/*! 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 102 Acetic acid, \(\mathrm{HC}_{2} \... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 102

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
\(\Delta H\) per mole of acetic acid is approximately -870.69 kJ/mol.

Step by step solution

01

Calculate Molar Mass of Acetic Acid

The first step is to determine the molar mass of acetic acid. The chemical formula for acetic acid is \( \mathrm{HC}_2\mathrm{H}_3\mathrm{O}_2 \). By summing up the atomic masses: \( \text{H: } 1 \times 1 \), \( \text{C: } 12 \times 2 \), \( \text{H: } 1 \times 3 \), \( \text{O: } 16 \times 2 \), the total molar mass is \( 60 \text{ g/mol} \).
02

Convert Mass to Moles

Next, we convert the mass of acetic acid used in the experiment to moles. We use the formula: moles = mass (g) / molar mass (g/mol). Thus, moles of acetic acid = \( \frac{3.58 \, \text{g}}{60 \, \text{g/mol}} = 0.0597 \, \text{mol} \).
03

Determine Heat Evolved per Mole

We know that 52.0 kJ of heat was evolved for 0.0597 mol of acetic acid. To find the heat evolved per mole, use the equation: \( \Delta H = \frac{\text{heat evolved}}{\text{moles of acetic acid}} \). Hence, \( \Delta H = \frac{52.0 \, \text{kJ}}{0.0597 \, \text{mol}} \approx -870.69 \, \text{kJ/mol} \).

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 91影视!

Key Concepts

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

Molar Mass Calculation
When you're asked to find the molar mass of a compound, you're essentially calculating the mass of one mole of that substance. For acetic acid, \( \mathrm{HC}_2\mathrm{H}_3\mathrm{O}_2 \), we need to add up the masses of all the atoms in its formula. Each hydrogen atom has a molar mass of \( 1 \text{ g/mol} \), carbon is \( 12 \text{ g/mol} \), and oxygen is \( 16 \text{ g/mol} \). So, acetic acid has:
  • 2 carbon atoms: \( 2 \times 12 = 24 \text{ g/mol} \)
  • 4 hydrogen atoms: \( 4 \times 1 = 4 \text{ g/mol} \)
  • 2 oxygen atoms: \( 2 \times 16 = 32 \text{ g/mol} \)
Adding these together, you get the total molar mass of acetic acid: \( 24 + 4 + 32 = 60 \text{ g/mol} \). This number tells you how much mass one mole of acetic acid has.
Stoichiometry
Stoichiometry is like the recipe for a chemical reaction. It helps you understand the relationship between the reactants and the products in a chemical equation. For the combustion of acetic acid, \( \mathrm{HC}_2 \mathrm{H}_3 \mathrm{O}_2(l) + 2 \mathrm{O}_2(g) \rightarrow 2 \mathrm{CO}_2(g) + 2 \mathrm{H}_2 \mathrm{O}(l) \), stochiometry tells us that:
  • One molecule of acetic acid reacts with two molecules of oxygen gas.
  • This results in two molecules of carbon dioxide and two molecules of water.
Using stoichiometry, you can predict how much product you'll get from given quantities of reactants or vice versa. In this experiment, we see how 3.58 grams of acetic acid is used to calculate moles, which helps in later steps.
Heat Evolution
Heat evolution is the energy released or absorbed during a chemical reaction. In this reaction, when acetic acid is burned, it releases heat. For the experiment, \( 52.0 \text{ kJ} \) of heat is evolved. To find how much heat is released per mole of acetic acid, you divide the total heat by the moles of acetic acid used in the experiment. Using the formula:\(\Delta H = \frac{\text{heat evolved (} 52.0 \text{ kJ)}}{\text{number of moles } (0.0597 \text{ mol)}} \approx -870.69 \text{ kJ/mol}\)Negative sign indicates that the reaction is exothermic, meaning it releases heat. This is key to understanding energy changes in chemical reactions.
Acetic Acid Combustion
The combustion of acetic acid is a type of chemical reaction where the acetic acid reacts with oxygen. The word "combustion" refers to burning, and it always involves oxygen. In this reaction:\( \mathrm{HC}_2 \mathrm{H}_3 \mathrm{O}_2(l) + 2 \mathrm{O}_2(g) \rightarrow 2 \mathrm{CO}_2(g) + 2 \mathrm{H}_2 \mathrm{O}(l) \), here,
  • The acetic acid burns completely in the presence of oxygen.
  • The products are carbon dioxide and water.
  • Such reactions are often exothermic, meaning they give off heat, which is consistent with our example where heat evolution was seen.
When understanding combustion, keep in mind that the reactants lose electrons, typically shown by the presence of oxygen as the oxidizing agent. This process helps in understanding how fuel energy content is calculated.

