Problem 63 - Chemistry: The Central Science

Question

(a) Will \(\mathrm{Ca}(\mathrm{OH})_{2}\) precipitate from solution if the \(\mathrm{pH}\) of a \(0.050 \mathrm{M}\) solution of \(\mathrm{CaCl}_{2}\) is adjusted to \(8.0 ?\) (b) Will \(\mathrm{Ag}_{2} \mathrm{SO}_{4}\) precipitate when \(100 \mathrm{~mL}\) of \(0.050 \mathrm{M} \mathrm{AgNO}_{3}\) is mixed with \(10 \mathrm{~mL}\) of \(5.0 \times 10^{-2} \mathrm{M} \mathrm{Na}_{2} \mathrm{SO}_{4}\) solution?

Step-by-Step Solution

Answer

(a) After calculating the hydroxide ion concentration [OH⁻] = 1.0 × 10^(-6) M, the ion product (IP) is found to be 5.0 × 10^(-14), which is less than the Ksp of Ca(OH)₂ (6.5 × 10^(-6)). Therefore, Ca(OH)₂ will not precipitate. (b) The initial concentrations of Ag⁺ and SO₄²⁻ ions are 0.0455 M and 4.55 × 10^(-3) M, respectively. The reaction quotient (Q) is 9.40 × 10^(-4). Since Q > Ksp for Ag₂SO₄ (1.20 × 10^(-5)), Ag₂SO₄ will precipitate.

Step 1: Calculate the hydroxide ion concentration for part (a)

We are given the pH of the solution, which is 8.0. We need to find the hydroxide ion concentration, [OH⁻], from this pH value. We can use the following formula: pOH = 14 - pH Once we have the pOH, we can calculate [OH⁻] using: [OH⁻] = 10^(-pOH)

Step 2: Calculate the ion product for part (a)

Now that we have [OH⁻], we can calculate the ion product (IP) for Ca(OH)₂ precipitation in the solution. The IP is calculated as follows: IP = [Ca²⁺][OH⁻]² We are given the concentration of Ca²⁺ ions as 0.050 M.

Step 3: Compare the IP with the Ksp value for part (a)

The solubility product constant, Ksp, for Ca(OH)₂ is 6.5 × 10^(-6). If the IP is higher than the Ksp, then Ca(OH)₂ will precipitate. Otherwise, it will remain in solution.

Step 4: Calculate the initial concentrations for part (b)

We are given the volumes and concentrations of AgNO₃ and Na₂SO₄ solutions. We need to calculate the initial concentrations of Ag⁺ and SO₄²⁻ ions after mixing the solutions. We can use the formula: Initial concentration = (volume × concentration) / total volume

Step 5: Calculate the reaction quotient (Q) for part (b)

Now that we have the initial concentrations of Ag⁺ and SO₄²⁻ ions, we can calculate the Q value, which is the ratio of products and reactants concentrations. For this case, the reaction is: Ag⁺ + SO₄²⁻ → Ag₂SO₄ The Q value can be calculated as follows: Q = [Ag⁺]²[SO₄²⁻]

Step 6: Compare the Q value with the Ksp value for part (b)

The solubility product constant, Ksp, for Ag₂SO₄ is 1.20 × 10^(-5). If the Q value is higher than the Ksp, then Ag₂SO₄ will precipitate. Otherwise, it will remain in solution.

Key Concepts

Precipitation Reactions

Precipitation reactions occur when two ionic substances in an aqueous solution combine to form an insoluble product, known as a precipitate. This happens because some combinations of ions form compounds that do not dissolve in water. The reaction usually involves mixing two soluble ionic compounds.
For example, when you mix calcium chloride (\(\mathrm{CaCl}_2\)) and sodium hydroxide (\(\mathrm{NaOH}\)) in water, calcium hydroxide (\(\mathrm{Ca(OH)_2}\)) can form as a precipitate under the right conditions.
Key points to remember:

• The formation of a precipitate depends on the solubility of the resulting compound.
• Solubility rules and the solubility product constant (Ksp) help predict if a precipitate will form.
• If the ion product exceeds the Ksp, precipitation occurs.

Ion Product

The ion product (\(IP\)) of a solution is a crucial concept in understanding solubility equilibrium. It helps determine whether a precipitate will form when two solutions are mixed. The ion product is similar to the reaction quotient (\(Q\)) but specifically refers to the concentrations of the ions in a solution.
In our example, for calcium hydroxide (\(\mathrm{Ca(OH)_2}\)), the formula for the ion product is:\[ IP = [\mathrm{Ca}^{2+}][\mathrm{OH}^-]^2 \]Here, \([\text{Ca}^{2+}]\) and \([\text{OH}^-]\) are the concentrations of calcium and hydroxide ions, respectively.
To decide whether calcium hydroxide will precipitate, compare the \(IP\) to the \(Ksp\) (solubility product constant). If \(IP > Ksp\), a precipitate forms.
Remember:

• The ion product depends on the concentrations of all ionic species in the mixture.
• A solution is supersaturated if the \(IP\) exceeds the \(Ksp\).
• Always calculate \(IP\) based on the current, not initial, concentrations after any reaction or dilution.

Reaction Quotient

In chemistry, the reaction quotient (\(Q\)) helps predict the direction of a chemical reaction. It’s a measure of the concentrations of reactants and products at any point in time, unlike the equilibrium constant which only applies at equilibrium. Reaction quotients are used in scenarios like precipitation reactions to ascertain whether a reaction has reached equilibrium or which direction it will proceed.
When dealing with precipitation reactions like the one involving silver sulfate (\(\mathrm{Ag_2SO_4}\)), the \(Q\) is calculated as follows:\[ Q = [\mathrm{Ag}^+]^2[\mathrm{SO_4}^{2-}] \]This helps determine if the solution is at equilibrium or if precipitation will occur.
Points to note:

• If \(Q < Ksp\), the solution is unsaturated, and more solute can dissolve.
• If \(Q = Ksp\), the solution is at equilibrium.
• If \(Q > Ksp\), the solution is supersaturated, and the compound will likely precipitate.

Understanding \(Q\) is essential for predicting whether an adjustment in conditions, such as mixing certain volumes of solutions, will result in the formation of a precipitate.