A List of Common General Chemistry Problems

Worked Examples and Worksheets

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This is a collection of worked general chemistry and introductory chemistry problems, listed in alphabetical order.

Alphabetical Index of Chemistry Problem Types

Included in this list are printable pdf chemistry worksheets so you can practice problems and then check your answers. You may also browse chemistry problems according to the type of problem.

A: Absolute Error to B: Boyle's Gas Law

  • Absolute Error
  • Accuracy Review
  • Acid-Base Titration
  • Activation Energy Calculation
  • Angle Between Two Vectors
  • Aqueous Solution Dilutions
  • Atomic Mass Overview
  • Atomic Mass & Isotopic Abundance
  • Atomic Mass from Atomic Abundance
  • Atomic Weight Calculation
  • Average of a Set of Numbers
  • Avogadro's Law
  • Avogadro's Gas Law
  • Avogadro's Number—Finding Mass of a Single Atom
  • Avogadro's Number—Mass of a Known Number of Molecules
  • Avogadro's Number—Finding Number of Molecules in a Known Mass
  • Balancing Chemical Equations—Tutorial
  • Balancing Chemical Equations—Example
  • Balancing Redox Reactions—Example and Tutorial
  • Balancing Redox Reactions in a Basic Solution—Example
  • Balancing Redox Equations—Tutorial
  • Bohr Atom Energy Levels
  • Bohr Atom Energy Change
  • Boiling Point Elevation
  • Bond Energies & Enthalpies
  • Bond Polarity
  • Boyle's Law
  • Boyle's Gas Law

C: Calorimetry & Heat Flow to D: Dilutions From Stock Conversions

  • Calorimetry & Heat Flow
  • Carbon-14 Dating
  • Celsius to Kelvin Temperature Conversion
  • Charles' Gas Law
  • Clausius-Clapeyron Equation
  • Concentration and Molarity—Determine a Concentration From A Known Mass of Solute
  • Concentration and Molarity—Preparing a Stock Solution
  • Concentration and Molarity—Finding Concentration of Ions in an Aqueous Solution
  • Covalent Bond Examples
  • Dalton's Law of Partial Pressures
  • de Broglie Wavelength Calculation
  • Density Calculation
  • Density of a Solid and a Liquid
  • Density Example Problem—Finding Mass From Density
  • Density of an Ideal Gas
  • Diamagnetism
  • Dilutions from Stock Solutions

E: Electron Configuration to G: Guy-Lussac's Gas Law

  • Electron Configuration
  • Electron Volt to Joule Conversion
  • Electronegativity
  • Empirical Formula
  • Calculate Empirical and Molecular Formula of a Compound
  • Enthalpy Change - Enthalpy Change of a Reaction
  • Enthalpy Change - Enthalpy Change of a Reaction of a Given Mass
  • Enthalpy Change - Enthalpy Change of Water
  • Entropy Calculation
  • Entropy Change
  • Entropy of Reaction
  • Equation of a Line
  • Equilibrium Constant
  • Equilibrium Constant for Gaseous Reactions
  • Equilibrium Concentration
  • Experimental Error
  • Feet to Inches Conversion
  • Free Energy and Pressure
  • Free Energy and Reaction Spontaneity
  • Formal Charge - Lewis Structure Resonance Structures
  • Freezing Point Depression
  • Frequency to Wavelength Conversion
  • Graham's Law
  • Gram to Mole Conversion
  • Guy-Lussac's Gas Law

H: Half-Life to Joule to E: Electron Volt Conversion

  • Heats of Formation
  • Henderson-Hasselbalch Equation
  • Henry's Law
  • Ideal Gas Example Problem
  • Ideal Gas Law
  • Ideal Gas—Constant Pressure
  • Ideal Gas—Constant Volume
  • Ideal Gas Example Problem—Partial Pressure
  • Ideal Gas Example Problem–Unknown Gas
  • Ideal Gas vs Real Gas—van der Waals Equation
  • Ionic Bond Examples
  • Ionic Bond from Electronegativity
  • Isotopes and Nuclear Symbols—Example 1
  • Isotopes and Nuclear Symbols—Example 2
  • Joule to Electron Volt Conversion

L: Law of Multiple Proportions to M: Molecular Mass Calculations

  • Law of Multiple Proportions
  • Length Conversion—Angstroms to Meters
  • Length Conversion—Angstroms to Nanometers
  • Length Conversion—Centimeters to Meters
  • Length Conversion—Feet to Kilometers
  • Length Conversion—Feet to Meters
  • Length Conversion—Kilometers to Meters
  • Length Conversion—Miles to Kilometers
  • Length Conversion — Millimeters to Centimeters
  • Length Conversion — Millimeters to Meters
  • Length Conversion — Micrometers to Meters
  • Length Conversion — Nanometers to Meters
  • Length Conversion — Nanometers to Angstroms
  • Length Conversion — Yards to Meters
  • Draw a Lewis Structure
  • Draw a Lewis Structure — Octet Rule Exception
  • Limiting Reactant & Theoretical Yield
  • Mass Conversions — Kilograms to Grams
  • Mass Conversions — Pounds to Kilograms
  • Mass Conversions — Ounces to Grams
  • Mass — Energy Relations in Nuclear Reactions
  • Mass of Liquid from Density
  • Mass Percent Composition
  • Mass Percent Composition—Example 2
  • Mass Relations in Balanced Equations
  • Mean of a Set of Numbers
  • Mean, Median, Mode and Range Example
  • Molarity to PPM Conversion
  • Mole — Gram Conversions
  • Mole Relations in Balanced Equations
  • Moles of C Atoms in 1 Mol Sucrose
  • Molecular Formula from Simplest Formula
  • Molecular Mass Calculations