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

Ammonia will burn in the presence of a platinum catalyst to produce nitric oxide, NO. $$ 4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g) $$ What is the heat of reaction at constant pressure? Use the following thermochemical equations: $$ \begin{aligned} \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) & \longrightarrow 2 \mathrm{NO}(g) ; \Delta H=180.6 \mathrm{~kJ} \\ \mathrm{~N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g) ; \Delta H &=-91.8 \mathrm{~kJ} \\ 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(g) ; \Delta H=-483.7 \mathrm{~kJ} \end{aligned} $$

Potassium superoxide, \(\mathrm{KO}_{2}\), is used in some rebreathing gas masks (in which the exhaled breath is recycled in a closed space). Water vapor in the exhaled air reacts with potassium superoxide to produce oxygen gas: $$ 4 \mathrm{KO}_{2}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 4 \mathrm{KOH}(s)+3 \mathrm{O}_{2}(g) $$ In an experiment at \(25^{\circ} \mathrm{C}\) and \(1.00 \mathrm{~atm}\) in which water vapor reacts with a quantity of potassium superoxide, it was found that \(2.70 \mathrm{~kJ}\) of heat was absorbed. The oxygen gas produced was then collected at \(23.0^{\circ} \mathrm{C}\) and \(789 \mathrm{mmHg}\). What volume (in liters) of oxygen was collected?

An iron skillet weighing \(1.63 \mathrm{~kg}\) is heated on a stove to \(178^{\circ} \mathrm{C}\). Suppose the skillet is cooled to room temperature, \(21^{\circ} \mathrm{C}\). How much heat energy (in joules) must be removed to affect this cooling? The specific heat of iron is \(0.449 \mathrm{~J} /\left(\mathrm{g} \cdot{ }^{\circ} \mathrm{C}\right)\)

Acetic acid, \(\mathrm{CH}_{3} \mathrm{COOH}\), is contained in vinegar. Suppose acetic acid was formed from its elements, according to the following equation: $$ 2 \mathrm{C}(\text { graphite })+2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CH}_{3} \mathrm{COOH}(l) $$ Find the enthalpy change, \(\Delta H,\) for this reaction, using the following data: $$ \begin{array}{c} \mathrm{CH}_{3} \mathrm{COOH}(l)+2 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l) \\ \Delta H=-874 \mathrm{~kJ} \\ \mathrm{C}(\text { graphite })+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g) ; \Delta H=-394 \mathrm{~kJ} \\ \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l) ; \Delta H=-286 \mathrm{~kJ} \end{array} $$

Hydrogen cyanide is a highly poisonous, volatile liquid. It can be prepared by the reaction $$ \mathrm{CH}_{4}(g)+\mathrm{NH}_{3}(g) \longrightarrow \mathrm{HCN}(g)+3 \mathrm{H}_{2}(g) $$ What is the heat of reaction at constant pressure? Use the following thermochemical equations: $$ \begin{array}{c} \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g) ; \Delta H=-91.8 \mathrm{~kJ} \\ \mathrm{C}(\text { graphite })+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{CH}_{4}(g) ; \Delta H=-74.9 \mathrm{~kJ} \\ \frac{1}{2} \mathrm{H}_{2}(g)+\mathrm{C}(\text { graphite })+\frac{1}{2} \mathrm{~N}_{2}(g) \longrightarrow \mathrm{HCN}(g) \\ \Delta H=135.1 \mathrm{~kJ} \end{array} $$
See all solutions

Recommended explanations on Chemistry Textbooks

The Earths Atmosphere

Read Explanation

Nuclear Chemistry

Read Explanation

Chemistry Branches

Read Explanation

Physical Chemistry

Read Explanation

Chemical Analysis

Read Explanation

Making Measurements

Read Explanation
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.