Buffers & Henderson-Hasselbalch practice questions

Question 1

A student prepares an aqueous solution of lactic acid, $\text{HC}_3\text{H}_5\text{O}_3\text{(aq)}$ ($p K_a = 3.86$), and adjusts its pH to $5.20$ by adding a small amount of $\text{NaOH(aq)}$. Which species, $\text{HC}_3\text{H}_5\text{O}_3\text{(aq)}$ or $\text{C}_3\text{H}_5\text{O}_3^-\text{(aq)}$, is present at a higher concentration in the solution, and why?

Accepted Answer

$\text{C}_3\text{H}_5\text{O}_3^-\text{(aq)}$, because the solution pH is greater than the $p K_a$, indicating that the deprotonated form predominated.

Answer

$\text{HC}_3\text{H}_5\text{O}_3\text{(aq)}$, because the solution pH is higher than the $p K_a$, indicating that protonation of the acid is favored.

Answer

$\text{HC}_3\text{H}_5\text{O}_3\text{(aq)}$, because lactic acid is a weak acid that only partially dissociates, so the protonated form remains predominant at any pH.

Answer

$\text{C}_3\text{H}_5\text{O}_3^-\text{(aq)}$, because the solution pH is greater than the $p K_a$, which means that $[\text{H}^+] > K_a$.

Question 2

A student prepares a buffer solution containing equal molar amounts of a weak acid, $\text{HA}$, and its conjugate base, $\text{A}^-$. Which of the following statements best explains why an equimolar mixture of $\text{HA}$ and $\text{A}^-$ achieves maximum buffer capacity for a fixed total solute concentration?

Accepted Answer

It provides maximum resistance to pH changes from both added acid and added base, because equal amounts of $\text{HA}$ (to react with added $\text{OH}^-$) and $\text{A}^-$ (to react with added $\text{H}_3\text{O}^+$) are present.

Answer

It provides maximum resistance to pH changes from both added acid and added base, because $\text{HA}$ neutralizes added $\text{H}_3\text{O}^+$ while $\text{A}^-$ neutralizes added $\text{OH}^-$.

Answer

It completely prevents any change in pH when acid or base is added, because $\text{HA}$ and $\text{A}^-$ continuously neutralize each other in solution.

Answer

It completely prevents any change in pH when acid or base is added, because an equimolar buffer solution always has a neutral pH equal to 7.0.

Question 3

A student prepares two buffer solutions at 25°C using ethanoic acid ($\text{CH}_3\text{COOH}$) and sodium ethanoate ($\text{CH}_3\text{COONa}$), as shown in the table below.

| Buffer Solution | Volume (mL) | $[\text{CH}_3\text{COOH}]$ (M) | $[\text{CH}_3\text{COONa}]$ (M) |
|---|---|---|---|
| Solution 1 | 100.0 | 0.10 | 0.10 |
| Solution 2 | 100.0 | 0.50 | 0.50 |

The student adds drops of 1.0 M $\text{HCl}$ to separate samples of each buffer. Which solution can neutralize a greater volume of the added $\text{HCl}$ before its pH drops significantly, and why?

Accepted Answer

Solution 2, because it contains a greater concentration of $\text{CH}_3\text{COO}^-$

Answer

Solution 1, because lower solute concentrations minimize repulsions between ions, allowing the weak base to react more rapidly with added $\text{H}_3\text{O}^+$.

Answer

Solution 1, because its initial pH is lower, making it better suited to absorb additional acidic species.

Answer

Solution 2, because its initial pH is higher than that of Solution 1, allowing more acid to be added before the solution becomes acidic.

Question 4

A student prepares a buffer containing comparable amounts of aqueous ammonia, $\text{NH}_3\text{(aq)}$, and ammonium chloride, $\text{NH}_4\text{Cl(aq)}$. The student then adds a small amount of hydrochloric acid, $\text{HCl(aq)}$, without exceeding the buffer capacity. Which of the following is the net ionic equation for the principal reaction that occurs?

Accepted Answer

$\text{H}_3\text{O}^+\text{(aq)}+\text{NH}_3\text{(aq)}\rightarrow\text{NH}_4^+\text{(aq)}+\text{H}_2\text{O(l)}$

Answer

$\text{H}_3\text{O}^+\text{(aq)}+\text{OH}^-\text{(aq)}\rightarrow 2\text{H}_2\text{O(l)}$

Answer

$\text{NH}_4^+\text{(aq)}+\text{H}_2\text{O(l)}\rightarrow\text{NH}_3\text{(aq)}+\text{H}_3\text{O}^+\text{(aq)}$

Answer

$\text{H}_3\text{O}^+\text{(aq)}+\text{Cl}^-\text{(aq)}+\text{NH}_3\text{(aq)}\rightarrow\text{NH}_4^+\text{(aq)}+\text{Cl}^-\text{(aq)}+\text{H}_2\text{O(l)}$

Question 5

A student attempts to prepare a buffer solution by mixing equal volumes of two $0.20 \, \text{M}$ aqueous solutions. Which of the following pairs of solutions will produce an effective buffer solution?

