Question

A student is asked to prepare a \(0.030 \mathrm{M}\) aqueous solution of \(\mathrm{PbCl}_{2}\) (a) Is this possible at \(25^{\circ} \mathrm{C} ?\) (Hint: Is dissolving \(0.030 \mathrm{~mol}\) of \(\mathrm{PbCl}_{2}\) at \(25^{\circ} \mathrm{C}\) possible? \()\) (b) If the student used water at \(100^{\circ} \mathrm{C}\), would this be possible?

Short answer

Explain your answer with the help of the solubility product constant (Ksp) and comparing the solubility with the required molarity at each temperature.

Step-by-step solution

Calculate the Solubility of PbCl2 at 25℃

First, we will calculate the solubility of PbCl2 at 25℃ using the solubility product constant (Ksp) formula. The solubility equation for PbCl2 is given by: PbCl2 -> Pb^2+ + 2Cl^- Then the solubility product constant (Ksp) formula is given by: Ksp = [Pb^2+][Cl^-]^2 Since the solubility of PbCl2 in moles/liter is 's', the concentration of Pb^2+ is 's' and Cl^- is '2s'. So, the Ksp formula becomes: Ksp = s * (2s)^2 = 4s^3 Given that Ksp = 1.7 x 10^-5 at 25℃, we can solve this for 's' to get solubility.

Compare the Solubility to the Required Molarity at 25℃

After you've got the solubility 's' from Step 1, you need to compare this to the required molarity, which is 0.030M. If the solubility is greater than or equal to the required molarity, then yes, it is possible to prepare a 0.030 M PbCl2 solution at 25℃.

Calculate the Solubility of PbCl2 at 100℃

Next, we repeat the same process for 100℃ using the given Ksp for this temperature, which is 1.3 x 10^-2. This will give us the solubility 's' at 100℃.

Compare the Solubility to the Required Molarity at 100℃

Finally, compare the solubility 's' you calculated at 100℃ to the required molarity, 0.030M. Again, if the solubility is greater than or equal to the required molarity, then yes, it is possible to prepare a 0.030 M PbCl2 solution at 100℃. In both cases, if the solubility is less than the required molarity it means it's not possible to prepare the PbCl2 solution at the given temperature.

Key concepts

PbCl2 Solubility

When working with chemical solutions, understanding the solubility of a compound is crucial. Lead(II) chloride, PbCl2, is an interesting compound because it has a low solubility in water at room temperature. This means that only a small amount of PbCl2 can dissolve in a given volume of water before the solution becomes saturated.

Solubility is often expressed in terms of moles per liter (M), and it varies with temperature. For PbCl2 at 25℃, the solubility product constant, Ksp, provides essential information about its solubility. The exercise asks if a 0.030M solution of PbCl2 is possible at 25℃, which directly involves understanding how much of it can dissolve at that temperature before it starts precipitating.

The process of dissolving and the subsequent equilibrium between the solid and its dissolved ions is represented by the Ksp expression. For PbCl2, this equilibrium involves the dissociation into Pb^2+ and Cl^- ions. As temperature increases, typically, the solubility of solids in liquids increases as well. Therefore, the solubility of PbCl2 at 100℃ is higher, enabling a more concentrated solution to be prepared.

Ksp Calculation

The solubility product constant, Ksp, is a fundamental parameter in the study of solubility and precipitation. It helps chemists understand how much of a compound can be dissolved in a solution before reaching saturation. In the case of PbCl2, the Ksp calculation is vital for determining whether a 0.030M solution can be prepared at a certain temperature.

To calculate Ksp, one must consider the stoichiometry of the dissolution reaction. For PbCl2, the dissociation in water forms one Pb^2+ ion and two Cl^- ions for every formula unit of PbCl2 that dissolves. The Ksp expression is thus set up as the product of the concentrations of these ions, raised to the power of their stoichiometric coefficients in the balanced dissolution equation: \[Ksp = [Pb^{2+}][Cl^{-}]^2\].

By solving the Ksp expression for 's', the solubility in moles per liter, we can compare it to the desired molarity to determine feasibility. If 's' is below the desired molarity, the solubility is too low, and not all the PbCl2 will dissolve to prepare the required solution.

Aqueous Solutions Preparation

The preparation of aqueous solutions requires a clear understanding of solubility and concentration. Once the solubility of a compound like PbCl2 is known, one can proceed to prepare a solution of the desired concentration, as long as it is below the solubility limit at the given temperature.

To make a 0.030M aqueous solution, one would typically measure the appropriate amount of PbCl2 and dissolve it in a predetermined volume of water. However, if the solubility is below the target concentration, the solution will become saturated and excess solid will remain undissolved. The role of temperature cannot be overstated; by heating the solvent, such as to 100℃, you can often dissolve a greater amount of the solute. This is precisely why the question of whether the same solution could be prepared at 100℃ is relevant.

When creating the solution, the process includes measuring the solute (PbCl2), adding it to a volume of water (which might be pre-heated if necessary to increase solubility), and then stirring to encourage dissolution. It is essential to allow the solution to come to the desired temperature before making a final volume adjustment to ensure accurate concentration.