/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 114 Three hydrocarbons that contain ... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

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.

Short Answer

Expert verified
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 by step solution

01

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):**\[ \mathrm{C}_4\mathrm{H}_6 + \frac{11}{2}\mathrm{O}_2 \rightarrow 4\mathrm{CO}_2 + 3\mathrm{H}_2\mathrm{O} \]
02

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:**\[ \Delta H_{rxn} = [4(-393.5) + 3(-285.8)] - [165 + 0] \approx -2484 \text{ kJ/mol} \]
03

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):** \[ \text{Molar mass = } 54 \text{ g/mol} \rightarrow \frac{-2484}{54} \approx -46.0 \text{ kJ/g} \]
04

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):** \[ \text{Hydrogen mass fraction} = \frac{6 \times 1}{54} \times 100 \approx 11.1\% \]
05

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.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The hydrocarbons cyclohexane \(\left(\mathrm{C}_{6} \mathrm{H}_{12}(I), \Delta H_{i}^{\circ}=-156\right.\) \(\mathrm{kJ} / \mathrm{mol}\) ) and 1 -hexene \(\left.\left(\mathrm{C}_{6} \mathrm{H}_{12}(I), \Delta H_{f}^{\circ}=-74 \mathrm{k}\right] / \mathrm{mol}\right)\) have the same empirical formula. (a) Calculate the standard enthalpy change for the transformation of cyclohexane to 1-hexene. (b) Which has greater enthalpy, cyclohexane or 1 -hexene? (c) Without doing a further calculation and knowing the answer to (b), do you expect cyclohexane of 1-hexene to have the larger combustion enthalpy?

When an 18.6 -g sample of solid potassium hydroxide dissolves in \(200.0 \mathrm{~g}\) of water in a coffee-cup calorimeter (Figure 5.18), the temperature rises from 23.7 to \(44.5^{\circ}\) C. (a) Calculate the quantity of heat (in kJ) released in the reaction. (b) Using your result from part (a), calculate \(\Delta H\) (in k]/mol KOH) for the solution process. Assume that the specific heat of the solution is the same as that of pure water.

Consider the following hypothetical reactions: $$ \begin{array}{l} \mathrm{A} \longrightarrow \mathrm{B} \quad \Delta H_{I}=+60 \mathrm{k} \mathrm{J} \\ \mathrm{B} \longrightarrow \mathrm{C} \quad \Delta H_{I}=-90 \mathrm{k} \mathrm{J} \end{array} $$ (a) Use Hess's law to calculate the enthalpy change for the reaction \(\mathrm{A} \longrightarrow \mathrm{C}\) (b) Construct an enthalpy diagram for substances \(A, B\), and \(\mathrm{C},\) and show how Hess's law applies.

A \(1.50-g\) sample of quinone \(\left(\mathrm{C}_{6} \mathrm{H}_{4} \mathrm{O}_{2}\right)\) is burned in a bomb calorimeter whose total heat capacity is \(8.500 \mathrm{~kJ} /{ }^{\circ} \mathrm{C}\). The temperature of the calorimeter increases from 25.00 to \(29.49^{\circ} \mathrm{C}\). (a) Write a balanced chemical equation for the bomb calorimeter reaction. (b) What is the heat of combustion per gram of quinone and per mole of quinone?

Under constant-volume conditions, the heat of combustion of naphthalene \(\left(\mathrm{C}_{10} \mathrm{H}_{8}\right)\) is \(40.18 \mathrm{~kJ} / \mathrm{g}\). A \(2.50-\mathrm{g}\) sample of naphthalene is burned in a bomb calorimeter. The temperature of the calorimeter increases from 21.50 to \(28.83^{\circ} \mathrm{C}\). (a) What is the total heat capacity of the calorimeter? (b) A 1.50-g sample of a new organic substance is combusted in the same calorimeter. The temperature of the calorimeter increases from 21.14 to \(25.08^{\circ} \mathrm{C}\). What is the heat of combustion per gram of the new substance? (c) Suppose that in changing samples, a portion of the water in the calorimeter were lost. In what way, if any, would this change the heat capacity of the calorimeter?

See all solutions

Recommended explanations on Chemistry Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.