Accepted Answer

$0.20 \, \text{M} \, \text{HF(aq)}$ and $0.20 \, \text{M} \, \text{NaF(aq)}$

Answer

$0.20 \, \text{M} \, \text{HCl(aq)}$ and $0.20 \, \text{M} \, \text{NaOH(aq)}$

Answer

$0.20 \, \text{M} \, \text{HF(aq)}$ and $0.20 \, \text{M} \, \text{NaOH(aq)}$

Answer

$0.20 \, \text{M} \, \text{HCl(aq)}$ and $0.20 \, \text{M} \, \text{NaF(aq)}$

Question 6

A student prepares a buffer solution by mixing $100. \, \text{mL}$ of a $1.0 \, \text{M}$ solution of a weak acid, $\text{HA}$ ($K_a = 1.0 \times 10^{-4}$), with $100. \, \text{mL}$ of a $0.10 \, \text{M}$ solution of $\text{NaA}$. What is the pH of the resulting buffer solution at $25^\circ\text{C}$?

Accepted Answer

$3.00$

Answer

$4.00$

Answer

$5.00$

Answer

$11.00$

Question 7

A student prepares a buffer at $25^\circ\text{C}$ by mixing the solutions shown in the table. The $pK_a$ of $\text{HA(aq)}$ is $5.00$.

| Solution | Concentration | Volume |
|----------|---------------|--------|
| $\text{HA(aq)}$ | $0.300\text{ M}$ | $50.0\text{ mL}$ |
| $\text{NaOH(aq)}$ | $0.100\text{ M}$ | $50.0\text{ mL}$ |

The $\text{OH}^-\text{(aq)}$ reacts completely with $\text{HA(aq)}$ according to $\text{HA(aq)}+\text{OH}^-\text{(aq)}\rightarrow\text{A}^-\text{(aq)}+\text{H}_2\text{O(l)}$. Which of the following correctly predicts the pH of the resulting buffer relative to the $pK_a$ of $\text{HA(aq)}$?

Accepted Answer

The pH is less than $pK_a$, because neutralization leaves twice as many moles of $\text{HA(aq)}$ as the moles of $\text{A}^-\text{(aq)}$ produced.

Answer

The pH is greater than $pK_a$, because producing some $\text{A}^-\text{(aq)}$ makes the conjugate base the predominant buffer component.

Answer

The pH is equal to $pK_a$, because mixing equal volumes produces equal amounts of $\text{HA(aq)}$ and $\text{A}^-\text{(aq)}$.

Answer

The pH is less than $pK_a$, because doubling the total volume decreases the $K_a$ of $\text{HA(aq)}$.

Question 8

A student prepares two acetate buffer mixtures at $25^\circ\text{C}$. Each mixture has a volume of $50.0\text{ mL}$. The student adds $2.00\text{ mL}$ of $0.100\text{ M}$ $\text{NaOH(aq)}$ to each mixture and records the data shown below.

| Mixture | Initial $[\text{CH}_3\text{COOH}]$ | Initial $[\text{CH}_3\text{COO}^-]$ | Initial pH | pH after addition |
|---------|----------------------------------------|-----------------------------------------|------------|-------------------|
| 1 | $0.100\text{ M}$ | $0.100\text{ M}$ | $4.74$ | $4.78$ |
| 2 | $0.0100\text{ M}$ | $0.0100\text{ M}$ | $4.74$ | $5.11$ |

Which statement correctly compares the buffer capacities and explains the results?

Accepted Answer

Mixture 1 has the greater buffer capacity because both mixtures initially have the same $[\text{CH}_3\text{COO}^-]/[\text{CH}_3\text{COOH}]$ ratio, but mixture 1 contains larger amounts of both components, so the added base causes a smaller fractional change in composition.

Answer

Mixture 1 has the greater buffer capacity because its tenfold higher $[\text{CH}_3\text{COO}^-]$ makes the ratio $[\text{CH}_3\text{COO}^-]/[\text{CH}_3\text{COOH}]$ ten times larger than that of mixture 2.

Answer

Mixture 2 has the greater buffer capacity because its larger increase in pH indicates that it neutralized a larger amount of the added base.

Answer

The mixtures have the same buffer capacity because their identical initial pH values indicate that they can neutralize equal amounts of added base.

Question 9

A student tests the response of a water-quality calibration buffer to added strong base. The buffer and added solution have the following properties at $25^\circ\text{C}$.

| Solution | Volume | Solute concentrations |
|---|---:|---|
| Buffer | $50.0\text{ mL}$ | $0.100\text{ M NH}_3$ and $0.500\text{ M NH}_4\text{Cl}$ |
| Added solution | $50.0\text{ mL}$ | $0.100\text{ M NaOH}$ |

For $\text{NH}_4^+\text{(aq)}$, $pK_a=9.25$. Assume that the volumes are additive and that $\log 2=0.30$. What is the pH of the solution after the solutions are mixed?

Accepted Answer

$8.95$

Answer

$8.55$

Answer

$9.55$

Answer

$12.70$

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