Question

Consider phosphorous acid, a polyprotic acid with formula \(\mathrm{H}_{3} \mathrm{PO}_{3}\) (a) Draw two plausible structures for \(\mathrm{H}_{3} \mathrm{PO}_{3} .\) For each one, predict the shape of the \(\mathrm{pH}\) titration curve for the titration of the \(\mathrm{H}_{3} \mathrm{PO}_{3}\left(K_{a 1}=1.0 \times 10^{-2}\right)\) with aqueous \(\mathrm{NaOH}\) (b) For the structure with the \(\mathrm{H}\) atoms in two different environments, calculate the \(\mathrm{pH}\) at the first and second equivalence points, assuming that \(30.00 \mathrm{~mL}\) of \(0.1240 \mathrm{M}\) \(\mathrm{H}_{3} \mathrm{PO}_{3}\left(K_{a 2}=2.6 \times 10^{-7}\right)\) is titrated with \(0.1000 \mathrm{M} \mathrm{NaOH} .\)

Short answer

First equivalence point pH is 4.3; second around 12.

Step-by-step solution

Understand the molecular structure of H3PO3

Phosphorous acid, \(\text{H}_3\text{PO}_3\), is a diprotic acid, meaning it can donate two protons. Its structure can be drawn with one \(\text{P=O}\) double bond and two \(\text{P-OH}\) bonds. The structure is often represented as \(\text{HPO(OH)}_2\), indicating that two hydrogen atoms are attached to oxygen atoms as hydroxyl groups.

Predict the shape of the pH titration curve

In a titration of \(\text{H}_3\text{PO}_3\) with \(\text{NaOH}\), we expect three segments in the pH curve. The first segment shows a rapid increase in pH as the first \(\text{H}^+\) ion is neutralized. The second segment has a more gradual pH change as the acid is converted into its basic form. The third segment will show a steeper rise again after all acidic protons have been titrated.

Calculate moles of H3PO3 and NaOH required

First, determine the number of moles of \(\text{H}_3\text{PO}_3\) using the formula: \(\text{moles} = \text{volume} \times \text{concentration}\). For \(\text{H}_3\text{PO}_3\), \(\text{moles} = 0.0300 \, \text{L} \times 0.1240 \, \text{M} = 0.00372\, \text{moles}.\) Similarly, calculate the moles of \(\text{NaOH}\) required to each endpoint.

Determine the volume of NaOH at equivalence points

Since \(\text{H}_3\text{PO}_3\) is diprotic, two molar equivalents of \(\text{NaOH}\) are needed. Calculate the volume of \(\text{NaOH}\) needed to reach the first equivalence point: \(\text{Volume} = \frac{0.00372\, \text{moles}}{0.1000\, \text{M}} = 0.0372\, \text{L} = 37.2\, \text{mL}\.\) The second equivalence point will require double this amount (74.4 mL).

Calculate pH at first equivalence point

At the first equivalence point, \(\text{H}_3\text{PO}_3\) will be converted to \(\text{H}_2\text{PO}_3^-\). To find the pH, use \(pH = \frac{pK_{a1} + pK_{a2}}{2}\). Using the provided \(pK_{a1} = -\log(1.0 \times 10^{-2}) = 2\) and \(pK_{a2} = -\log(2.6 \times 10^{-7}) \approx 6.6\), \(pH = \frac{2 + 6.6}{2} = 4.3\.\)

Calculate pH at second equivalence point

At the second equivalence point, all acidic protons are neutralized, and the solution forms \(\text{PO}_4^{3-}\) ions. The pH calculation will involve the equilibrium of the bare \(\text{PO}_4^{3-}\) ion, often leading to a much higher pH. Due to the strong base nature of \(\text{PO}_4^{3-}\), expect a pH above neutral, often around 12 to 13.

Key concepts

Polyprotic Acids

Polyprotic acids are a fascinating class of acids capable of donating more than one hydrogen ion ( H^+ ) in solution. One example is phosphorous acid ( H_3PO_3 ), which is specifically referred to as a diprotic acid since it can release two H^+ ions.

These types of acids are characterized by more complex titration behavior compared to monoprotic acids, which only donate one hydrogen ion.

• Primary Ionization: The initial release of the first H^+ ion, typically resulting in a significant change in pH.
• Secondary Ionization: The subsequent release of a second H^+ ion, which generally results in a more gradual change in pH.

Understanding how polyprotic acids like H_3PO_3 behave is crucial for predicting their titration curves and calculating various equilibrium points during titrations.

Titration Curve

A titration curve represents how the pH of a solution changes as a titrant is added. It provides valuable insights into the neutralization process of the acid or base being titrated.

For polyprotic acids such as phosphorous acid ( H_3PO_3 ), the titration curve can be more complex. There are typically distinct phases in the curve:

• Initial Slope: A rapid increase in pH as the first acidic hydrogen is neutralized by the base.
• Buffer Region: A flatter portion indicating the presence of a buffer solution, providing resistance to changes in pH.
• Equivalence Points: Specific points where moles of acid equal moles of base added, characterized by steep changes in pH.

Each segment on the titration curve tells us something about the interaction between the acid and base, helping to determine unknown concentrations and pK_a values.

Equivalence Point

The equivalence point is a critical stage in a titration where the amount of titrant added equals the amount of substance in the solution being titrated. For polyprotic acids like H_3PO_3 , there are typically multiple equivalence points corresponding to each ionizable proton.

When considering the first equivalence point:

• Initial Neutralization: At this point, the first hydrogen ion has been completely neutralized.
• pH Value: The pH at the first equivalence point for H_3PO_3 can be calculated as an average of the pK_a values.

At the second equivalence point:

• Complete Neutralization: Both ionizable hydrogen ions are neutralized, resulting in the formation of PO_4^{3-} ions.
• Higher pH Levels: The strong base nature of the resulting ions often results in a pH well above neutral.

Grasping the concept of equivalence points helps chemists to effectively interpret titration curves and predict the composition of solutions at various stages.

Acid-Base Chemistry

Acid-base chemistry is an integral part of understanding how acids and bases interact with each other. It explores the behavior of substances that can donate ( acid ) or accept ( base ) hydrogen ions in chemical reactions.

With acids like H_3PO_3 , fundamental concepts come into play:

• Proton Donor: H_3PO_3 acts as a donor of hydrogen ions in reactions, playing a crucial role in determining solution pH.
• Neutralization Reaction: When an acid such as H_3PO_3 reacts with a base like NaOH , they neutralize each other, forming water and salt.

In-depth understanding of acid-base chemistry allows us to predict reaction outcomes, calculate solution pH, and effectively conduct titrations. This branch of chemistry is vital in fields ranging from biochemistry to industrial processes, illustrating the wide scope and importance of studying acid-base interactions.