Problem 114 - Chemistry: An Atoms-Focused Approach

Question

Why does adding \(\mathrm{CaCl}_{2}\) to a \(\mathrm{HPO}_{4}^{2-} / \mathrm{PO}_{4}^{3-}\) buffer increase the ratio of \(\mathrm{HPO}_{4}^{2-}\) ions to \(\mathrm{PO}_{4}^{3-}\) ions?

Step-by-Step Solution

Answer

Answer: Adding CaCl2 to a HPO4²⁻/PO4³⁻ buffer causes the ratio of HPO4²⁻ ions to PO4³⁻ ions to increase.

Step 1: Identify the important ions in the buffer and the added salt

In the given buffer, we have the HPO4²⁻ and PO4³⁻ ions. When we add CaCl2 to the buffer, it dissociates into Ca²⁺ and Cl⁻ ions. The Cl⁻ ions will not interact with the buffer, so we will focus on how Ca²⁺ ions interact with HPO4²⁻ and PO4³⁻ ions.

Step 2: Understand the interactions between the ions

Ca²⁺ ions have a strong affinity for negative charges due to their positive charge. Therefore, they tend to form complexes with negatively charged ions, such as HPO4²⁻ and PO4³⁻ ions. The Ca²⁺ ions will form more stable complexes with PO4³⁻ ions than with HPO4²⁻ ions, since PO4³⁻ ions have a higher negative charge.

Step 3: Write the reaction of Ca²⁺ ions with the buffer components

The complex formation between Ca²⁺ ions and the buffer components can be represented by the following reactions: 1. \[Ca^{2+} + HPO_{4}^{2-} \rightleftharpoons CaHPO_{4}(s)\] 2. \[Ca^{2+} + PO_{4}^{3-} \rightleftharpoons CaPO_{4}(s)\] In both reactions, the complexes formed (CaHPO4 and CaPO4) are solid and will precipitate out of the solution.

Step 4: Determine the effects of adding Ca²⁺ ions on the buffer components

When the Ca²⁺ ions are added to the buffer, they will preferentially bind to PO4³⁻ ions to form the CaPO4 complex due to the higher negative charge on PO4³⁻ ions. As a result, the concentration of PO4³⁻ ions in the buffer will decrease. The complex formation between Ca²⁺ and HPO4²⁻ ions will also occur, but to a lesser extent than with PO4³⁻ ions. The decrease in PO4³⁻ ions concentration will cause a shift in the equilibrium of the following reaction, which represents the buffering action: \[HPO_{4}^{2-} \rightleftharpoons H^{+} + PO_{4}^{3-}\] According to Le Chatelier's principle, the equilibrium will shift to the right to counter the decrease in PO4³⁻ ions concentration. This shift will result in an increase in HPO4²⁻ ions concentration as well as an increase in H⁺ ions concentration.

Step 5: Conclude the effect on the ratio of HPO4²⁻ ions to PO4³⁻ ions

As a result of adding CaCl2 to the buffer and the subsequent interactions between Ca²⁺ ions and the buffer components, the concentration of PO4³⁻ ions will decrease while the concentration of HPO4²⁻ ions will increase. Thus, the ratio of HPO4²⁻ ions to PO4³⁻ ions will increase.

Key Concepts

Ions Interaction

In the realm of chemistry, ions interaction plays a crucial role, especially when it comes to buffer systems. When \(\text{CaCl}_{2} \)is added to a \(\mathrm{HPO}_{4}^{2-} / \mathrm{PO}_{4}^{3-} \)buffer, the \(\text{CaCl}_{2} \)quickly dissociates into \(\text{Ca}^{2+} \)and \(\text{Cl}^- \)ions in the solution. Among these, the \(\text{Cl}^- \)ions do not actively interact with the phosphate buffer ions due to their lower reactivity and the fact that the main interactions involved stem from the positively charged \(\text{Ca}^{2+} \)ions.

These \(\text{Ca}^{2+} \)ions, being positively charged, are naturally inclined to interact with negatively charged ions in the solution. Both \(\text{HPO}_{4}^{2-} \)and \(\text{PO}_{4}^{3-} \)ions in the buffer are negatively charged, but the interaction is not uniform across these ions. It tends to be more pronounced with \(\text{PO}_{4}^{3-} \)because it has a higher negative charge. The preferential binding occurs because the strength of interaction becomes greater as the charge disparity between the ions increases. This interaction heavily impacts the availability and concentration of the ions in the solution.

The resulting change in ion concentration from such interactions sets off a cascade of chemical responses in the solution, fundamentally altering the dynamics of the buffer system.

Le Chatelier's Principle

Le Chatelier's Principle provides insight into how a chemical equilibrium reacts to external changes, structuring itself to counterbalance disturbances effectively. When we introduce \(\text{Ca}^{2+} \)ions into the \(\text{HPO}_{4}^{2-} / \text{PO}_{4}^{3-} \)buffer, these ions bind significantly with \(\text{PO}_{4}^{3-} \)to form \(\text{CaPO}_{4} \)solid. This precipitate decreases the \(\text{PO}_{4}^{3-} \)ions' concentration available in solution.

According to Le Chatelier's Principle, the system strives to counteract this decrease in \(\text{PO}_{4}^{3-} \)ions concentration by shifting the equilibrium towards the production of more \(\text{PO}_{4}^{3-} \)ions. Consequently, the reaction \(\text{HPO}_{4}^{2-} \rightleftharpoons \text{H}^{+} + \text{PO}_{4}^{3-} \)accommodates this shift by converting more \(\text{HPO}_{4}^{2-} \)into \(\text{PO}_{4}^{3-} \)and \(\text{H}^{+} \)ions.

• Increase in \(\text{HPO}_{4}^{2-} \)in the equilibrium as \(\text{PO}_{4}^{3-} \)levels are restored.
• Higher \(\text{H}^{+} \)ions concentration makes the solution slightly more acidic.

This principle highlights the buffer's ability to adapt and resist shifts from adding new substances, maintaining stability in the face of chemical fluctuations.

Complex Formation

Complex formation in chemistry involves the stable association of a central metal ion, such as \(\text{Ca}^{2+} \), with ligands that donate electron pairs. In the scenario of a \(\text{HPO}_{4}^{2-} / \text{PO}_{4}^{3-} \)buffer, \(\text{Ca}^{2+} \)ions introduced into the solution tend to form complexes with \(\text{PO}_{4}^{3-} \)ions because of their stronger negative charge, forming a solid complex like \(\text{CaPO}_{4} \).

The stability of these complexes relies on the bonds formed between the \(\text{Ca}^{2+} \)and the phosphate ions. The more negatively charged the phosphate, the greater the likelihood of forming a stable complex. This is fundamental to understand as complex formation reduces the free ions in the solution significantly, thus shifting chemical equilibria.

• Complex formation can lead to precipitation, where new solid forms are established, such as \(\text{CaPO}_{4} \)
• Lessens free ion availability in solution, impacting the solution's chemical behavior.

This process not only affects equilibrium but also determines solubility and reactivity, typically making complex formation a crucial aspect of chemical processes like buffering.