/*! 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 87 When calcium carbonate, \(\mathr... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 87

When calcium carbonate, \(\mathrm{CaCO}_{3}\) (the major constituent of limestone and seashells), is heated, it decomposes to calcium oxide (quicklime). $$\mathrm{CaCO}_{3}(s) \longrightarrow \mathrm{CaO}(s)+\mathrm{CO}_{2}(g) ; \Delta H=177.9 \mathrm{~kJ}$$ How much heat is required to decompose \(21.3 \mathrm{~g}\) of calcium carbonate?

Short Answer

Expert verified
To decompose 21.3 g of calcium carbonate, approximately 37.9 kJ of heat is required.

Step by step solution

01

Calculate Molar Mass of CaCO3

First, find the molar mass of \(\mathrm{CaCO}_{3}\) by adding the atomic masses of calcium (Ca), carbon (C), and oxygen (O). Use the atomic masses: \(\text{Ca} = 40.08\ \text{g/mol},\ \text{C} = 12.01\ \text{g/mol},\ \text{O} = 16.00\ \text{g/mol}\). The molar mass of \(\mathrm{CaCO}_3\) is then calculated as follows:\[\text{Molar mass of } \mathrm{CaCO}_3 = 40.08 + 12.01 + (16.00 \times 3) = 100.09\ \text{g/mol}.\]
02

Convert Mass to Moles

Next, convert the given mass of \(21.3\ \text{g}\) of \(\mathrm{CaCO}_3\) to moles using the molar mass calculated in Step 1.\[\text{Moles of } \mathrm{CaCO}_3 = \frac{21.3\ \text{g}}{100.09\ \text{g/mol}} \approx 0.213\ \text{mol}.\]
03

Calculate Heat Required

Now, use the standard enthalpy change (\(\Delta H\)) of the decomposition reaction to calculate the heat required for the moles calculated in Step 2. The enthalpy change \(\Delta H = 177.9 \text{ kJ/mol}\) represents the heat needed to decompose \(1\ \text{mol}\) of \(\mathrm{CaCO}_3\).\[\text{Heat required} = 0.213\ \text{mol} \times 177.9\ \text{ kJ/mol} \approx 37.8737\ \text{ kJ}.\]
04

Finalize the Result

Round the calculated heat to an appropriate number of significant figures based on the given data. Here, rounding to three significant figures:\[\text{Heat required} \approx 37.9\ \text{kJ}.\]

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.

Calcium Carbonate Decomposition
Calcium carbonate (\(\text{CaCO}_3\)) is a chemical compound that naturally occurs in limestone and seashells. When it undergoes decomposition, this process transforms the compound into calcium oxide (\(\text{CaO}\)) and carbon dioxide (\(\text{CO}_2\)) gas. This reaction can be written as follows:\[\text{CaCO}_3(s) \longrightarrow \text{CaO}(s) + \text{CO}_2(g)\]This type of reaction occurs when calcium carbonate is heated to high temperatures. Understanding this process is essential as it plays a significant role in industries like cement production and is part of the geological carbon cycle. During decomposition, a solid (\(\text{CaCO}_3\)) becomes another solid (\(\text{CaO}\)) and a gas (\(\text{CO}_2\)), indicating a change from a compound broken into simpler substances.
Enthalpy Change
Enthalpy change (\(\Delta H\)) is a crucial concept in understanding chemical reactions. It signifies the heat absorbed or released under constant pressure during a chemical reaction. For the decomposition of calcium carbonate, this change is expressed as \(\Delta H = 177.9\ \text{kJ/mol}\).This positive sign of \(\Delta H\) indicates that the reaction is endothermic, meaning it absorbs heat from the surroundings.
This value implies that 177.9 kJ of energy is required to decompose one mole of calcium carbonate. Enthalpy change measurement helps predict how much heat a specific reaction needs or produces, guiding industrial processes to ensure energy efficiency. When calculating heat for a given mass of a reactant, this value becomes pivotal in setting a theoretical energy budget for the reaction processes.
Molar Mass Calculation
Calculating molar mass plays a critical role in chemical reactions as it helps convert between mass and moles. The molar mass of a compound is the sum of the atomic masses of all atoms in a molecule. For calcium carbonate (\(\text{CaCO}_3\)):
  • Calcium (Ca) has an atomic mass of 40.08 g/mol.
  • Carbon (C) has an atomic mass of 12.01 g/mol.
  • Oxygen (O)'s atomic mass is 16.00 g/mol, and there are three oxygen atoms in calcium carbonate.
Combining these, the molar mass of \(\text{CaCO}_3\) is calculated as:\[40.08 + 12.01 + (16.00 \times 3) = 100.09\ \text{g/mol}\]Knowing this allows us to convert a given mass to moles by dividing the mass by the molar mass. This calculation is fundamental in stoichiometry, enabling the determination of reactant or product moles in a chemical equation.

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

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

A \(19.6-\mathrm{g}\) sample of a metal was heated to \(61.67^{\circ} \mathrm{C}\). When the metal was placed into \(26.7 \mathrm{~g}\) of water in a calorimeter, the temperature of the water increased from \(25.00^{\circ} \mathrm{C}\) to \(30.00^{\circ} \mathrm{C}\). What is the specific heat of the metal?

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: $$\begin{aligned}\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) & \longrightarrow 2 \mathrm{NO}(g) ; \Delta H=180.6 \mathrm{~kJ} \\ \mathrm{~N}_{2}(g)+3 \mathrm{H}_{2}(g) & \longrightarrow 2 \mathrm{NH}_{3}(g) ; \Delta H=-91.8 \mathrm{~kJ} \\ 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) & \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(g) ; \Delta H=-483.7\mathrm{~kJ}\end{aligned}$$

Define the heat capacity of a substance. Define the specific heat of a substance.

What is the original definition of the calorie? What is the present definition?
See all solutions

Recommended explanations on Chemistry Textbooks

Kinetics

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Physical Chemistry

Read Explanation

Inorganic Chemistry

Read Explanation

Making Measurements

Read Explanation

Chemistry Branches

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.