Exercises: Extension: buffer solutions

A buffer solution consists of a weak acid or base and its conjugate species in similar concentrations. At $25\,\mathrm{^\circ C}$, three aqueous solutions are prepared by mixing equal volumes of the following pairs of solutes, each at an initial concentration of $0.10\,\mathrm{mol\times L^{-1}}$:

1) $\mathrm{CH_3COOH}$ and $\mathrm{CH_3COONa}$

2) $\mathrm{HCl}$ and $\mathrm{NaCl}$

3) $\mathrm{NH_3}$ and $\mathrm{NH_4Cl}$

1. a) Justify, with reasoning, which of these three mixtures constitute a buffer solution.
2. b) Explain which component of each buffer mixture neutralizes a small amount of strong acid and which neutralizes a small amount of strong base.

The Henderson-Hasselbalch equation for a conjugate acid-base pair $\mathrm{HA/A^-}$ is written as:

$$\mathrm{pH} = \mathrm{p}K_a + \log\left(\frac{[\mathrm{A^-}]}{[\mathrm{HA}]}\right)$$

At $25\,\mathrm{^\circ C}$ there is a buffer made up of benzoic acid ($\mathrm{C_6H_5COOH}$, $K_a = 6.3\times 10^{-5}$) and sodium benzoate ($\mathrm{C_6H_5COONa}$).

1. a) State two fundamental hypotheses or assumptions that justify using the analytical concentrations of the prepared components in this equation as an approximation to the equilibrium concentrations.
2. b) If a $\mathrm{pH} = 4.50$ is to be set, calculate the molar ratio $[\mathrm{A^-}]/[\mathrm{HA}]$ at equilibrium at that temperature.

Human blood plasma contains a key physiological buffer system made up of carbonic acid and the bicarbonate ion:

$$\mathrm{CO_2(ac)} + \mathrm{H_2O(l)} \rightleftharpoons \mathrm{H_2CO_3(ac)} \rightleftharpoons \mathrm{HCO_3^-(ac)} + \mathrm{H^+(ac)}$$

At body temperature, the effective value of $\mathrm{p}K_a$ for the bicarbonate/total dissolved CO₂ system is $6.10$, and the $\mathrm{pH}$ of the plasma is maintained at around $7.40$ under normal conditions.

1. a) Calculate the ratio $[\mathrm{HCO_3^-}]/[\mathrm{CO_2^*}]$ in blood plasma at that $\mathrm{pH}$.
2. b) Describe chemically how this buffer pair responds to an increase in the concentration of protons from cellular metabolism, preventing sudden drops in $\mathrm{pH}$. Here $[\mathrm{CO_2^*}]=[\mathrm{CO_2(ac)}]+[\mathrm{H_2CO_3}]$ and the effective relationship $\mathrm{pH}=6.10+\log([\mathrm{HCO_3^-}]/[\mathrm{CO_2^*}])$ is used; total dissolved CO₂ is not identified with the concentration of molecular carbonic acid.

In the lab, the resistance to change in $\mathrm{pH}$ of two solutions of equal volume ($100\,\mathrm{mL}$) at $25\,^\circ\mathrm{C}$ is compared: beaker A contains pure deionized water and beaker B contains an acetic acid / sodium acetate buffer $0.10\,\mathrm{mol\times L^{-1}}$ of each component ($K_a = 1.75\times 10^{-5}$, $\mathrm{p}K_a = 4.76$). The same dose of $1.0\,\mathrm{mL}$ of $\mathrm{HCl}$ $0.10\,\mathrm{mol\times L^{-1}}$ is added to both beakers. The figure summarizes the experiment and the $\mathrm{pH}$ values recorded before and after the addition.

1. a) Explain the difference in the change in $\mathrm{pH}$ between beaker A ($\Delta\mathrm{pH} = -4.00$) and beaker B ($\Delta\mathrm{pH} = -0.01$), deducing the reactions involved.
2. b) Define the concept of finite buffer capacity and state what would happen qualitatively to the $\mathrm{pH}$ of beaker B if $150\,\mathrm{mL}$ of $\mathrm{HCl}$ $0.10\,\mathrm{mol\times L^{-1}}$ were added.

$250\,\mathrm{mL}$ of a buffer solution containing acetic acid ($\mathrm{CH_3COOH}$) $0.20\,\mathrm{mol\times L^{-1}}$ and sodium acetate ($\mathrm{CH_3COONa}$) $0.30\,\mathrm{mol\times L^{-1}}$ is available. To this solution, $0.010\,\mathrm{mol}$ of solid sodium hydroxide ($\mathrm{NaOH}$) is added, with no appreciable change in the final volume. Data at $25\,\mathrm{^\circ C}$: $K_a(\mathrm{CH_3COOH}) = 1.8\times 10^{-5}$.

1. a) Write the chemical neutralization reaction that takes place first and calculate the amounts of acetic acid and acetate ion present after neutralization.
2. b) Calculate the $\mathrm{pH}$ of the resulting solution at $25\,\mathrm{^\circ C}$ using the Henderson-Hasselbalch equation. For buffers, use the approximation $\mathrm{pH}=\mathrm{p}K_a+\log(n_{\mathrm{base}}/n_{\mathrm{ácido}})$ after stoichiometric neutralization. For the ammonium/ammonia pair, $K_a=K_w/K_b$. If one component is used up, solve the equilibrium of the remaining species. Assume ideal behavior and additive volumes.

