How do you determine the solubility of zinc hydroxide?
Determining the solubility of zinc hydroxide (( \text{Zn(OH)}_2 )) involves several steps and considerations, particularly due to its slightly soluble nature in water. Here are the key methods and factors involved:
Experimental Methods
Precipitation and Equilibration
Zinc hydroxide can be precipitated from an aqueous zinc sulfate solution using ammonia (( \text{NH}_3 )) and then washed to remove any sulfate ions. The precipitated zinc hydroxide is then dissolved in a small excess of ammonia to form a solution, which is subsequently transferred to a container and allowed to form crystals, often in the orthorhombic form1.
Solubility Determinations
To determine the solubility, zinc hydroxide is added to test tubes along with either hydrochloric acid (( \text{HCl} )) or sodium hydroxide (( \text{NaOH} )) to adjust the pH. The test tubes are sealed and shaken gently in constant temperature baths. Samples of the solution in contact with solid zinc hydroxide are periodically removed for analysis, typically using atomic absorption spectrophotometry. The concentration of zinc in these solutions is measured until it reaches a constant value, usually after about 10 days, indicating equilibrium1.
Calculations Using Equilibrium Constants
Solubility Product (( K_{sp} ))
The solubility product constant (( K_{sp} )) for zinc hydroxide can be calculated from the concentrations of ( \text{Zn}^{2+} ) and ( \text{OH}^- ) ions in the saturated solution. The general equation for the dissolution of zinc hydroxide is: [ \text{Zn(OH)}2(s) \rightleftharpoons \text{Zn}^{2+}(aq) + 2\text{OH}^-(aq) ] [ K{sp} = [\text{Zn}^{2+}][\text{OH}^-]^2 ]
Stepwise Equilibrium Constants
In addition to ( K_{sp} ), stepwise equilibrium constants for the association of ( \text{Zn}^{2+} ) with ( \text{OH}^- ) ions can be evaluated. These constants account for the formation of various hydroxy complexes of zinc, such as ( \text{Zn(OH)}^+ ), ( \text{Zn(OH)}_2(aq) ), ( \text{Zn(OH)}_3^- ), and ( \text{Zn(OH)}_4^{2-} )13.
pH Dependence
The solubility of zinc hydroxide is highly dependent on the pH of the solution. At different pH values, the concentration of ( \text{OH}^- ) ions changes, which in turn affects the solubility. For example, at higher pH values, the solubility increases due to the formation of hydroxy complexes3.
Example Calculations
For a given pH, the solubility can be calculated using the equilibrium constants and the concentration of ( \text{OH}^- ) ions. For instance, at pH 5, 9, and 13, the solubility can be calculated using the stepwise equilibrium constants and the concentration of hydroxide ions at each pH3.
Here is a simplified example for pH 9: [ \text{Solubility} = K_1 + \frac{K_1 \cdot K_2}{[\text{OH}^-]} + \frac{K_1 \cdot K_2 \cdot K_3}{[\text{OH}^-]^2} + \frac{K_1 \cdot K_4}{[\text{OH}^-]^3} + \frac{K_1 \cdot K_4 \cdot K_5}{[\text{OH}^-]^4} ] Where ( K_1, K_2, K_3, K_4, ) and ( K_5 ) are the stepwise equilibrium constants, and ( [\text{OH}^-] ) is the concentration of hydroxide ions at the given pH3.
Reported Values
Experimental determinations have reported various solubility values for zinc hydroxide, typically in the range of ( 10^{-5} ) to ( 10^{-6} ) mol dm(^{-3}) at different temperatures and pH conditions4. For example, at 25°C, the solubility has been reported as approximately ( 1.92 \times 10^{-5} ) mol dm(^{-3})4.