Question

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 follows: (a) methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right),-22.6 \mathrm{~kJ} ;(\mathrm{b})\) 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 combustion of these alcohols in \(\mathrm{kJ} / \mathrm{mol}\).

Short answer

The heats of combustion are: methanol -724 kJ/mol, ethanol -1370 kJ/mol, n-propanol -2010 kJ/mol.

Step-by-step solution

Determine Molar Mass of Methanol

The molecular formula of methanol is \( \mathrm{CH}_3\mathrm{OH} \). To find the molar mass, add the atomic masses of each element: \( \text{Molar Mass of Methanol} = 12.01 \text{ (C) + 3}\times\text{1.01 (H) + 16.00 (O) + 1.01 (H)} = 32.04 \text{ g/mol} \).

Calculate Heat of Combustion for Methanol

Given that 1.00 g of methanol releases \( -22.6 \text{ kJ} \), convert this to per mole using the molar mass: \[\text{Heat of combustion (methanol)} = \left( \frac{-22.6 \text{ kJ}}{1.00 \text{ g}} \right) \times 32.04 \text{ g/mol} = -724 \text{ kJ/mol} \].

Determine Molar Mass of Ethanol

The molecular formula of ethanol is \( \mathrm{C}_2\mathrm{H}_5\mathrm{OH} \). Calculate the molar mass: \( \text{Molar Mass of Ethanol} = 2 \times 12.01 \text{ (C) + 6} \times \text{1.01 (H) + 16.00 (O)} = 46.08 \text{ g/mol} \).

Calculate Heat of Combustion for Ethanol

Given that 1.00 g of ethanol releases \( -29.7 \text{ kJ} \), convert this to per mole using the molar mass: \[\text{Heat of combustion (ethanol)} = \left( \frac{-29.7 \text{ kJ}}{1.00 \text{ g}} \right) \times 46.08 \text{ g/mol} = -1370 \text{ kJ/mol} \].

Determine Molar Mass of n-Propanol

The molecular formula of \( n \)-propanol is \( \mathrm{C}_3\mathrm{H}_7\mathrm{OH} \). Calculate the molar mass: \( \text{Molar Mass of n-Propanol} = 3 \times 12.01 \text{ (C) + 8}\times \text{1.01 (H) + 16.00 (O)} = 60.10 \text{ g/mol} \).

Calculate Heat of Combustion for n-Propanol

Given that 1.00 g of \( n \)-propanol releases \( -33.4 \text{ kJ} \), convert this to per mole using the molar mass: \[\text{Heat of combustion (n-propanol)} = \left( \frac{-33.4 \text{ kJ}}{1.00 \text{ g}} \right) \times 60.10 \text{ g/mol} = -2010 \text{ kJ/mol} \].

Key concepts

Molar Mass

The molar mass is a crucial concept in chemistry that helps us understand how much one mole of a given substance weighs. It is expressed in grams per mole (\( ext{g/mol} \)). To calculate the molar mass, you add the atomic masses of all the atoms in a molecule. This is particularly important when working with heat of combustion as it allows us to convert energy values from per gram to per mole.
This conversion shows more accurately how much energy is released when a full mole of a substance undergoes combustion. Knowing the molar mass makes it easier to measure and predict outcomes in chemical reactions.

Alcohols

Alcohols are a group of organic compounds characterized by the presence of one or more hydroxyl (\( ext{-OH} \)) groups attached to a carbon atom. They are widely used in various applications, from industrial solvents to alcoholic beverages.

• Methanol (\( ext{CH}_3 ext{OH} \)) is often used as a solvent and fuel.
• Ethanol (\( ext{C}_2 ext{H}_5 ext{OH} \)) is commonly found in alcoholic drinks.
• n-Propanol (\( ext{C}_3 ext{H}_7 ext{OH} \)) is used in pharmaceuticals and cosmetics.

Understanding the properties of these alcohols helps us in various industries.

Enthalpy Change

Enthalpy change, denoted as \( ext{ΔH} \), is a measure of the total heat content in a chemical reaction. It's an important thermodynamic property that reflects the heat absorbed or released at constant pressure. For combustion reactions, the heat of combustion is the enthalpy change when one mole of a substance is burned completely in oxygen. It's usually a negative value, signifying that the process releases energy to the surroundings, i.e., it is exothermic.
Enthalpy changes help gauge reaction favorability and feasibility in industrial processes.

Methanol

Methanol, with the chemical formula \( ext{CH}_3 ext{OH} \), is the simplest alcohol. It has a molar mass of 32.04 g/mol and is a light, volatile, colorless, flammable liquid with a distinctive alcohol-like odor. Methanol is used in the production of formaldehyde and acetic acid. Being toxic, it must be handled with care.
In combustion, methanol releases \( -724 \text{ kJ/mol} \), highlighting its potential use as a fuel source.

Ethanol

Ethanol (\( ext{C}_2 ext{H}_5 ext{OH} \)) is a common alcohol with numerous uses, including in beverages, as a fuel additive, and as a biomedical solvent. It has a molar mass of 46.08 g/mol.
Ethanol's heat of combustion is \( -1370 \text{ kJ/mol} \). This value shows the energy potential when ethanol completely burns, which is why it is often considered as a biofuel. Its energy release makes it a potential candidate for blending with gasoline.

n-Propanol

n-Propanol, or 1-propanol (\( ext{C}_3 ext{H}_7 ext{OH} \)), is an alcohol that finds its applications in the manufacturing of cosmetics and antiseptics. With a molar mass of 60.10 g/mol, this primary alcohol is also used as a solvent and intermediate in chemical synthesis.
The exothermic combustion of n-propanol results in a heat release of \( -2010 \text{ kJ/mol} \), making it more energy-dense than methanol and ethanol.

Chemical Reactions

Chemical reactions involve the transformation of substances in which reactants are converted into products. They obey the law of conservation of mass, meaning the mass of the products in a chemical reaction must equal the mass of the reactants.
In the context of combustion, alcohols react with oxygen to produce carbon dioxide and water, releasing energy. The balanced chemical equations help predict the stoichiometry of the reaction and the amount of energy transferred.