N: Nernst Equation to P: Protons, Neutrons, and Electrons

  • Nernst Equation
  • Neutralizing a Base with an Acid
  • Osmotic Pressure
  • Oxidation and Reduction
  • Oxidation or Reduction?
  • Assigning Oxidation States
  • Paramagnetism
  • Percent Composition by Mass
  • Percent Error
  • pH Calculation
  • pH Calculation — Example 2
  • pH of a Strong Acid
  • pH of a Strong Base
  • Phosphate Buffer Preparation
  • pOH Calculation
  • Polyprotic Acid pH
  • Population Standard Deviation
  • Precision Review
  • Predicting Formulas of Compounds with Polyatomic Ions
  • Predicting Formulas of Ionic Compounds
  • Prepare a Solution (Molarity)
  • Pressure Conversion - Pa to atm
  • Pressure Conversion — millibar to atm
  • Pressure Conversion — atm to Pa
  • Pressure Conversion — bars to atm
  • Pressure Conversion — atm to bars
  • Pressure Conversion — psi to atm
  • Pressure Conversion — atm to psi
  • Pressure Conversion — psi to Pa
  • Pressure Conversion — psi to millibars
  • Protons & Electrons in Ions
  • Protons & Electrons in Ions — Example 2
  • Protons, Neutrons, and Electrons in Atoms/Ions

R: Radioactive Decay to T: Titration Concentration

  • Radioactive Decay — α Decay
  • Radioactive Decay — Electron Capture
  • Radioactive Decay — β - Decay
  • Raoult's Law — Example 1
  • Raoult's Law — Example 2
  • Raoult's Law — Example 3
  • Rate of Radioactive Decay
  • Rates of Reaction
  • Reactions in Aqueous Solution
  • Reaction Quotient
  • Redox Reaction
  • Relative Error
  • Root Mean Square Velocity of Ideal Gas Molecules
  • Sample Standard Deviation
  • Scientific Notation
  • Significant Figures
  • Simplest Formula from Percent Composition
  • Solubility from Solubility Product
  • Solubility Product from Solubility
  • Temperature Conversions
  • Temperature Conversions—Kelvin to Celsius & Fahrenheit
  • Temperature Conversions—Celsius to Fahrenheit
  • Temperature Conversions—Celsius to Kelvin
  • Temperature Conversions—Kelvin to Celsius
  • Temperature Conversions—Fahrenheit to Celsius
  • Temperature Conversions—Fahrenheit to Kelvin
  • Temperature That Fahrenheit Equals Celsius
  • Theoretical Yield
  • Theoretical Yield #2
  • Titration Concentration

U: Uncertainty to W: Wavelength to Frequency Conversion

  • Uncertainty
  • Unit Cancelling — English to Metric
  • Unit Cancelling — Metric to Metric
  • Unit Conversions
  • Unit Conversion — What Is The Speed Of Light In Miles Per Hour?
  • Vector Scalar Product
  • Volume Conversions — Cubic Centimeters to Liters
  • Volume Conversions — Cubic Feet to Cubic Inches
  • Volume Conversions — Cubic Feet to Liters
  • Volume Conversions — Cubic Inches to Cubic Centimeters
  • Volume Conversions — Cubic Inches to Cubic Feet
  • Volume Conversions — Cubic Meters to Cubic Feet
  • Volume Conversions — Cubic Meters to Liters
  • Volume Conversions — Gallons to Liters
  • Volume Conversions — Cubic Inches to Liters
  • Volume Conversions — Fluid Ounces to Milliliters
  • Volume Conversions — Liters to Milliliters
  • Volume Conversions — Microliters to Milliliters
  • Volume Conversions — Milliliters to Liters
  • Volume Percent
  • Wavelength to Frequency Conversion

Chemistry Worksheets (Pdf to Download or Print)

