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Chapter 6: Problem 96

Acetic acid, \(\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\), is the sour constituent of vinegar (acetum is Latin for "vinegar"). In an experiment, \(3.58 \mathrm{~g}\) of acetic acid was burned. $$ \mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}(l)+2 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l) $$ If \(52.0 \mathrm{~kJ}\) of heat evolved, what is \(\Delta H\) per mole of acetic acid?

Short Answer

Expert verified
\(\Delta H \approx -872.14 \text{ kJ/mol}\)

Step by step solution

01

Convert Mass to Moles

First, determine the molar mass of acetic acid, HC extsubscript{2}H extsubscript{3}O extsubscript{2}. The molar mass is calculated as follows: C (2 atoms) is 2 脳 12.01 g/mol, H (4 atoms) is 4 脳 1.008 g/mol, and O (2 atoms) is 2 脳 16.00 g/mol. Thus, the molar mass of acetic acid is 60.05 g/mol. Then convert the mass of acetic acid burned in the experiment to moles:\[ \text{Moles of } \text{HC}_2\text{H}_3\text{O}_2 = \frac{3.58 \text{ g}}{60.05 \text{ g/mol}} \approx 0.0596 \text{ mol} \]
02

Calculate 螖H for the Reaction

The given heat evolved from burning 3.58 g of acetic acid is 52.0 kJ. Since the question asks for the enthalpy change per mole, we need to calculate the heat change for one mole of acetic acid. This is done by dividing the total heat evolved by the number of moles of acetic acid that were burned:\[ \Delta H = \frac{52.0 \text{ kJ}}{0.0596 \text{ mol}} \approx 872.14 \text{ kJ/mol} \]
03

Interpret the Result

As the reaction releases heat, it is exothermic. Thus, the enthalpy change, \(\Delta H\), should be negative to indicate that it releases energy. Incorporate this sign:\[ \Delta H \approx -872.14 \text{ kJ/mol} \]

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Key Concepts

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

Acetic Acid Combustion
Acetic acid combustion is a process where acetic acid reacts with oxygen to produce carbon dioxide and water. In the chemical equation given, acetic acid (\( \mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}(l) \)) reacts with oxygen (\( \mathrm{O}_{2}(g) \)) to form carbon dioxide (\( \mathrm{CO}_{2}(g) \)) and water (\( \mathrm{H}_{2} \mathrm{O}(l) \)).When performing combustion:
  • One molecule of acetic acid requires two molecules of oxygen to combust completely.
  • The products of this reaction are always carbon dioxide and water.
  • The reaction releases energy in the form of heat, which is measured as the heat evolved.
These properties make it a classic example of a combustion reaction. This specific reaction is important in studying enthalpy changes since it provides insights into the heat exchange during chemical transformations.
Molar Mass Calculation
To solve problems involving chemistry reactions, especially when dealing with enthalpy changes, it鈥檚 vital to calculate the molar mass correctly. Molar mass represents the mass of one mole of a substance, usually expressed in grams per mole (g/mol).Let's understand it with acetic acid:
  • A molecule of acetic acid (\( \mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2} \)) consists of:
    • 2 Carbon (C) atoms with a mass of 12.01 g/mol each, totaling 24.02 g/mol,
    • 4 Hydrogen (H) atoms at 1.008 g/mol each, totaling 4.032 g/mol,
    • 2 Oxygen (O) atoms with a mass of 16.00 g/mol each, totaling 32.00 g/mol.
  • Adding these gives acetic acid a molar mass of 60.05 g/mol.
This calculation allows us to convert from grams to moles, a crucial step in determining the enthalpy change from the experimental data.
Exothermic Reactions
Exothermic reactions are types of chemical reactions that release energy, usually in the form of heat. In these reactions, the energy needed to break the bonds in the reactants is less than the energy released when new bonds form in the products.Important aspects:
  • Heat is a byproduct, making the surroundings warmer.
  • The enthalpy change (\( \Delta H \)) is negative, indicating that energy exits the system.
  • Common examples include combustion reactions, like the acetic acid combustion.
In the exercise provided, the acetic acid combustion is clearly exothermic, as it involves the evolution of 52.0 kJ of heat. By calculating the enthalpy change per mole, we establish that the enthalpy change for the reaction is \( \Delta H \approx -872.14 \text{ kJ/mol} \), confirming the release of energy.

