Data suggest that zinc lozenges may significantly shorten the duration of a cold. If the solubility of zinc acetate, Zn(CH3COO)2, is 43.0 g/L, what is the solubility product (Ksp) of this compound?

To find the solubility product (Ksp) of zinc acetate, \( Zn(CH_3COO)_2 \), we first need to understand the dissolution reaction and then use the solubility information to calculate the Ksp.

The dissolution reaction for zinc acetate in water is as follows:

\[ Zn(CH_3COO)_2 (s) \rightleftharpoons Zn^{2+} (aq) + 2CH_3COO^- (aq) \]

For every mole of zinc acetate that dissolves, one mole of zinc ions (\( Zn^{2+} \)) and two moles of acetate ions (\( CH_3COO^- \)) are formed.

The expression for the solubility product constant (Ksp) for zinc acetate is:

\[ Ksp = [Zn^{2+}][CH_3COO^-]^2 \]

Given that the solubility of zinc acetate is 43.0 g/L, we will convert this to moles per liter (molarity), using the molar mass of zinc acetate.

The molar mass of zinc acetate \( Zn(CH_3COO)_2 \) is the sum of the molar masses of zinc (65.38 g/mol) and twice that of acetate (2 * 59.04 g/mol for the two acetate groups):

\[ Molar \, mass \, of \, Zn(CH_3COO)_2 = 65.38 \, g/mol + 2 \times 59.04 \, g/mol = 183.46 \, g/mol \]

Now, we use this molar mass to convert the solubility from g/L to mol/L (molarity):

\[ Solubility \, in \, mol/L = \frac{43.0 \, g/L}{183.46 \, g/mol} = 0.234 \, mol/L \]

This molarity represents the concentration of \( Zn^{2+} \) ions in a saturated solution. Since the dissolution reaction produces twice as many acetate ions, their concentration will be twice that of \( Zn^{2+} \):

\[ [CH_3COO^-] = 2 \times 0.234 \, mol/L = 0.468 \, mol/L \]

Now we can calculate Ksp:

\[ Ksp = [Zn^{2+}][CH_3COO^-]^2 = (0.234 \, mol/L)(0.468 \, mol/L)^2 \] \[ Ksp = (0.234 \, mol/L)(0.219 \, mol/L)^2 \] \[ Ksp = 0.234 \, mol/L \times 0.219 \, mol/L \times 0.219 \, mol/L \] \[ Ksp = 0.234 \, mol/L \times 0.048 \, (mol/L)^2 \] \[ Ksp = 0.0112 \, (mol/L)^3 \]

Note: Significant figures should be considered in calculations, but since the question does not specify, standard practice is to use the least number of significant figures in the given information. However, because the final Ksp value's significant figures have not been specified, I have provided the unrounded calculation for the Ksp.