  • Metric to English Conversions Worksheet
  • Metric to English Conversions Answers
  • Metric to Metric Conversions Worksheet
  • Metric to Metric Conversions Answers
  • Temperature Conversions Worksheet
  • Temperature Conversions Answers
  • Temperature Conversions Worksheet #2
  • Temperature Conversions Answers #2
  • Moles to Grams Conversions Worksheet
  • Moles to Grams Conversions Answers
  • Formula or Molar Mass Worksheet
  • Formula or Molar Mass Worksheet Answers
  • Practicing Balancing Chemical Equations — Worksheet
  • Balancing Chemical Equations — Answers
  • Practicing Balancing Chemical Equations — Worksheet #2
  • Balancing Chemical Equations — Answers #2
  • Practicing Balancing Chemical Equations — Worksheet #3
  • Balancing Chemical Equations — Answers #3
  • Common Acid Names & Formulas — Worksheet
  • Acid Names and Formulas — Answers
  • Practice Calculations with Moles — Worksheet
  • Mole Calculations — Answers
  • Practice Mole Relations in Balanced Equations — Worksheet
  • Mole Relations in Balanced Equations — Answers
  • Gas Laws Answers
  • Gas Laws Answers — Shown Work
  • Limiting Reagent — Worksheet
  • Limiting Reagent — Answers
  • Calculating Molarity — Worksheet
  • Calculating Molarity — Answers
  • Acid & Base pH — Worksheet
  • Acid & Base pH — Answers
  • Electron Configurations — Worksheet
  • Electron Configurations — Answers
  • Balancing Redox Reactions — Worksheet
  • Balancing Redox Reactions — Answers
  • Printable Chemistry Worksheets
  • 20 Practice Chemistry Tests
  • Overview of High School Chemistry Topics
  • How to Balance Equations - Printable Worksheets
  • Chemistry Unit Conversions
  • Topics Typically Covered in Grade 11 Chemistry
  • AP Chemistry Course and Exam Topics
  • Mole Ratio: Definition and Examples
  • Stoichiometry Definition in Chemistry
  • Balancing Chemical Equations
  • Chemistry Vocabulary Terms You Should Know
  • Calculate Simplest Formula From Percent Composition
  • Converting Cubic Inches to Cubic Centimeters
  • Bar to Atm - Converting Bars to Atmospheres Pressure
  • Balanced Equation Definition and Examples

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Chemistry Problems

Use chemistry problems as a tool for mastering chemistry concepts. Some of these examples show using formulas while others include lists of examples.

Acids, Bases, and pH Chemistry Problems

Learn about acids and bases. See how to calculate pH, pOH, K a , K b , pK a , and pK b .

  • Practice calculating pH.
  • Get example pH, pK a , pK b , K a , and K b calculations.
  • Get examples of amphoterism.

Atomic Structure Problems

Learn about atomic mass, the Bohr model, and the part of the atom.

  • Practice identifying atomic number, mass number, and atomic mass.
  • Get examples showing ways to find atomic mass.
  • Use Avogadro’s number and find the mass of a single atom .
  • Review the Bohr model of the atom.
  • Find the number of valence electrons of an element’s atom.

Chemical Bonds

Learn how to use electronegativity to determine whether atoms form ionic or covalent bonds. See chemistry problems drawing Lewis structures.

  • Identify ionic and covalent bonds.
  • Learn about ionic compounds and get examples.
  • Practice identifying ionic compounds.
  • Get examples of binary compounds.
  • Learn about covalent compounds and their properties.
  • See how to assign oxidation numbers.
  • Practice drawing Lewis structures.
  • Practice calculating bond energy.

Chemical Equations

Practice writing and balancing chemical equations.

  • Learn the steps of balancing equations.
  • Practice balancing chemical equations (practice quiz).
  • Get examples finding theoretical yield.
  • Practice calculating percent yield.
  • Learn to recognize decomposition reactions.
  • Practice recognizing synthesis reactions.
  • Practice recognizing single replacement reactions.
  • Recognize double replacement reactions.
  • Find the mole ratio between chemical species in an equation.

Concentration and Solutions

Learn how to calculate concentration and explore chemistry problems that affect chemical concentration, including freezing point depression, boiling point elevation, and vapor pressure elevation.

  • Get example concentration calculations in several units.
  • Practice calculating normality (N).
  • Practice calculating molality (m).
  • Explore example molarity (M) calculations.
  • Get examples of colligative properties of solutions.
  • See the definition and examples of saturated solutions.
  • See the definition and examples of unsaturated solutions.
  • Get examples of miscible and immiscible liquids.

Error Calculations

Learn about the types of error and see worked chemistry example problems.

  • See how to calculate percent.
  • Practice absolute and relative error calculations.
  • See how to calculate percent error.
  • See how to find standard deviation.
  • Calculate mean, median, and mode.
  • Review the difference between accuracy and precision.

Equilibrium Chemistry Problems

Learn about Le Chatelier’s principle, reaction rates, and equilibrium.

  • Solve activation energy chemistry problems.
  • Review factors that affect reaction rate.
  • Practice calculating the van’t Hoff factor.

Practice chemistry problems using the gas laws, including Raoult’s law, Graham’s law, Boyle’s law, Charles’ law, and Dalton’s law of partial pressures.

  • Calculate vapor pressure.
  • Solve Avogadro’s law problems.
  • Practice Boyle’s law problems.
  • See Charles’ law example problems.
  • Solve combined gas law problems.
  • Solve Gay-Lussac’s law problems.

Some chemistry problems ask you identify examples of states of matter and types of mixtures. While there are any chemical formulas to know, it’s still nice to have lists of examples.

  • Practice density calculations.
  • Identify intensive and extensive properties of matter.
  • See examples of intrinsic and extrinsic properties of matter.
  • Get the definition and examples of solids.
  • Get the definition and examples of gases.
  • See the definition and examples of liquids.
  • Learn what melting point is and get a list of values for different substances.
  • Get the azeotrope definition and see examples.
  • See how to calculate specific volume of a gas.
  • Get examples of physical properties of matter.
  • Get examples of chemical properties of matter.
  • Review the states of matter.

Molecular Structure Chemistry Problems

See chemistry problems writing chemical formulas. See examples of monatomic and diatomic elements.

