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# 9: Acids/Bases, Common Ion Effect, and Buffers (Worksheet)

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Work in groups on these problems. You should try to answer the questions without referring to your textbook. If you get stuck, try asking another group for help.

## Unit I: Solubility (A Heterogeneous Equilbrium)

Both ionic salts and covalent molecules dissolve in solutions to varying degrees. The limit to how much salt can be dissolved in a given volume of water is given by the solubility product, $$K_{sp}$$, which is the relevant equilibrium constant for the process (just with a special name) and naturally depends on the type of salt and temperature or other species in solution (the common ion effect). Before beginning with calculations, let's calibrate things a bit:

### Q9.1: Definition of $$K_{sp}$$

Write the relevant solubility product for dissolving $$\ce{AgCl}$$ (with a molar mass of 143.3 g/mol) in water:

$\ce{AgCl (s) -> Ag^{+}(aq) + Cl^{−}(aq)} \label{W1}$

This specific equilibrium constant is $$1.8 \times 10^{−10}$$ at 25 °C (Reference Table E3 on the Libretexts).

### Q9.2: Thermodynamic and Intermolecular Forces

How to you expect $$K_{sp}$$ to change under the following conditions:

1. If $$\Delta G_{solution}$$ for the dissolving process were made more negative?
2. If $$\Delta H_{solution}$$ for the dissolving process were made more negative?
3. If $$\Delta S_{solution}$$ for the dissolving process were made more negative?
4. If the lattice energy for $$\ce{AgCl}$$ were increased and all other factors maintained the same?
5. If the solvation energies for $$\ce{Ag^{+}}$$ and $$\ce{Cl^{-}}$$ were increased and all other factors maintained the same?
6. If the intermolecular forces between the solute and solvent molecules were increased and all other factors maintained the same?
7. If the entropy of dissolving were increased and and all other factors maintained the same?

### Q9.3: A Le Chatelier

If a system is under equilibrium, then the solubility constant expression you derived for $$AgCl$$ involves the activities of both undissolved solute and dissolve solute ions (i.e., both exist). How would this equilibrium shift for Reaction $$\ref{W1}$$, if the amount of dissolved species were to be removed? This is essentially saying that $$Q < K_{sp}$$.

### Q9.4: Solubility

If $$Q$$ can never equal $$K_{sp}$$ for a dissolving process, that means that all of the solute dissolves into solution (i.e., an equilibrium can never be established between solid $$\ce{AgCl}$$ and dissolved $$\ce{Ag^{+} (aq)}$$ and $$\ce{Cl^{-} (aq)}$$ ions) and no $$\ce{AgCl (s)}$$ will exist. Adding more $$\ce{AgCl(s)}$$ will result in increasing $$\ce{Ag^{+} (aq)}$$ and $$\ce{Cl^{-} (aq)}$$ ions until that equilibrium is established - the system is then saturated.

### Q9.5: ICE Table

Construct an ICE table to demonstrate what will happen when one adds $$\ce{AgCl(s)}$$ to a saturated solution of $$\ce{Ag^{+} (aq)}$$ and $$\ce{Cl^{-} (aq)}$$ ions. What is $$Q$$ before adding $$\ce{AgCl(s)}$$ and afterward?

### Q9.5: Solubility Again

Based off of the above discussions, what is the maximum concentration of $$\ce{Ag^{+}}$$ that can be generated by adding $$\ce{AgCl(s)}$$ to water?

What is the maximum concentration of $$\ce{Cl^{-}}$$ that can be generated by adding $$\ce{AgCl(s)}$$ to water?

What is mass of $$\ce{AgCl}$$ that can be dissolved by adding $$\ce{AgCl(s)}$$ to 1 L of water?

The amount above is generally referred to as the solubility of a substance ($$\ce{AgCl}$$. However, you can also express this as a molar solubility instead, which is the number of moles of the solute that can be dissolved per liter. What is the molar solubility of $$\ce{AgCl}$$?

## Unit II: Common Ion Effects (Sharing Species)

### Q9.6: Intuition

Sodium chloride $$\ce{NaCl}$$ is appreciably more soluble than $$\ce{AgCl}$$ in water ($$K_{sp} = 36$$). From a simple Le Chatelier argument, how would you expect the concentration of $$\ce{Ag^+}$$ to shift if some $$\ce{NaCl}$$ were added to a saturated solution of $$\ce{AgCl}$$?

