{54} \approx -46.0 \text{ kJ/g} \]

Step 4: Calculate Hydrogen Percentage by Mass

Calculate the percentage of hydrogen in each compound:- **Butane (C4H10):** \[ \text{Hydrogen mass fraction} = \frac{10 \times 1}{58} \times 100 \approx 17.2\% \]- **1-Butene (C4H8):** \[ \text{Hydrogen mass fraction} = \frac{8 \times 1}{56} \times 100 \approx 14.3\% \]- **1-Butyne (C4H6):** \[ \text{Hydrogen mass fraction} = \frac{6 \times 1}{54} \times 100 \approx 11.1\% \]

Step 5: Relationship Between Hydrogen Content and Fuel Value

Observe the trend between the hydrogen percentage and the fuel value. Higher hydrogen content in a hydrocarbon generally correlates with a higher fuel value, as seen with butane having both the highest hydrogen percentage and fuel value compared to butene and butyne.

Key Concepts

Hydrocarbons

Hydrocarbons are simple organic compounds made entirely of hydrogen (H) and carbon (C) atoms. They are classified based on the types of bonds between the carbon atoms: alkanes, alkenes, and alkynes.

• Alkanes: These are saturated hydrocarbons with single bonds (e.g., butane).
• Alkenes: These contain at least one carbon-carbon double bond (e.g., 1-butene).
• Alkynes: These have one or more carbon-carbon triple bonds (e.g., 1-butyne).

Hydrocarbons are widely used as fuels because they combust easily, releasing significant amounts of energy. During combustion, these compounds burn in oxygen to produce carbon dioxide and water, making them excellent energy sources.
Understanding the different types of hydrocarbons and their combustion reactions is crucial when analyzing their energy outputs. In this case, we're looking at butane, 1-butene, and 1-butyne, all of which are hydrocarbons with four carbon atoms.

Molar Enthalpy

Molar enthalpy of combustion is the heat released when one mole of a substance is completely burned in oxygen. It's an important measure in thermochemistry, especially when studying fuels and their efficiencies. The process involves calculating the difference between the enthalpies of the products and the enthalpies of the reactants.
Here's the equation employed: \[ \Delta H_{rxn} = \sum \Delta H_f^{\circ} (\text{products}) - \sum \Delta H_f^{\circ} (\text{reactants})\]
This equation helps us determine the heat exchange during a reaction under standard conditions.
For example, in the combustion of butane, 1-butene, and 1-butyne, different values of molar enthalpy were calculated, showcasing the distinct amount of energy released per mole for each hydrocarbon. The concept of molar enthalpy is vital for determining the efficiency and better understanding of how much usable energy a specific amount of fuel can provide.

Hydrogen Content

Hydrogen content in hydrocarbons significantly influences their combustion characteristics and energy output. By determining the percentage of hydrogen by mass in a compound, we gather insights into how much energy it can release.
Calculating the hydrogen content involves analyzing the number of hydrogen atoms and their respective mass in relation to the overall compound:\[ \text{Hydrogen mass fraction} = \frac{\text{(number of H atoms)} \times 1}{\text{Molar mass of compound}} \times 100\]
For example, butane with a higher hydrogen content releases more energy compared to 1-butene and 1-butyne under similar conditions. Generally, a higher hydrogen to carbon ratio indicates a greater potential for energy release, as seen in typical hydrocarbon fuels where hydrogen acts as a potent energy carrier.

Fuel Value

Fuel value, often expressed in kilojoules per gram (kJ/g), measures how much energy a substance can provide when completely burned. This metric is crucial for evaluating and comparing different fuels.
Calculating fuel value involves converting molar enthalpy (in kJ/mol) to amount of energy per mass unit:\[ \text{Fuel value (kJ/g)} = \frac{\Delta H_{rxn}}{\text{Molar mass (g/mol)}}\]
In the context of the three hydrocarbons discussed, butane demonstrates the highest fuel value due to its higher hydrogen content, which translates to greater energy release. Observing fuel values helps in choosing the most efficient hydrocarbon for specific energy applications, where higher values are preferred for greater energy efficiency. The correlation between hydrogen content and fuel value further aids in selecting optimal fuels for various industrial and commercial uses.