  • Practice empirical and molecular formula problems.
  • Practice simplest formula problems.
  • See how to calculate molecular mass.
  • Get examples of the monatomic elements.
  • See examples of binary compounds.
  • Calculate the number of atoms and molecules in a drop of water.

Nomenclature

Practice chemistry problems naming ionic compounds, hydrocarbons, and covalent compounds.

  • Practice naming covalent compounds.
  • Learn hydrocarbon prefixes in organic chemistry.

Nuclear Chemistry

These chemistry problems involve isotopes, nuclear symbols, half-life, radioactive decay, fission, fusion.

  • Review the types of radioactive decay.

Periodic Table

Learn how to use a periodic table and explore periodic table trends.

  • Know the trends in the periodic table.
  • Review how to use a periodic table.
  • Explore the difference between atomic and ionic radius and see their trends on the periodic table.

Physical Chemistry

Explore thermochemistry and physical chemistry, including enthalpy, entropy, heat of fusion, and heat of vaporization.

  • Practice heat of vaporization chemistry problems.
  • Practice heat of fusion chemistry problems.
  • Calculate heat required to turn ice into steam.
  • Practice calculating specific heat.
  • Get examples of potential energy.
  • Get examples of kinetic energy.
  • See example activation energy calculations.

Spectroscopy and Quantum Chemistry Problems

See chemistry problems involving the interaction between light and matter.

  • Calculate wavelength from frequency or frequency from wavelength.

Stoichiometry Chemistry Problems

Practice chemistry problems balancing formulas for mass and charge. Learn about reactants and products.

  • Get example mole ratio problems.
  • Calculate percent yield.
  • Learn how to assign oxidation numbers.
  • Get the definition and examples of reactants in chemistry.
  • Get the definition and examples of products in chemical reactions.

Unit Conversions

There are some many examples of unit conversions that they have their own separate page!

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How to Solve a Chemistry Problem

Last Updated: February 15, 2024

This article was co-authored by Anne Schmidt . Anne Schmidt is a Chemistry Instructor in Wisconsin. Anne has been teaching high school chemistry for over 20 years and is passionate about providing accessible and educational chemistry content. She has over 9,000 subscribers to her educational chemistry YouTube channel. She has presented at the American Association of Chemistry Teachers (AATC) and was an Adjunct General Chemistry Instructor at Northeast Wisconsin Technical College. Anne was published in the Journal of Chemical Education as a Co-Author, has an article in ChemEdX, and has presented twice and was published with the AACT. Anne has a BS in Chemistry from the University of Wisconsin, Oshkosh, and an MA in Secondary Education and Teaching from Viterbo University. This article has been viewed 16,555 times.

Chemistry problems can vary in many different ways. Some questions are conceptual and others are quantitative. Each problem requires its own approach, and each has a different way to solve it correctly. What you can do is make a set of steps that can help us with any problems that you come across in the field of chemistry. Using these steps should help give you a guideline to working on any chemistry problem you encounter.

Starting the Problem

Step 1 Read the problem completely.

Finishing the Problem

Step 1 Check your units again.

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Chemistry Research: Review Books & Practice Problems

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General Chemistry

Schaum's Outlines provide overviews of a topic and include hundreds of solved problems that you can use to practice your skills.

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Overviews and practice problems for general chemistry can often be found with call numbers QD42 . Alternative textbook are in QD31 .

Here are a few examples of the books you can find in that area:

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Organic Chemistry

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Overviews and practice problems for organic chemistry can generally be found with call numbers QD256 - 257 . Alternative organic chemistry textbook are in QD251 .

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Test Preparation

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  • Preparing for you ACS Examination in Physical Chemistry Call Number: QD456 .H65 2009 ON RESERVE - Bring this call number to the Main Circulation desk

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Looking for MCAT study guides in other subject areas? Check out the Biology Research guide for a full list.

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Chemistry Steps

Chemistry Steps

general chemistry solved problems

General Chemistry

Acids and bases.

In this set of practice problems, we will work on examples correlating the acidity and basicity of a solution with pH, calculating the pH of strong and weak acids and bases, the pH and pOH relationship, and calculating the pH of salt solutions. 

The links to corresponding topics are given below:

  • Definitions of Acids and Bases
  • Acid-Base Reactions
  • Acid-Base Titrations
  • Conjugate Acid and Conjugate Base
  • Autoionization of Water and  K w
  • The pH and Acidity
  • Acid Strength,  K a , and p K a
  • Base Strength, K b and p K b
  • K a , p K a , K b , and p K b Relationship
  • The pH of a Strong Acid and Base
  • pH + pOH = 14
  • The pH of a Weak Acid
  • The pH of a Weak Base
  • The pH of Polyprotic Acids
  • The acidity of a Salt Solution
  • The pH of a Salt Solution
  • The pH of Salts With Acidic Cations and Basic Anions

Autoionization of Water and pH

Arrange the following solutions in the order of increasing acidity (least acidic to most acidic):

(a) pH = 9.8

(b) pH = 1.2

(c) pH = 4.7

(d) pH = 6.4

Arrange the following solutions in the order of increasing basicity (least basic to most basic):

