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 \(\mathrm{AgC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}, K_{\mathrm{sp}}=2.3 \times 10^{-3}\)

Short answer

To determine whether a precipitate will form, calculate the Qsp and compare it to the Ksp value. If Qsp exceeds Ksp, a precipitate will form.

Step-by-step solution

- Calculate the final concentrations

First, find the number of moles of both reactants pre-mixing. For AgNO3, use the volume and concentration to calculate moles: moles = 0.022 L * 0.100 mol/L. Then do the same for NaC2H3O2: moles = 0.045 L * 0.0260 mol/L. After that, calculate the combined volume of the two solutions, 0.022 L + 0.045 L. Next, find the final concentration of each by dividing the moles of each reactant by the total combined volume.

- Write the reaction and expression for the solubility product

Write down the dissociation reaction for silver acetate. AgC2H3O2 (s) ⇌ Ag+ (aq) + C2H3O2- (aq). Write the expression for the solubility product (Ksp) of silver acetate: Ksp = [Ag+] [C2H3O2-].

- Calculate the ionic product and compare it with Ksp

Now calculate the product of the final concentrations of Ag+ and C2H3O2- ions. This is the ionic product (Qsp). Qsp = [Ag+]final * [C2H3O2-]final. If Qsp > Ksp, the solution is supersaturated, and a precipitate will form. If Qsp = Ksp, the solution is at equilibrium, and if Qsp < Ksp, the solution is unsaturated, and no precipitate will form.

- Conclusion

Compare the calculated ionic product Qsp to the given Ksp. If the calculated Qsp is larger than 2.3 x 10^-3, then a precipitate of silver acetate will form. Otherwise, no precipitate will form.

Key concepts

Precipitation Reaction

A precipitation reaction occurs when two soluble ionic compounds in solution are mixed together to form an insoluble compound, known as the precipitate. This process is a physical change where the ionic compounds exchange ions to form new compounds. In the given exercise, we have a potential reaction between silver nitrate (AgNO3) and sodium acetate (NaC2H3O2) which might lead to the formation of silver acetate (AgC2H3O2), an insoluble compound.

The reaction can be represented as:

• AgNO3 (aq) + NaC2H3O2 (aq) → AgC2H3O2 (s) + NaNO3 (aq)

Here, AgC2H3O2 (s) is the precipitate. Whether it will form or not depends on the concentrations of Ag+ and C2H3O2- ions in the final mixture and the solubility product constant, Ksp, of silver acetate.

Ionic Product

The ionic product (Qsp) of a solute is the product of the molar concentrations of the ions produced when the solute dissolves in solution, raised to the power of their stoichiometric coefficients. This concept is used to predict the formation of a precipitate. In the exercise given, to determine if a precipitate will form, we compare the ionic product of silver acetate with its Ksp. To calculate the ionic product, we use the final concentrations of the ions:

• Qsp = [Ag+]final * [C2H3O2-]final

If the Qsp exceeds the Ksp, the concentrations are too high to remain in solution, causing excess ions to combine and form a precipitate. Essentially, Qsp helps us decide the fate of the reactants in a chemical mixture and can predict the formation of a precipitate before the mixture is even created.

Chemical Equilibrium

Chemical equilibrium is a state in a chemical reaction where the rates of the forward and reverse reactions are equal, so the concentrations of reactants and products remain constant over time. At equilibrium, there is no net change in the concentration of the components of the reaction. The solubility product constant (Ksp) is specific to the equilibrium state of a solid dissolving into its ions in a solution.

When we discuss the Ksp in the context of our exercise given, it represents the maximum product of the ionic concentrations of AgC2H3O2 in a saturated solution, where the forward dissolving reaction and reverse precipitation reaction occur at the same rate. A comparison between the actual ionic product (Qsp) and Ksp enables us to understand if the system is at equilibrium (Qsp = Ksp), if a precipitate will form because the system is supersaturated (Qsp > Ksp), or if the system is unsaturated (Qsp < Ksp) and no precipitate will form.