Book cover for General Chemistry: Principles and Modern Applications

General Chemistry: Principles and Modern Applications

Ralph H. Petrucci, F. Geoffrey Herring, Jeffry D. Madura, Carey Bissonnette

ISBN #9780132931281

11th Edition

3,230 Questions

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293,395 Students Helped

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Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

This chapter integrates thermochemistry and basic quantum theory, providing a framework for understanding energy changes in chemical reactions and the structure of atoms. Key ideas include the principles of heat and work transfer, the conservation of energy as stated in the first law of thermodynamics, and the techniques of calorimetry used to measure energy changes. Additionally, the chapter lays the foundation for understanding electron behavior through electromagnetic radiation, energy levels, and quantum numbers, which are crucial for predicting reaction energetics and atomic structure.

Learning Objectives

1

Explain the principles of thermochemistry, including energy transfer as heat and work and the application of the first law of thermodynamics.

2

Describe how calorimetry techniques (bomb and coffee-cup calorimeters) are used to measure changes in internal energy and enthalpy.

3

Apply Hess’s law and the concept of standard enthalpy of formation to calculate energy changes in chemical reactions.

4

Outline the basics of quantum theory of electrons, including electromagnetic radiation, energy levels in the hydrogen atom, and the role of quantum numbers in defining electron orbitals.

Key Concepts

CONCEPT

DEFINITION

Thermochemistry

The study of energy changes, particularly heat and work, associated with chemical reactions and physical changes.

First Law of Thermodynamics

A statement of energy conservation, which asserts that the change in internal energy of a system is equal to the heat added to the system plus the work done on the system (ΔU = q + w).

Calorimetry

An experimental technique used to measure the amount of heat involved in a chemical or physical process, often using devices such as bomb or coffee-cup calorimeters.

Hess’s Law

A principle stating that the total enthalpy change during a chemical reaction is the same regardless of the pathway taken, allowing for calculation of reaction energies by summing known steps.

Standard Enthalpy of Formation

The change in enthalpy when one mole of a compound is formed from its elements under standard conditions.

Electromagnetic Radiation

Energy emitted in the form of waves or particles, which includes visible light, X-rays, and other forms; crucial for studying electron transitions in atoms.

Quantum Numbers

Numbers that describe the unique quantum state of an electron in an atom, including its energy level, orbital shape, magnetic orientation, and spin.

Energy Levels

Discrete states in which electrons in an atom can exist, each corresponding to a specific amount of energy.

Example Problems

Example 1

Calculate the quantity of heat, in kilojoules, (a) required to raise the temperature of 9.25 Lof water from 22.0 to $29.4^{\circ} \mathrm{C} ;$ (b) associated with a $33.5^{\circ} \mathrm{C}$ decrease in temperature in a $5.85 \mathrm{kg}$ aluminum bar (specific heat capacity of aluminum $=0.903 \mathrm{Jg}^{-1} \mathrm{C}^{-1}$ ).

Example 2

Calculate the final temperature that results when (a) a 12.6 g sample of water at $22.9^{\circ} \mathrm{C}$ absorbs $875 \mathrm{J}$ of heat; (b) a 1.59 kg sample of platinum at $78.2^{\circ} \mathrm{C}$ gives off $1.05 \mathrm{kcal}$ of heat $\left(c_{p}=0.032 \mathrm{cal} \mathrm{g}^{-1} \mathrm{C}^{-1}\right)$

Example 3

Refer to Example $7-2 .$ The experiment is repeated with several different metals substituting for the lead. The masses of metal and water and the initial temperatures of the metal and water are the same as in Figure $7-3$. The final temperatures are (a) $\mathrm{Zn}, 38.9^{\circ} \mathrm{C}$ (b) $\mathrm{Pt}, 28.8^{\circ} \mathrm{C} ;$ (c) $\mathrm{Al}, 52.7^{\circ} \mathrm{C}$. What is the specific heat capacity of each metal, expressed in $\mathrm{J} \mathrm{g}^{-1} \mathrm{C}^{-1} ?$

Example 4

A 75.0 g piece of $\mathrm{Ag}$ metal is heated to $80.0^{\circ} \mathrm{C}$ and dropped into $50.0 \mathrm{g}$ of water at $23.2^{\circ} \mathrm{C} .$ The final temperature of the $\mathrm{Ag}-\mathrm{H}_{2} \mathrm{O}$ mixture is $27.6^{\circ} \mathrm{C}$. What is the specific heat capacity of silver?

Example 5

A 465 g chunk of iron is removed from an oven and plunged into $375 \mathrm{g}$ water in an insulated container. The temperature of the water increases from 26 to $87^{\circ} \mathrm{C}$. If the specific heat capacity of iron is $0.449 \mathrm{Jg}^{-1}^{\circ} \mathrm{C}^{-1}$ what must have been the original temperature of the iron?
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Step-by-Step Explanations

QUESTION

How do you calculate the change in internal energy (ΔU) using data from a bomb calorimeter?

STEP-BY-STEP ANSWER:

Step 1: Identify the amount of heat (q) released or absorbed during the reaction from the calorimeter data.
Step 2: Note that in a bomb calorimeter, the work done is nearly zero, so the change in internal energy is approximately equal to the heat measured.
Step 3: Apply the formula ΔU = q (+ w, if work is significant; however, in a bomb calorimeter, w ≈ 0).
Step 4: Substitute the measured value of q into the equation to obtain ΔU.
Final Answer: ΔU ≈ q, where q is the heat change measured by the calorimeter.

Calorimetry Calculation

QUESTION

Given a series of reactions with known enthalpy changes, how would you determine the overall enthalpy change of a target reaction?

STEP-BY-STEP ANSWER:

Step 1: Write down the target reaction and the provided reactions with their enthalpy changes.
Step 2: Manipulate (reverse or multiply) the provided reactions so that when they are added, the target reaction is obtained.
Step 3: Remember that when a reaction is reversed, the sign of the enthalpy change is also reversed, and when multiplied by a coefficient, the enthalpy change is multiplied by the same factor.
Step 4: Sum the adjusted enthalpy changes of the provided reactions.
Final Answer: The overall enthalpy change for the target reaction is the sum of the modified enthalpy changes, as dictated by Hess's law.

Application of Hess's Law

QUESTION

How do you determine the internal energy change (ΔU) when both heat and work are involved in a reaction?

STEP-BY-STEP ANSWER:

Step 1: Start with the first law of thermodynamics equation: ΔU = q + w.
Step 2: Determine the sign and value of q (heat exchanged) from the experimental or given data.
Step 3: Determine the sign and value of w (work done) in the process; work done on the system is positive and work done by the system is negative.
Step 4: Substitute q and w into the equation to compute ΔU.
Final Answer: The internal energy change, ΔU, is calculated as the sum of heat and work (ΔU = q + w).

First Law of Thermodynamics Application

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Common Mistakes

  • Confusing heat (q) with work (w) and not applying correct sign conventions for each.
  • Neglecting the fact that in bomb calorimetry, the work component is nearly zero, leading to miscalculations of internal energy change.
  • Misapplying Hess's law by incorrectly reversing or scaling reactions, which leads to an incorrect sum of enthalpy changes.
  • Overlooking the discrete nature of electron energy levels in quantum theory, resulting in misconceptions about continuous energy spectra.
  • Failing to properly define and use quantum numbers, which are essential for describing electron orbitals accurately.