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Chapter 6: Problem 55

Methanol, ethanol, and \(n\) -propanol are three common alcohols. When \(1.00 \mathrm{~g}\) of each of these alcohols is burned in air, heat is liberated as shown by the following data: (a) methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right),-22.6 \mathrm{~kJ}\); (b) ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right),-29.7 \mathrm{~kJ}\) (c) \(n\) -propanol \(\left(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{OH}\right),-33.4 \mathrm{~kJ} .\) Calculate the heats of combus- tion of these alcohols in \(\mathrm{kJ} / \mathrm{mol}\).

Short Answer

Expert verified
Methanol: -724.33 kJ/mol, Ethanol: -1367.18 kJ/mol, n-propanol: -2008.67 kJ/mol.

Step by step solution

01

Calculate Molar Masses

First, find the molar masses of each alcohol. For methanol \( \mathrm{CH}_3\mathrm{OH} \), the atoms' molar masses are: Carbon (12.01 g/mol), Hydrogen (1.01 g/mol), and Oxygen (16.00 g/mol). Therefore, \( 12.01 + (3 \times 1.01) + 16.00 + 1.01 = 32.05 \mathrm{~g/mol} \). For ethanol \( \mathrm{C}_2\mathrm{H}_5\mathrm{OH} \), Carbon (12.01 g/mol), Hydrogen (1.01 g/mol), and Oxygen (16.00 g/mol), leading to \( (2 \times 12.01) + (6 \times 1.01) + 16.00 = 46.08 \mathrm{~g/mol} \). For \( n \)-propanol \( \mathrm{C}_3\mathrm{H}_7\mathrm{OH} \), \( (3 \times 12.01) + (8 \times 1.01) + 16.00 = 60.11 \mathrm{~g/mol} \).
02

Heat of Combustion per Gram to per Mole

Convert the given heat of combustion per gram to per mole by multiplying with the molar mass from Step 1. For methanol, \(-22.6 \mathrm{~kJ/g} \times 32.05 \mathrm{~g/mol} = -724.33 \mathrm{~kJ/mol} \). For ethanol, \(-29.7 \mathrm{~kJ/g} \times 46.08 \mathrm{~g/mol} = -1367.18 \mathrm{~kJ/mol} \). For \(n\)-propanol, \(-33.4 \mathrm{~kJ/g} \times 60.11 \mathrm{~g/mol} = -2008.67 \mathrm{~kJ/mol} \).

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Key Concepts

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

Heat of Combustion
When an alcohol burns, it releases energy in the form of heat. The term "heat of combustion" refers to the energy released when a specific amount of a substance is completely combusted in the presence of oxygen. This is often measured in kilojoules (kJ) per mole. By converting the energy released per gram to per mole, we can better understand the energy output efficiency of different alcohols.
Consider this example:
  • Methanol releases -22.6 kJ per gram when burned.
  • When converting this to kJ per mole, we multiply by the molar mass (found in our calculations).
  • The result is approximately -724.33 kJ/mol.
Such conversions allow chemists and engineers to compare energy outputs efficiently. For common alcohols like methanol, ethanol, and n-propanol, comparing their heats of combustion highlights their potential use as fuels.
Molar Mass Calculation
Molar mass calculations are crucial in chemistry for converting between moles and grams. This is especially important in thermochemistry where precise measurements of energy are required. The molar mass is the mass of one mole of a substance and is expressed in grams per mole (g/mol).
To calculate the molar mass of a compound like an alcohol, follow these steps:
  • Identify the individual elements in the chemical formula and their respective atomic masses.
  • For methanol (\(\mathrm{CH}_3\mathrm{OH}\)), you have one carbon (12.01 g/mol), four hydrogens (1.01 g/mol each), and one oxygen (16.00 g/mol).
  • Add these up: \[ 12.01 + 4 \times 1.01 + 16.00 = 32.05 \text{ g/mol} \]
Accurate molar mass calculations ensure that the conversion from energy per gram to energy per mole is precise, enabling reliable comparisons between different substances.
Alcohols
Alcohols are organic compounds with one or more hydroxyl (-OH) groups attached to a carbon atom. Common alcohols include methanol, ethanol, and n-propanol, each differing in the number and arrangement of carbon and hydrogen atoms in their molecular structures. This difference affects their physical properties and chemical behavior.
Key points about alcohols include:
  • Methanol, with a simple structure (\(\mathrm{CH}_3\mathrm{OH}\)), is often used as an industrial solvent and antifreeze.
  • Ethanol (\(\mathrm{C}_2\mathrm{H}_5\mathrm{OH}\)) is the type of alcohol found in alcoholic beverages, but it is also used as a fuel additive.
  • \( n \)-propanol (\(\mathrm{C}_3\mathrm{H}_7\mathrm{OH}\)), with three carbon atoms, is utilized in cosmetics and cleaning products.
Understanding the structure and function of these alcohols helps in grasping their applicability in various industries and their energetic properties when used as fuels.

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Most popular questions from this chapter

Suggest ways (with appropriate equations) that would enable you to measure the \(\Delta H_{\mathrm{f}}^{\circ}\) values of \(\mathrm{Ag}_{2} \mathrm{O}(s)\) and \(\mathrm{CaCl}_{2}(s)\) from their elements. No calculations are necessary.

Calculate the standard enthalpy change for the reaction $$ 2 \mathrm{Al}(s)+\mathrm{Fe}_{2} \mathrm{O}_{3}(s) \longrightarrow 2 \mathrm{Fe}(s)+\mathrm{Al}_{2} \mathrm{O}_{3}(s) $$ given that $$ \begin{aligned} 2 \mathrm{Al}(s)+\frac{3}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{Al}_{2} \mathrm{O}_{3}(s) \\ \Delta H_{\mathrm{rxn}}^{\circ}=&-1669.8 \mathrm{~kJ} / \mathrm{mol} \\ 2 \mathrm{Fe}(s)+\frac{3}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{Fe}_{2} \mathrm{O}_{3}(s) \\ \Delta H_{\mathrm{rxn}}^{\circ}=-822.2 \mathrm{~kJ} / \mathrm{mol} \end{aligned} $$

Calculate the work done in joules when 1.0 mole of water vaporizes at \(1.0 \mathrm{~atm}\) and \(100^{\circ} \mathrm{C}\). Assume that the volume of liquid water is negligible compared with that of steam at \(100^{\circ} \mathrm{C},\) and ideal gas behavior.

Define calorimetry and describe two commonly used calorimeters. In a calorimetric measurement, why is it important that we know the heat capacity of the calorimeter? How is this value determined?

From the following heats of combustion, $$ \begin{aligned} \mathrm{CH}_{3} \mathrm{OH}(l)+\frac{3}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l) \\ \Delta H_{\mathrm{rxn}}^{\circ}=&-726.4 \mathrm{~kJ} / \mathrm{mol} \\ \mathrm{C}(\text { graphite })+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g) \\ \Delta H_{\mathrm{rxn}}^{\circ}=-393.5 \mathrm{~kJ} / \mathrm{mol} \\ \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l) \\ \Delta H_{\mathrm{rxn}}^{\circ}=-285.8 \mathrm{~kJ} / \mathrm{mol} \end{aligned} $$ calculate the enthalpy of formation of methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right)\) from its elements: $$ \mathrm{C} \text { (graphite) }+2 \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(l) $$
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