A basic buffer solution is prepared by dissolving ammonia ($\mathrm{NH_3}$) and ammonium chloride ($\mathrm{NH_4Cl}$) in water at $25\,\mathrm{^\circ C}$, so that the initial concentrations are $[\mathrm{NH_3}] = 0.15\,\mathrm{mol\times L^{-1}}$ and $[\mathrm{NH_4^+}] = 0.10\,\mathrm{mol\times L^{-1}}$. To $500\,\mathrm{mL}$ of this mixture, $5.0\,\mathrm{mL}$ of concentrated hydrochloric acid $1.0\,\mathrm{mol\times L^{-1}}$ is added. Data at $25\,\mathrm{^\circ C}$: $K_b(\mathrm{NH_3}) = 1.8\times 10^{-5}$, $K_w = 1.0\times 10^{-14}$.

1. a) Calculate the initial $\mathrm{pH}$ of the buffer solution.
2. b) Set up the material balance after the addition of the strong acid and determine the new value of $\mathrm{pH}$ once chemical equilibrium has been reached. For buffers, use the approximation $\mathrm{pH}=\mathrm{p}K_a+\log(n_{\mathrm{base}}/n_{\mathrm{ácido}})$ after stoichiometric neutralization. For the ammonium/ammonia pair, $K_a=K_w/K_b$. If one component is used up, solve the equilibrium of the remaining species. Assume ideal behavior and additive volumes.

You have $200\,\mathrm{mL}$ of a buffer made up of methanoic acid (formic acid, $\mathrm{HCOOH}$, $K_a = 1.8\times 10^{-4}$) $0.12\,\mathrm{mol\times L^{-1}}$ and sodium methanoate ($\mathrm{HCOONa}$) $0.080\,\mathrm{mol\times L^{-1}}$ at $25\,\mathrm{^\circ C}$. The useful buffering capacity is considered exhausted when the $\mathrm{pH}$ falls below $\mathrm{p}K_a - 1.00$.

1. a) Calculate the volume of $\mathrm{HCl}$ $0.50\,\mathrm{mol\times L^{-1}}$ solution that must be added to reach approximately the lower limit of the buffering capacity ($\mathrm{pH} = \mathrm{p}K_a - 1.00$).
2. b) Calculate the $\mathrm{pH}$ that would be obtained if the exact stoichiometric amount of $\mathrm{HCl}$ needed to neutralize all the methanoate ion initially present were added, assuming additive volumes. For buffers, use the approximation $\mathrm{pH}=\mathrm{p}K_a+\log(n_{\mathrm{base}}/n_{\mathrm{ácido}})$ after stoichiometric neutralization. For the ammonium/ammonia pair, $K_a=K_w/K_b$. If one component is used up, solve the equilibrium of the remaining species. Assume ideal behavior and additive volumes.

It is planned to prepare in the lab $500\,\mathrm{mL}$ of a buffer solution at $25\,\mathrm{^\circ C}$ with a $\mathrm{pH} = 7.00$, using anhydrous sodium dihydrogenphosphate ($\mathrm{NaH_2PO_4}$, molar mass $120.0\,\mathrm{g\times mol^{-1}}$) and anhydrous disodium hydrogenphosphate ($\mathrm{Na_2HPO_4}$, molar mass $142.0\,\mathrm{g\times mol^{-1}}$). The total analytical concentration of phosphate must be $C_T = [\mathrm{H_2PO_4^-}] + [\mathrm{HPO_4^{2-}}] = 0.10\,\mathrm{mol\times L^{-1}}$.

Data at $25\,\mathrm{^\circ C}$: $K_{a2}(\mathrm{H_3PO_4}) = 6.2\times 10^{-8}$, $K_w = 1.0\times 10^{-14}$.

1. a) Determine the molar ratio $[\mathrm{HPO_4^{2-}}]/[\mathrm{H_2PO_4^-}]$ required to obtain the specified $\mathrm{pH}$.
2. b) Calculate the mass in grams of each of the two anhydrous solid salts that must be weighed on an analytical balance to prepare the $500\,\mathrm{mL}$ of buffer. For buffers, use the approximation $\mathrm{pH}=\mathrm{p}K_a+\log(n_{\mathrm{base}}/n_{\mathrm{ácido}})$ after stoichiometric neutralization. For the ammonium/ammonia pair, $K_a=K_w/K_b$. If one component is used up, solve the equilibrium of the remaining species. Assume ideal behavior and additive volumes.

A student has $100\,\mathrm{mL}$ of a solution containing only acetic acid ($\mathrm{CH_3COOH}$) $0.10\,\mathrm{mol\times L^{-1}}$ at $25\,\mathrm{^\circ C}$. The student successively adds $\mathrm{NaOH}$ $0.20\,\mathrm{mol\times L^{-1}}$ solution.

Data at $25\,\mathrm{^\circ C}$: $K_a(\mathrm{CH_3COOH}) = 1.8\times 10^{-5}$, $K_w = 1.0\times 10^{-14}$.

1. a) Calculate the volume of $\mathrm{NaOH}$ that must be added to obtain a buffer solution of $\mathrm{pH} = 5.00$, and calculate the moles of $\mathrm{HCl}$ that could be added before the $\mathrm{pH}$ falls again to $4.74$ ($\mathrm{p}K_a$).
2. b) If a total volume of $\mathrm{NaOH}$ is subsequently added until a cumulative volume of $50\,\mathrm{mL}$ of base has been added, show that the buffering capacity has been exhausted and calculate the $\mathrm{pH}$ of the resulting solution at that equivalence point. For buffers, use the approximation $\mathrm{pH}=\mathrm{p}K_a+\log(n_{\mathrm{base}}/n_{\mathrm{ácido}})$ after stoichiometric neutralization. For the ammonium/ammonia pair, $K_a=K_w/K_b$. If one component is used up, solve the equilibrium of the remaining species. Assume ideal behavior and additive volumes.