(a) pOH = 5.2

(b) pOH = 11.6

(c) pOH = 3.4

(d) pOH = 1.9

Calculate the pH for each of the following solutions at 25 o C:

(a) [H 3 O + ] = 1.3 x 10 -2 M

(b) [H 3 O + ] = 1.6 x 10 -3 M

(c) [OH – ] = 1.8 x 10 -3 M

 Calculate the [OH – ] of each of the following solutions at 25 o C. Identify the solution as neutral, acidic, or basic.

a) [H + ] = 2.5 x 10 -6 M

b) [H + ] = 8.3 x 10 -4 M

c) [H + ] = 4.6 M

d) [H + ] = 3.9 x 10 -2 M

Given the pH values, calculate [H 3 O + ] and [OH – ] for each solution at 25 o C. Identify each solution as neutral, acidic, or basic.

a) pH = 7.20

b) pH = 15.3

c) pH = 4.60

The pH of Strong Acids and Bases

Calculate the pH for each of the following solutions:

(a) 0.15 M HCl

(b) 0.60 M HClO 4

(c) 1.4 M KOH

Calculate the pH of each of the following solutions:

(a) 0.0025 M HI, (b) 0.84 M NaOH

Calculate the pH of the solution prepared by dissolving 24.0 g of HCl in 662 mL of water.

How many grams of KOH is needed to prepare a 680.0 mL solution with a pH of 9.80?

Calculate the pH of the solution prepared by diluting 40.0 mL of 3.00  M  HNO 3  with 210.0 mL of water.

The pH of Weak Acids

Calculate the pH of a 0.45 M solution of HCN. K a (HCN) = 4.9 x 10 -10

Calculate the pH of a 0.74 M solution of acetic acid. K a (CH 3 CO 2 H) = 1.7 x 10 -5

0.86 g benzoic acid (C 6 H 5 CO 2 H, K a = 6.4 x 10 -5 ) was dissolved in enough water to make 1.0 L of solution. Calculate the pH and concentration of all species present in the solution.

Calculate the pH of a 2.0 M solution of hydrofluoric acid, HF if K a (HF) = 6.6 x 10 -4

What is the acid ionization constant ( K a ) of a weak acid (HA) if its 0.246 M solution has a pH of 2.68?

A solution of nitrous acid (HNO 2 , K a = 7.2 x 10 -4 ) has a pH of 3.1. What was the initial concentration of nitrous acid in the solution?

Calculate the pH of a 0.40 M H 2 S solution given that K a1 = 1.0 x 10 -7 ; K a2 = 1.0 x 10 -19 .

The pH of Weak Bases

Explain why all of these are weak bases by writing the equations for their reaction with water and the corresponding expression for K b .

(a) NH 3 (b)  HCO 3 – (c)  CN- (d) CH 3 NH 2 (e) C 5 H 5 N (f) F –

Determine the pH of a 0.85 M solution of ammonia (NH 3 ).

Triethylamine, (C 2 H 5 ) 3 N is a common organic weak base with K b of 4.0 x 10 -4 . Calculate [OH – ], [H + ], and the pH of 0.25 M solution of triethylamine.

Calculate [OH – ], [H + ], and the pH of 0.40 M solution of caffeine (p K b = 10.4).

Calculate the percentage of ethyl amine (CH 3 CH 2 NH 2 ) that is ionized by reacting with water in its 0.64 molar aqueous solution ( K b = 5.6 x 10 -4 ).

Morphine is among the most popular alkaloids that are used as pain killers. Like all the others, it contains a nitrogen atom which makes it a weak base. What is the K b of morphine at a certain temperature if its 0.340 M solution has a pH of 10.9?

The Acid–Base Properties of Salts

For each ion, determine if it acts as a weak base in an aqueous solution. For those that do, write an equation to show why they make the solution basic.

a) Cl – b)   BrO – c)   CN – d)   ClO 3 – e)   CH 3 CO 2 – f)   I – g)   NO 2 – h)   F –

Predict whether the aqueous solutions of the following compounds are acidic, basic, or neutral: (a) KBr (b) FeCl 2 , (c) Na 2 CO 3 , (d) Al(NO 3 ) 3 (e) KClO 4 , (f) Na 2 SO 3 , (g) NH 4 ClO 3

Which of the following salts would produce the most basic aqueous solution?

KF b. NaBr c. NH 4 Cl d. MgCl 2 e. Mg(NO 3 ) 2

Calculate the pH of a 0.74 M solution of NaOBr ( K a HBrO = 2.90 x 10 -9 ).

Calculate the pH of the 0.26 M solution of NH 4 ClO 3 ( K b NH 3 = 1.8 x 10 -5 ).

Calculate the pH of a 0.35 M solution of KNO 2 ( K a = 4.0 x 10 -4 ).

Calculate the pH of a 1.0 M solution of sodium acetate (CH 3 CO 2 Na) considering that the K a of acetic acid (CH 3 CO 2 H is 1.7 x 10 -5 .

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5.E: Chemical Thermodynamics (Practice Problems with Answers)

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These are homework exercises to accompany the Textmap created for "Chemistry: The Central Science" by Brown et al. Complementary General Chemistry question banks can be found for other Textmaps and can be accessed here . In addition to these publicly available questions, access to private problems bank for use in exams and homework is available to faculty only on an individual basis; please contact Delmar Larsen for an account with access permission.

