In-class Problem Set #1
- Page ID
- 70801
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Problem #1
After completing this problem, the student will be able to:
- Write the reaction of a weak base with water
- Identify a chemical that is a weak base
- Write the equilibrium constant expression for a reaction of a weak base with water
- Use the expression KaKb = Kw to solve for Ka if given Kb (or vice versa)
- Prove that KaKb = Kw by writing out and multiplying the appropriate equilibrium constant expressions
- Relate and deploy the concept of a conjugate pair (two species that differ by H+)
- Recall that the conjugate pair of a weak acid is a weak base (and vice versa)
- Rank the relative strengths of bases or acids
- Write an expression for the amount of each species present at equilibrium
- Recall that Kw = [H3O+][OH-]
- Analyze the value of K to determine whether approximations can be made in the calculation.
- Predict whether the change in the concentration of base is negligible compared to the initial concentration
- Predict whether the amount of hydroxide ion initially in solution will likely be small compared to the amount produced
- Make any valid approximations and solve the equilibrium constant expression for concentrations
- Validate any approximations using the 5% criteria
- Recall typical Ka (or pKa) and Kb (or pKb) values for weak acids and bases, respectively
- Recall that pH = -log[H3O+], pKa = -logKa and pKb = -logKb
Problem #2
After completing this problem, the student will be able to:
- Solve the problem using either the Ka or Kb expression using procedures established in problem 1
- Determine whether, for a conjugate pair, the base is a stronger base than the acid is an acid
- Recall that a solution that has appreciable concentrations of both members of a conjugate pair is a buffer
- Demonstrate qualitatively using appropriate reactions how a buffer can resist changes in pH
- Derive the Henderson-Hasselbalch expression for a buffer
- Use the Henderson-Hasselbalch expression to explain and show quantitatively that a buffer solution resists changes in pH
- Calculate the pH of a buffer using the Henderson-Hasselbalch expression
- Relate the criteria that are used in selecting a buffer
Problem #3
After completing this problem, the student will be able to:
- Relate the common chemical nomenclature that is used to denote cationic and anionic species (Name, using the appropriate suffixes, chemical species that are cationic or anionic)
- Identify a compound that is a weak acid
- Identify whether an anion is an anion of a strong acid
- Identify whether a cation is a cation of a strong base
- Recall that the conjugate pair of a strong acid or base is produced to an extent of 100% and exists as a spectator ion in solution
- Solve for the pH of a solution of a weak acid
Problem #4 and 5
After completing these problems, the student will be able to:
- Determine that a weak acid and a weak base undergo a neutralization reaction
- Write a neutralization reaction
- Write the equilibrium constant expression for Kn
- Prove that Kn = KaKb/Kw
- Determine Kn for a neutralization reaction
- Explain why the Kn value for a neutralization reaction will always be large when either the acid or base is strong
- Explain when Kn is expected to be large and when Kn may be small for a neutralization reaction
- Determine whether a neutralization reaction goes to completion
- Be able to solve for the final concentration of all four species present in a neutralization reaction
- Explain why a neutralization reaction involving a weak acid and a weak base will often lead to the formation of a buffer.
- Calculate the concentration of species present in a neutralization reaction with a large value of K.
- Solve for the final pH of a solution in which a neutralization reaction occurs.