Problem 105 - Chemistry: Atoms First

Question

What is the effect on the amount of CaHPO \(_{4}\) that dissolves and the concentrations of \(\mathrm{Ca}^{2+}\) and \(\mathrm{HPO}_{4}^{-}\) -when each of the following are added to a mixture of solid \(\mathrm{CaHPO}_{4}\) and water at equilibrium? (a) \(\mathrm{CaCl}_{2}\) (b) HCl (c) \(\mathrm{KClO}_{4}\) (d) \(\mathrm{NaOH}\) (e) \(\mathrm{CaHPO}_{4}\)

Step-by-Step Solution

Answer

The addition of (a) CaCl2 decreases CaHPO4 dissolution, (b) HCl increases CaHPO4 dissolution, (c) KClO4 has no effect, (d) NaOH increases CaHPO4 dissolution, and (e) additional CaHPO4 will not change dissolution or concentrations at equilibrium.

Step 1: Understanding the Equilibrium of CaHPO4 Dissolving

CaHPO4 dissolves in water to create an equilibrium with its ions: CaHPO4 (s) ↔ Ca2+ (aq) + HPO4^2− (aq). The addition of other substances can shift this equilibrium according to Le Chatelier's Principle, which states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium moves to counteract the change.

Step 2: Effect of Adding CaCl2

Adding CaCl2 increases the concentration of Ca2+ ions in solution. According to Le Chatelier's Principle, the equilibrium will shift to the left to reduce the concentration of Ca2+ ions, resulting in less CaHPO4 dissolving.

Step 3: Effect of Adding HCl

HCl dissociates to H+ and Cl- ions in solution. H+ ions can react with HPO4^2− ions to form H2PO4−, thereby reducing the concentration of HPO4^2− ions and shifting the equilibrium to the right. This results in more CaHPO4 dissolving to restore the HPO4^2− concentration.

Step 4: Effect of Adding KClO4

KClO4 is a neutral salt that does not produce any ions that would interact with Ca2+ or HPO4^2−. Therefore, the addition of KClO4 will have no effect on the equilibrium position of the reaction and the concentrations of Ca2+ and HPO4^2− ions will remain unchanged.

Step 5: Effect of Adding NaOH

NaOH dissociates into Na+ and OH- ions. OH- ions can react with Ca2+ to form Ca(OH)2, a precipitate, thus reducing the concentration of Ca2+ ions and shifting the equilibrium to the right, helping more CaHPO4 to dissolve.

Step 6: Effect of Adding CaHPO4

Adding more CaHPO4 to the mixture does not change the concentrations of the ions in the solution since it is a solid and will not dissolve until the existing CaHPO4 has dissolved. The equilibrium position remains the same.

Key Concepts

Chemical Equilibrium

In simple terms, chemical equilibrium is the state of a chemical reaction where the rate of the forward reaction equals the rate of the reverse reaction, meaning that the amounts of reactants and products remain constant over time. It's a delicate balance, like a see-saw that's perfectly level. In our case, when CaHPO4 dissolves in water, it separates into Ca²⁺ and HPO4²⁻ ions, achieving equilibrium.

Suppose you're at a party and the room is just the right amount of crowded (this is our equilibrium). Suddenly, more guests flood in (extra ions are added to the solution). The room gets too crowded, and some people might leave to make space (the reaction shifts to reduce the ion concentration). This event is guided by Le Chatelier's Principle, a concept named after the French chemist who proposed that a system at equilibrium will try to counteract any change imposed on it.

To illustrate, imagine you're on that see-saw and it's balanced. If a friend sits on one end, naturally, you'd shift towards them to balance it again. That's exactly what happens on a molecular level when equilibrium is disturbed.

Solubility and Precipitation

The concepts of solubility and precipitation are pivotal in understanding how a substance like CaHPO4 behaves in water. Solubility is the ability of a substance to dissolve in a solvent like water. CaHPO4 has limited solubility; it will dissolve up to a point and then stop once equilibrium is reached.

Now, picture a dance floor that's only fun if it's neither empty nor too packed - that's your solution at the perfect state of solubility. But when the music changes, say from pop to reggae, some dancers might sit out because they don't enjoy the new tune (precipitation). Add NaOH to our chemical mix, and it's like changing the song. Some Ca²⁺ ions pair up with OH− ions to form Ca(OH)2, which is like our dancers leaving the floor because this new compound is not soluble and falls out of the solution as a precipitate.

This is a common theme in chemical reactions - the conditions determine what stays dissolved and what becomes a solid, much like the mood of the party influencing who stays on the dance floor.

Ion Concentration in Solution

Understanding the ion concentration in solution is essential when predicting how a reaction will proceed. When we dissolve the salt CaHPO4 in water, we're essentially making a 'soup' with a specific amount of Ca²⁺ and HPO4²⁻ ions. If we add more ingredients, like CaCl2 or HCl, it's like we're adding more carrots or salt to our soup; the taste changes, and we need to adjust.

For each substance we add, the impact on ion concentration varies. When CaCl2 enters the mix, the extra Ca²⁺ ions are like unexpected saltiness, there’s just too much, and the system reacts to dilute it. On the flip side, when we add HCl, the resulting H+ ions react with HPO4²⁻, and the equilibrium shifts to bring back the original 'flavor balance' by dissolving more CaHPO4.

Just like cooking, manipulating the concentrations of ions in a chemical solution can drastically alter the outcome, either increasing solubility, causing precipitation, or leaving the system unchanged. The chef, in this case, is Le Chatelier's Principle, ensuring our reaction 'meal' is just right - not too concentrated, not too diluted.