19.1: Spontaneous Processes

19.2: entropy and the second law of thermodynamics, conceptual problems.

  • A Russian space vehicle developed a leak, which resulted in an internal pressure drop from 1 atm to 0.85 atm. Is this an example of a reversible expansion? Has work been done?
  • Which member of each pair do you expect to have a higher entropy? Why?
  • solid phenol or liquid phenol
  • 1-butanol or butane
  • cyclohexane or cyclohexanol
  • 1 mol of N 2 mixed with 2 mol of O 2 or 2 mol of NO 2
  • 1 mol of O 2 or 1 mol of O 3
  • 1 mol of propane at 1 atm or 1 mol of propane at 2 atm
  • Determine whether each process is reversible or irreversible.
  • ice melting at 0°C
  • salt crystallizing from a saline solution
  • evaporation of a liquid in equilibrium with its vapor in a sealed flask
  • a neutralization reaction
  • cooking spaghetti
  • the reaction between sodium metal and water
  • oxygen uptake by hemoglobin
  • evaporation of water at its boiling point
  • Explain why increasing the temperature of a gas increases its entropy. What effect does this have on the internal energy of the gas?
  • For a series of related compounds, does ΔS vap increase or decrease with an increase in the strength of intermolecular interactions in the liquid state? Why?
  • Is the change in the enthalpy of reaction or the change in entropy of reaction more sensitive to changes in temperature? Explain your reasoning.
  • Solid potassium chloride has a highly ordered lattice structure. Do you expect ΔS soln to be greater or less than zero? Why? What opposing factors must be considered in making your prediction?
  • Aniline (C 6 H 5 NH 2 ) is an oily liquid at 25°C that darkens on exposure to air and light. It is used in dying fabrics and in staining wood black. One gram of aniline dissolves in 28.6 mL of water, but aniline is completely miscible with ethanol. Do you expect ΔS soln in H 2 O to be greater than, less than, or equal to ΔS soln in CH 3 CH 2 OH? Why?

Conceptual Answers

  • No, it is irreversible; no work is done because the external pressure is effectively zero.
  • irreversible
  • Water has a highly ordered, hydrogen-bonded structure that must reorganize to accommodate hydrophobic solutes like aniline. In contrast, we expect that aniline will be able to disperse randomly throughout ethanol, which has a significantly less ordered structure. We therefore predict that ΔS soln in ethanol will be more positive than ΔS soln in water.

Numerical Problems

  • Liquid nitrogen, which has a boiling point of −195.79°C, is used as a coolant and as a preservative for biological tissues. Is the entropy of nitrogen higher or lower at −200°C than at −190°C? Explain your answer. Liquid nitrogen freezes to a white solid at −210.00°C, with an enthalpy of fusion of 0.71 kJ/mol. What is its entropy of fusion? Is freezing biological tissue in liquid nitrogen an example of a reversible process or an irreversible process?
  • Using the second law of thermodynamics, explain why heat flows from a hot body to a cold body but not from a cold body to a hot body.
  • One test of the spontaneity of a reaction is whether the entropy of the universe increases: ΔS univ > 0. Using an entropic argument, show that the following reaction is spontaneous at 25°C:

4Fe(s) + 3O 2 (g) → 2Fe 2 O 3 (s)

Why does the entropy of the universe increase in this reaction even though gaseous molecules, which have a high entropy, are consumed?

  • Calculate the missing data in the following table.

Based on this table, can you conclude that entropy is related to the nature of functional groups? Explain your reasoning.

The text states that the magnitude of ΔS vap tends to be similar for a wide variety of compounds. Based on the values in the table, do you agree?

19.3: The Molecular Interpretation of Entropy

19.4: entropy changes in chemical reactions, 19.5: gibbs free energy.