### Q9.7: Spectator Ions

Does the $$\ce{Na^{+}}$$ affect any equilibrium shift (why or why not)?

### Q9.8: ICE

Construct an ICE table to describe the effect of adding $$1 \times 10^{-3} M$$ of $$Na^+$$ and $$Cl^-$$ ions to a saturated solution of $$AgCl$$. Remember that the I row in the table is the saturated solution condition + the added solute (olne can call this a IACE table, but that is a silly acronym).

### Q9.9: Equilibrated System

Using the ICE table you constructed in Q9.8 and the fact that the equilibrium constant (i.e., $$K_{sp}$$ for this system) does not change, what is the final concentration of $$\ce{Ag^{+}}$$ in solution after adding the salt to the original solution?

### Q9.10:

In general, how would you describe the change of solubility of a ionic compound upon adding an additional solute that shares a common ion?

## Unit III: Acids and Base Equilibria

### Q9.11: Acetic Acid is a Weak Acid

Acetic acid ($$\ce{HC_2H_3O_2}$$) is a weak acid that will dissociate in aqueous solutions to generate hydrated protons and acetate ions:

$\ce{HC2H3O2 (aq) + H2O (l) <=> H3O^{+} (aq) + C2H3O2^{-} (aq)} \label{W3}$

The equilibrium constant for this reaction is an acid dissociation constant ($$K_a$$), but is just an equilibrium constant with equilibrium constant properties. Use the Law of Mass Action to construct the equation of the acid dissociation constant in terms of concentrations of relevant species in this reaction (pay attention to phase).

### Q9.12: Logarithms are the Way of the Future

Another way to tabulate $$K_a$$ values is as $$pK_a$$ values which are defined as

$pK_A = -\log_{10} K_a$

Why would we adopt a new formalism to to represent an equilibrium constnat? (Hint: it has nothing to do with scientists loving logarithms)? If $$K_a$$ defined in Q9.11 is $$1.8 \times 10^{-5}$$, what is the corresponding $$pK_a$$ for acetic acid?

### Q9.13: ICE Table

Construct an ICE Table to describe the reaction in Equation $$\ref{W3}$$ when 0.010 mol acetic acid is added to 100.0 mL of water.

### Q9.14: Solve the ICE Table

Given the information above about the value of $$K_a$$ (or $$pKa$$), identify the concentration of hydronium in solution upon equilibration. As with $$pK_a$$, we can construct a new value $$pH$$ that describes this

$pH \approx -\log_{10} [H_3O^+] \label{W4}$

Why is Equation $$\ref{W4}$$ written with a $$\approx$$ instead of a $$=$$ sign? What is the pH of the solution described in Q9.13. You can assume all $$H_3O^+$$ originate from the added acetic acid, however, there is another source of $$H_3O^+$$ ions; what do you think it is?

### Q9.15: Unbuffered Solution

Consider what will happen if we add 0.005 mol of HCl to this solution (fully dissociates). The strong acid will react with the acetate ion. What is the pH of this new solution?

### Q9.16

However, we often find it useful and accurate to make the approximation that the weak acid is only slightly dissociated. Thus the equilibrium concentration of $$HC_2H_3O_2$$ is approximately equal to the initial concentration:

$[ HC_2H_3O_2 ]_{eq} \approx [ HC_2H_3O_2 ]_o$

Is this a justified assumption for the solution you described in Q9.13 and Q9.14 (why or why not)?

### Q9.17: Common Ion Effect in Acids and Bases Equilibria

Construct an ICE table for adding 0.010 mol sodium acetate, $$NaC_2H_3O_2$$ into a 100.0 mL solution of 0.010 mol acetic acid (assume approximation above). What is the pH of this new solution? Does this result make sense within a Le Chatelier picture?

### Q9.18: Buffer

Consider what will happen if we add 0.005 mol of HCl to this solution (fully dissociates). The strong acid will react with the acetate ion. What is the pH of this new solution?

### Q9.19

Explain the origin of the difference between the final pH calculated in Q9.18 and Q9.15.

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