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Most popular questions from this chapter

An industrial process for manufacturing sulfuric acid, \(\mathrm{H}_{2} \mathrm{SO}_{4}\), uses hydrogen sulfide, \(\mathrm{H}_{2} \mathrm{~S}\), from the purification of natural gas. In the first step of this process, the hydrogen sulfide is burned to obtain sulfur dioxide, \(\mathrm{SO}_{2}\). $$ \begin{aligned} 2 \mathrm{H}_{2} \mathrm{~S}(g)+3 \mathrm{O}_{2}(g) & \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l)+2 \mathrm{SO}_{2}(g) \\ \Delta H^{\circ} &=-1124 \mathrm{~kJ} \end{aligned} $$ The density of sulfur dioxide at \(25^{\circ} \mathrm{C}\) and \(1.00 \mathrm{~atm}\) is \(2.62 \mathrm{~g} / \mathrm{L}\) and the molar heat capacity is \(30.2 \mathrm{~J} /\left(\mathrm{mol} \cdot{ }^{\circ} \mathrm{C}\right) .\) (a) How much heat would be evolved in producing \(1.00 \mathrm{~L}\) of \(\mathrm{SO}_{2}\) at \(25^{\circ} \mathrm{C}\) and \(1.00\) atm? (b) Suppose heat from this reaction is used to heat \(1.00 \mathrm{~L}\) of \(\mathrm{SO}_{2}\) from \(25^{\circ} \mathrm{C}\) and \(1.00 \mathrm{~atm}\) to \(500^{\circ} \mathrm{C}\) for its use in the next step of the process. What percentage of the heat evolved is required for this?

The equation for the combustion of \(2 \mathrm{~mol}\) of butane can be written $$ 2 \mathrm{C}_{4} \mathrm{H}_{10}(g)+\mathrm{O}_{2}(g) \longrightarrow 8 \mathrm{CO}_{2}(g)+10 \mathrm{H}_{2} \mathrm{O}(g) ; \Delta H<\mathrm{O} $$ Which of the following produces the least heat? a. Burning 1 mol of butane. b. Reacting \(1 \mathrm{~mol}\) of oxygen with excess butane. c. Burning enough butane to produce \(1 \mathrm{~mol}\) of carbon dioxide. d. Burning enough butane to produce 1 mol of water. e. All of the above reactions \((a, b, c\), and \(d)\) produce the same amount of heat.

Hydrogen is an ideal fuel in many respects; for example, the product of its combustion, water, is nonpolluting. The heat given off in burning hydrogen to gaseous water is \(5.16 \times 10^{4}\) Btu per pound. What is this heat energy in joules per gram? ( 1 Btu = 252 cal; see also Table \(1.4 .\) )

A bullet weighing 245 grains is moving at a speed of \(2.52 \times 10^{3} \mathrm{ft} / \mathrm{s} .\) Calculate the kinetic energy of the bullet in joules and in calories. One grain equals \(0.0648 \mathrm{~g}\).

When \(23.6 \mathrm{~g}\) of calcium chloride, \(\mathrm{CaCl}_{2}\), was dissolved in water in a calorimeter, the temperature rose from \(25.0^{\circ} \mathrm{C}\) to \(38.7^{\circ} \mathrm{C}\). If the heat capacity of the solution and the calorimeter is \(1258 \mathrm{~J} /{ }^{\circ} \mathrm{C}\), what is the enthalpy change when \(1.20 \mathrm{~mol}\) of calcium chloride dissolves in water? The solution process is $$ \mathrm{CaCl}_{2}(s) \longrightarrow \mathrm{Ca}^{2+}(a q)+2 \mathrm{Cl}^{-}(a q) $$
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