  • How does each example illustrate the fact that no process is 100% efficient?
  • burning a log to stay warm
  • the respiration of glucose to provide energy
  • burning a candle to provide light
  • Neither the change in enthalpy nor the change in entropy is, by itself, sufficient to determine whether a reaction will occur spontaneously. Why?
  • If a system is at equilibrium, what must be the relationship between ΔH and ΔS?
  • The equilibrium 2AB⇌A 2 B 2 is exothermic in the forward direction. Which has the higher entropy—the products or the reactants? Why? Which is favored at high temperatures?
  • Is ΔG a state function that describes a system or its surroundings? Do its components—ΔH and ΔS—describe a system or its surroundings?
  • How can you use ΔG to determine the temperature of a phase transition, such as the boiling point of a liquid or the melting point of a solid?
  • Occasionally, an inventor claims to have invented a “perpetual motion” machine, which requires no additional input of energy once the machine has been put into motion. Using your knowledge of thermodynamics, how would you respond to such a claim? Justify your arguments.
  • Must the entropy of the universe increase in a spontaneous process? If not, why is no process 100% efficient?
  • The reaction of methyl chloride with water produces methanol and hydrogen chloride gas at room temperature, despite the fact that ΔH ∘ rxn = 7.3 kcal/mol. Using thermodynamic arguments, propose an explanation as to why methanol forms.
  • In order for the reaction to occur spontaneously, ΔG for the reaction must be less than zero. In this case, ΔS must be positive, and the TΔS term outweighs the positive value of ΔH.
  • Use the tables in the text to determine whether each reaction is spontaneous under standard conditions. If a reaction is not spontaneous, write the corresponding spontaneous reaction.
  • \(\mathrm{H_2(g)}+\frac{1}{2}\mathrm{O_2(g)}\rightarrow\mathrm{H_2O(l)}\)
  • 2H 2 (g) + C 2 H 2 (g) → C 2 H 6 (g)
  • (CH 3 ) 2 O(g) + H 2 O(g) → 2CH 3 OH(l)
  • CH 4 (g) + H 2 O(g) → CO(g) + 3H 2 (g)
  • K 2 O 2 (s) → 2K(s) + O 2 (g)
  • PbCO 3 (s) → PbO(s) + CO 2 (g)
  • P 4 (s) + 6H 2 (g) → 4PH 3 (g)
  • 2AgCl(s) + H 2 S(g) → Ag 2 S(s) + 2HCl(g)
  • Nitrogen fixation is the process by which nitrogen in the atmosphere is reduced to NH 3 for use by organisms. Several reactions are associated with this process; three are listed in the following table. Which of these are spontaneous at 25°C? If a reaction is not spontaneous, at what temperature does it become spontaneous?
  • A student was asked to propose three reactions for the oxidation of carbon or a carbon compound to CO or CO 2 . The reactions are listed in the following table. Are any of these reactions spontaneous at 25°C? If a reaction does not occur spontaneously at 25°C, at what temperature does it become spontaneous?
  • Tungsten trioxide (WO 3 ) is a dense yellow powder that, because of its bright color, is used as a pigment in oil paints and water colors (although cadmium yellow is more commonly used in artists’ paints). Tungsten metal can be isolated by the reaction of WO 3 with H 2 at 1100°C according to the equation WO 3 (s) + 3H 2 (g) → W(s) + 3H 2 O(g). What is the lowest temperature at which the reaction occurs spontaneously? ΔH° = 27.4 kJ/mol and ΔS° = 29.8 J/K.
  • Sulfur trioxide (SO 3 ) is produced in large quantities in the industrial synthesis of sulfuric acid. Sulfur dioxide is converted to sulfur trioxide by reaction with oxygen gas.
  • Write a balanced chemical equation for the reaction of SO 2 with O 2 (g) and determine its ΔG°.
  • What is the value of the equilibrium constant at 600°C?
  • If you had to rely on the equilibrium concentrations alone, would you obtain a higher yield of product at 400°C or at 600°C?
  • Calculate ΔG° for the general reaction MCO 3 (s) → MO(s) + CO 2 (g) at 25°C, where M is Mg or Ba. At what temperature does each of these reactions become spontaneous?
  • The reaction of aqueous solutions of barium nitrate with sodium iodide is described by the following equation:

Ba(NO 3 ) 2 (aq) + 2NaI(aq) → BaI 2 (aq) + 2NaNO 3 (aq)

You want to determine the absolute entropy of BaI 2 , but that information is not listed in your tables. However, you have been able to obtain the following information:

You know that ΔG° for the reaction at 25°C is 22.64 kJ/mol. What is ΔH° for this reaction? What is S° for BaI 2 ?

Numerical Answers

  • −237.1 kJ/mol; spontaneous as written
  • −241.9 kJ/mol; spontaneous as written
  • 8.0 kJ/mol; spontaneous in reverse direction.
  • 141.9 kJ/mol; spontaneous in reverse direction.
  • Not spontaneous at any T
  • Not spontaneous at 25°C; spontaneous above 7400 K
  • Spontaneous at 25°C
  • MgCO 3 : ΔG° = 63 kJ/mol, spontaneous above 663 K; BaCO 3 : ΔG° = 220 kJ/mol, spontaneous above 1562 K

19.6: Free Energy and Temperature

19.7: free energy and the equilibrium constant.

