Problem 68 - Chemistry The Molecular Nature of Matter

Question

Would a precipitate of silver acetate form if \(22.0 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{AgNO}_{3}\) were added to \(45.0 \mathrm{~mL}\) of \(0.0260 \mathrm{M}\) \(\mathrm{NaC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\) ? For \(\mathrm{AgC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}, K_{\mathrm{sp}}=2.3 \times 10^{-3}\)

Step-by-Step Solution

Answer

No precipitate will form if Q < Ksp after calculations.

Step 1: Calculate the initial moles of AgNO3 and NaC2H3O2

To find the initial moles of each reactant, use the concentration (Molarity, M) and volume (in liters, L). For AgNO3: moles of AgNO3 = 0.100 M x 0.022 L. For NaC2H3O2: moles of NaC2H3O2 = 0.0260 M x 0.045 L.

Step 2: Calculate the final total volume of the solution

The final volume is the sum of the volumes of the two solutions mixed: V_total = 22.0 mL + 45.0 mL.

Step 3: Calculate the final concentrations of Ag+ and C2H3O2-

After mixing, use the total volume to calculate the final concentrations of Ag+ and C2H3O2- ions. For Ag+: [Ag+] = moles of AgNO3 / V_total. For C2H3O2-: [C2H3O2-] = moles of NaC2H3O2 / V_total.

Step 4: Calculate the reaction quotient Q

For the reaction Ag+ + C2H3O2- = AgC2H3O2, the reaction quotient Q is Q = [Ag+][C2H3O2-]. Use the concentrations calculated in Step 3 for this.

Step 5: Compare Q to the solubility product constant Ksp

Determine whether a precipitate will form by comparing Q to Ksp. If Q > Ksp, a precipitate will form because the solution is supersaturated. If Q < Ksp, no precipitate forms because the solution is unsaturated.

Key Concepts

Solubility Product Constant (Ksp)

Understanding the solubility product constant (Ksp) is critical when predicting whether a precipitate will form in a chemical solution. Ksp is specific to each ionic compound and represents the product of the concentrations of the ions when the substance is dissolved to the point of saturation. It's important to note that the concentrations are raised to the power of their respective coefficients in the balanced chemical equation.

For example, the Ksp expression for silver acetate (AgC2H3O2) would involve the concentrations of silver ions ([Ag+]) and acetate ions ([C2H3O2-]) as follows: Ksp = [Ag+][C2H3O2-].The Ksp value is constant at a given temperature. If the ionic product of a solution exceeds this constant, the solution is supersaturated, and a precipitate of the ionic compound is likely to form, as the solution can no longer hold the excess of ions in solution.

Reaction Quotient (Q)

The reaction quotient (Q) is the mathematical comparison of the concentrations of products and reactants at any point during a reaction, not just at equilibrium. For a reaction such as Ag+ + C2H3O2- = AgC2H3O2, Q is determined by measuring the concentrations of the ions in solution, similar to the Ksp equation: Q = [Ag+][C2H3O2-].It plays a key role in predicting the direction of the reaction. If Q is less than Ksp, the reaction will proceed to form more products (solid precipitate, in this case). If Q equals Ksp, the system is at equilibrium and no net change occurs. However, if Q is greater than Ksp, the reaction will shift to form more reactants, which means a precipitate will form as the system tries to return to equilibrium. Calculating Q allows us to predict whether the addition of reactants will lead to a precipitate.

Molarity Calculations

Molarity is a measure of concentration used to describe the amount of solute in a given volume of solution. It is typically expressed in moles per liter (mol/L or M). Calculations of molarity are fundamental when determining the reaction quotient and assessing solubility. To calculate the molarity of a solution after a dilution or mixing, as in our original exercise, you need to know the initial moles of solute and the final total volume of the solution. The basic formula for molarity is:

\[M = \frac{\text{moles of solute}}{\text{liters of solution}}\].

In the context of precipitation reactions, understanding molarity can help us assess whether the concentrations of ionic species in a mixed solution exceed the solubility product constant, potentially leading to the formation of a precipitate. This calculation is essential for predicting concentration changes that occur when solutions are combined.