Problem 123 - Chemistry and Chemical Reactivity

Question

Oyster beds in the oceans require chloride ions for growth. The minimum concentration is \(8 \mathrm{mg} / \mathrm{L}\) (8 parts per million). To analyze for the amount of chloride ion in a 50.0 -mL sample of water, you add a few drops of aqueous potassium chromate and then titrate the sample with \(25.60 \mathrm{mL}\) of 0.001036 M silver nitrate. The silver nitrate reacts with chloride ion, and, when the ion is completely removed, the silver nitrate reacts with potassium chromate to give a red precipitate. (a) Write a balanced net ionic equation for the reaction of silver nitrate with chloride ions. (b) Write a complete balanced equation and a net ionic equation for the reaction of silver nitrate with potassium chromate, indicating whether each compound is water-soluble or not. (c) What is the concentration of chloride ions in the sample? Is it sufficient to promote oyster growth?

Step-by-Step Solution

Answer

The chloride ion concentration is 5.30 mg/L, which is insufficient for oyster growth.

Step 1: Write the Balanced Net Ionic Equation for Silver Nitrate and Chloride Ions

The reaction between silver nitrate (AgNO₃) and chloride ions (Cl⁻) results in the formation of silver chloride (AgCl), a white precipitate. The balanced net ionic equation is:\[\text{Ag}^+ (aq) + \text{Cl}^- (aq) \rightarrow \text{AgCl} (s)\]This equation shows only the ions directly involved in the formation of the precipitate, omitting the spectator ions.

Step 2: Write the Complete Balanced Equation for Silver Nitrate and Potassium Chromate

The reaction of silver nitrate (AgNO₃) with potassium chromate (K₂CrO₄) forms a red precipitate of silver chromate. Here is the complete reaction:\[2\text{AgNO}_3 (aq) + \text{K}_2\text{CrO}_4 (aq) \rightarrow \text{Ag}_2\text{CrO}_4 (s) + 2\text{KNO}_3 (aq)\]In this equation, Ag₂CrO₄ is not water-soluble (precipitate) and KNO₃ remains in solution.

Step 3: Write the Net Ionic Equation for the Reaction with Potassium Chromate

The net ionic equation focuses on the formation of silver chromate, excluding the spectator ions:\[2\text{Ag}^+ (aq) + \text{CrO}_4^{2-} (aq) \rightarrow \text{Ag}_2\text{CrO}_4 (s)\]This shows only the ions forming the red precipitate, removing the potassium and nitrate ions which do not participate in the reaction.

Step 4: Calculate the Amount of Chloride Ions Present

Given that 25.60 mL of 0.001036 M silver nitrate (AgNO₃) was used, we calculate the moles of silver ions:\[moles\text{ of } Ag^+ = 0.0256 \text{ L} \times 0.001036 \text{ M} = 2.65104 \times 10^{-5} \text{ moles}\]Each mole of Ag⁺ reacts with one mole of Cl⁻, so the moles of chloride ions are the same.

Step 5: Calculate Cholride Ion Concentration and Evaluate

Now calculate the concentration of chloride ions in the 50.0 mL (0.0500 L) sample:\[[Cl^-] = \frac{2.65104 \times 10^{-5} \text{ moles}}{0.0500 \text{ L}} = 5.30 \text{ mg/L}\]This concentration is less than the required 8 mg/L (or ppm) for oyster growth.

Key Concepts

Silver Nitrate Titration

Titration is a common technique in chemistry used to determine the concentration of a solute in a solution. In this exercise, silver nitrate is used to titrate a water sample to find the concentration of chloride ions. Silver nitrate acts as a titrant. It reacts in a 1:1 ratio with chloride ions to form silver chloride, which precipitates out as a solid. This type of titration is a "precipitation titration" because it involves the formation of a precipitate (solid) during the reaction. The endpoint of this titration is discovered when an excess of silver nitrate reacts with potassium chromate, forming a noticeable red precipitate of silver chromate. This signals that all chloride ions have reacted and the titration is complete. Understanding this process helps us evaluate the concentration of ions in solutions, which is crucial in biological settings like oyster beds, where ion concentration directly affects growth and survival.

Net Ionic Equation

A net ionic equation illustrates only the chemical species directly participating in a chemical reaction. Other ions in the solution, known as "spectator ions," are not included because they do not change state or composition during the reaction. In the original exercise, when silver nitrate reacts with chloride ions, the net ionic equation is: \(\text{Ag}^+ (aq) + \text{Cl}^- (aq) \rightarrow \text{AgCl} (s)\). This shows silver ions combining with chloride ions to form a solid silver chloride precipitate. Net ionic equations are useful because they simplify chemical reactions, clarifying which ions are actually interacting during the process. They are particularly important in titrations and other reactions in solution by highlighting the actual chemical change, helping students and chemists understand the core interaction without distractions from unchanging ions.

Oyster Growth

Oysters require a specific concentration of chloride ions in their environment to thrive. Chloride ions are essential because they aid in osmoregulation, the process by which organisms maintain fluid balance and substance concentration across their cellular membranes. In the context of the exercise, analyzing the chloride ion concentration is crucial for assessing whether the water can support oyster growth. The calculated chloride concentration of 5.30 mg/L is below the threshold of 8 mg/L needed by oysters. This suggests a deficiency that could impact their ability to grow efficiently. Monitoring these levels is important for managing oyster beds sustainably. In real-world applications, ensuring the correct ionic concentration in oyster habitats supports the health of both the organisms and the ecosystems they inhabit.