Question

The solubility of \(\mathrm{MnSO}_{4} \cdot \mathrm{H}_{2} \mathrm{O}\) in water at \(20^{\circ} \mathrm{C}\) is \(70 \mathrm{~g}\) per \(100 \mathrm{~mL}\) of water. (a) \(\mathrm{ls}\) a \(1.22 \mathrm{M}\) solution of \(\mathrm{MnSO}_{4} \cdot \mathrm{H}_{2} \mathrm{O}\) in water at \(20^{\circ} \mathrm{C}\) saturated, supersaturated, or unsaturated? (b) Given a solution of \(\mathrm{MnSO}_{4} \cdot \mathrm{H}_{2} \mathrm{O}\) of unknown concentration, what experiment could you perform to determine whether the new solution is saturated, supersaturated, or unsaturated?

Short answer

(a) The saturation concentration of MnSO4·H2O at 20°C is found to be 4.57 M. Since the given concentration of the solution is 1.22 M, which is less than the saturation concentration (1.22 M < 4.57 M), the solution is unsaturated. (b) To determine whether the unknown solution is saturated, supersaturated, or unsaturated, gradually add more MnSO4·H2O to the solution while stirring and observe. When no more solute dissolves, mark the added solute amount as the saturation point. Then, add a seed crystal. If the seed crystal dissolves, the original solution was unsaturated. If it remains unchanged, the original solution was saturated. If the seed crystal causes more solute to rapidly come out of the solution, the original solution was supersaturated.

Step-by-step solution

Part (a)

Step 1: Calculate the molarity of solubility. Given the solubility as 70 g/100 mL, we can convert that into molarity. First, calculate the molar mass of MnSO4·H2O: Mn: 54.93 g/mol S: 32.06 g/mol O4: 4 × 16.00 g/mol = 64.00 g/mol H2: 2 × 1.01 g/mol = 2.02 g/mol Total molar mass: 54.93+32.06+64.00+2.02 = 153.01 g/mol Then, determine the amount of MnSO4·H2O in moles: Amount (mol) = (70 g) / (153.01 g/mol) = 0.457 moles Then, calculate molarity: Molarity = 0.457 moles / 0.100 L = 4.57 M Step 2: Determine if the given concentration is saturated, supersaturated, or unsaturated. Now compare the calculated molarity of solubility (4.57 M) to the given concentration (1.22 M). Since 1.22 M < 4.57 M, the solution is unsaturated.

Part (b)

Step 1: Add more solute to the unknown solution. Gradually add more MnSO4·H2O to the unknown solution while stirring. Observe the solution after each addition. Step 2: Determine the saturation point. Eventually, no more solute may dissolve in the solution, even with stirring. This point indicates that the solution has reached saturation. Mark down the amount of added solute. Step 3: Add a seed crystal. After reaching saturation, add a seed crystal (a small crystal of MnSO4·H2O) to the solution in a controlled environment (20°C). Observe the solution. Step 4: Analyze the observations. If the seed crystal dissolves, the original solution was unsaturated. If the seed crystal remains unchanged, the original solution was saturated. If the addition of the seed crystal causes more solute to rapidly come out of the solution, the original solution was supersaturated.

Key concepts

Molarity Calculation

Understanding the molarity of a solution is a fundamental aspect of chemistry that allows us to describe the concentration of a solute in a solution. To put it simply, molarity (M) is the number of moles of the solute per liter of solution. To calculate molarity, one should use the formula:
\[ M = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \]
In our exercise concerning manganese(II) sulfate monohydrate (\(\mathrm{MnSO}_{4} \cdot \mathrm{H}_{2} \mathrm{O}\)), the molarity was found by first determining the molar mass of the compound. Due to the molar mass being a combination of the atomic weights of all atoms in the molecule, a precise calculation is critical. The molarity is then achieved by dividing the moles of the solute, which is derived from the known solubility, by the volume of the solution, remembering to convert all units appropriately to maintain consistency.

Saturated Solution

When discussing solutions, 'saturated' is a term used to describe a point where no additional solute can be dissolved in the solvent at a given temperature and pressure. At this stage, the solution is in equilibrium with the undissolved solute.
To determine if a solution is saturated, as in the exercise, we compare the solution's molarity to the molarity of solubility. If the solution's molarity is less than the solubility molarity, it indicates that the solution can still dissolve more solute and therefore, it is unsaturated. A saturated solution responds to additional solute by either not dissolving it or forming a precipitate.

Supersaturated Solution

Supersaturated solutions are fascinating phenomena in chemistry. They occur when a solution contains more dissolved solute than it would under normal circumstances. It is essentially a 'forced' state, achieved by dissolving solute at an elevated temperature and then gently cooling down. These solutions are unstable and upon seeding, or sometimes even spontaneously, the excess solute precipitates out, rapidly forming crystals.
In practice, to determine whether a solution is supersaturated, one can introduce a 'seed crystal'. If the introduction of this seed causes a sudden precipitation, it confirms that the solution was indeed supersaturated. It had more solute dissolved than the saturation point at the current temperature.

Precipitation

Precipitation in chemistry refers to the process by which solutes come out of solution, typically forming a solid. This can occur naturally over time or be induced by changes in the conditions of the solution such as temperature, pressure, or by adding other substances.
In the context of our exercise, precipitation would be significant in determining whether a new unknown concentration of manganese(II) sulfate monohydrate is saturated or supersaturated. If after the saturation point is reached, additional solute forms a precipitate or if seeding induces crystallization, precipitation confirms that the saturation limit has been surpassed. The process of precipitation is also crucial in many industrial and biological applications for purification and synthesis of materials.