  • Do you expect products or reactants to dominate at equilibrium in a reaction for which ΔG° is equal to
  • 1.4 kJ/mol?
  • 105 kJ/mol?
  • −34 kJ/mol?
  • The change in free energy enables us to determine whether a reaction will proceed spontaneously. How is this related to the extent to which a reaction proceeds?
  • What happens to the change in free energy of the reaction N 2 (g) + 3F 2 (g) → 2NF 3 (g) if the pressure is increased while the temperature remains constant? if the temperature is increased at constant pressure? Why are these effects not so important for reactions that involve liquids and solids?
  • Compare the expressions for the relationship between the change in free energy of a reaction and its equilibrium constant where the reactants are gases versus liquids. What are the differences between these expressions?
  • Carbon monoxide, a toxic product from the incomplete combustion of fossil fuels, reacts with water to form CO 2 and H 2 , as shown in the equation CO(g)+H 2 O(g)⇌CO 2 (g)+H 2 (g), for which ΔH° = −41.0 kJ/mol and ΔS° = −42.3 J cal/(mol·K) at 25°C and 1 atm.
  • What is ΔG° for this reaction?
  • What is ΔG if the gases have the following partial pressures: P CO = 1.3 atm, \(P_{\mathrm{H_2O}}\) = 0.8 atm, \(P_{\mathrm{CO_2}}\) = 2.0 atm, and \(P_{\mathrm{H_2}}\) = 1.3 atm?
  • What is ΔG if the temperature is increased to 150°C assuming no change in pressure?
  • Methane and water react to form carbon monoxide and hydrogen according to the equation CH 4 (g) + H 2 O(g) ⇌ CO(g) + 3H 2 (g).
  • What is the standard free energy change for this reaction?
  • What is K p for this reaction?
  • What is the carbon monoxide pressure if 1.3 atm of methane reacts with 0.8 atm of water, producing 1.8 atm of hydrogen gas?
  • What is the hydrogen gas pressure if 2.0 atm of methane is allowed to react with 1.1 atm of water?
  • At what temperature does the reaction become spontaneous?
  • Calculate the equilibrium constant at 25°C for each equilibrium reaction and comment on the extent of the reaction.
  • CCl 4 (g)+6H 2 O(l)⇌CO 2 (g)+4HCl(aq); ΔG° = −377 kJ/mol
  • Xe(g)+2F 2 (g)⇌XeF 4 (s); ΔH° = −66.3 kJ/mol, ΔS° = −102.3 J/(mol·K)
  • PCl 3 (g)+S⇌PSCl 3 (l); ΔG ∘ f (PCl 3 ) = −272.4 kJ/mol, ΔG ∘ f (PSCl 3 ) = −363.2 kJ/mol
  • 2KClO 3 (s)⇌2KCl(s)+3O 2 (g); ΔG° = −225.8 kJ/mol
  • CoCl 2 (s)+6H 2 O(g)⇌CoCl 2 ⋅6H 2 O(s); ΔH ∘ rxn = −352 kJ/mol, ΔS ∘ rxn = −899 J/(mol·K)
  • 2PCl 3 (g)+O 2 (g)⇌2POCl 3 (g); ΔG ∘ f (PCl 3 ) = −272.4 kJ/mol, ΔG ∘ f (POCl 3 ) = −558.5 kJ/mol
  • The gas-phase decomposition of N 2 O 4 to NO 2 is an equilibrium reaction with K p = 4.66 × 10 −3 . Calculate the standard free-energy change for the equilibrium reaction between N 2 O 4 and NO 2 .
  • The standard free-energy change for the dissolution K 4 Fe(CN) 6 ⋅H 2 O(s)⇌4K + (aq)+Fe(CN) 6 4− (aq)+H 2 O(l) is 26.1 kJ/mol. What is the equilibrium constant for this process at 25°C?
  • Ammonia reacts with water in liquid ammonia solution (am) according to the equation NH 3 (g) + H 2 O(am) ⇌ NH 4 + (am) + OH − (am). The change in enthalpy for this reaction is 21 kJ/mol, and ΔS° = −303 J/(mol·K). What is the equilibrium constant for the reaction at the boiling point of liquid ammonia (−31°C)?
  • At 25°C, a saturated solution of barium carbonate is found to have a concentration of [Ba 2 + ] = [CO 3 2− ] = 5.08 × 10 −5 M. Determine ΔG° for the dissolution of BaCO 3 .
  • Lead phosphates are believed to play a major role in controlling the overall solubility of lead in acidic soils. One of the dissolution reactions is Pb 3 (PO 4 ) 2 (s)+4H + (aq)⇌3Pb 2 + (aq)+2H 2 PO 4 − (aq), for which log K = −1.80. What is ΔG° for this reaction?
  • The conversion of butane to 2-methylpropane is an equilibrium process with ΔH° = −2.05 kcal/mol and ΔG° = −0.89 kcal/mol.
  • What is the change in entropy for this conversion?
  • Based on structural arguments, are the sign and magnitude of the entropy change what you would expect? Why?
  • What is the equilibrium constant for this reaction?
  • The reaction of CaCO 3 (s) to produce CaO(s) and CO 2 (g) has an equilibrium constant at 25°C of 2 × 10 −23 . Values of ΔH ∘ f are as follows: CaCO 3 , −1207.6 kJ/mol; CaO, −634.9 kJ/mol; and CO 2 , −393.5 kJ/mol.
  • What is the equilibrium constant at 900°C?
  • What is the partial pressure of CO 2 (g) in equilibrium with CaO and CaCO 3 at this temperature?
  • Are reactants or products favored at the lower temperature? at the higher temperature?
  • In acidic soils, dissolved Al 3 + undergoes a complex formation reaction with SO 4 2− to form [AlSO 4 + ]. The equilibrium constant at 25°C for the reaction Al 3 + (aq)+SO 4 2− (aq)⇌AlSO 4 + (aq) is 1585.
  • How does this value compare with ΔG° for the reaction Al 3 + (aq)+F − (aq)⇌AlF 2 + (aq), for which K = 10 7 at 25°C?
  • Which is the better ligand to use to trap Al 3 + from the soil?
  • −28.4 kJ/mol
  • −26.1 kJ/mol
  • −19.9 kJ/mol
  • 1.21 × 10 66 ; equilibrium lies far to the right.
  • 1.89 × 10 6 ; equilibrium lies to the right.
  • 5.28 × 10 16 ; equilibrium lies far to the right.
  • 13.3 kJ/mol
  • 5.1 × 10 −21
  • 10.3 kJ/mol
  • 129.5 kJ/mol
  • Products are favored at high T; reactants are favored at low T.

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