The osmotic pressure of a saturated solution of strontium sulfate at 25 C is 21 torr. What is the solubility product of this salt at 25 C?

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Identify the formula for osmotic pressure: \( \Pi = iCRT \), where \( \Pi \) is the osmotic pressure, \( i \) is the van't Hoff factor, \( C \) is the molarity of the solution, \( R \) is the gas constant (0.0821 L atm/mol K), and \( T \) is the temperature in Kelvin.

Convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature. For 25 C, the temperature in Kelvin is 298.15 K.

Convert the osmotic pressure from torr to atm for use in the formula. (1 atm = 760 torr).

Calculate the molarity of the solution (\( C \)) using the osmotic pressure formula rearranged: \( C = \frac{\Pi}{iRT} \). For strontium sulfate (\( SrSO_4 \)), which dissociates into \( Sr^{2+} \) and \( SO_4^{2-} \), the van't Hoff factor (\( i \)) is 2.

Use the calculated molarity to find the solubility product (\( K_{sp} \)) of strontium sulfate. The solubility product is given by \( K_{sp} = [Sr^{2+}][SO_4^{2-}] \), where the concentrations are the solubility of \( SrSO_4 \) in moles per liter.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Osmotic Pressure

Osmotic pressure is the pressure required to prevent the flow of solvent into a solution through a semipermeable membrane. It is directly related to the concentration of solute particles in the solution. The formula for osmotic pressure (π) is π = iCRT, where 'i' is the van 't Hoff factor, 'C' is the molarity of the solution, 'R' is the ideal gas constant, and 'T' is the temperature in Kelvin.

Solubility Product (Ksp)

The solubility product constant (Ksp) is an equilibrium constant that applies to the solubility of sparingly soluble ionic compounds. It is defined as the product of the molar concentrations of the ions, each raised to the power of their coefficients in the balanced equation. For strontium sulfate (SrSO4), Ksp = [Sr^2+][SO4^2-], where the concentrations are derived from the solubility of the salt.

Dissociation of Ionic Compounds

When ionic compounds dissolve in water, they dissociate into their constituent ions. For strontium sulfate, it dissociates into one strontium ion (Sr^2+) and one sulfate ion (SO4^2-). Understanding this dissociation is crucial for calculating the Ksp, as the concentrations of the ions in solution directly influence the solubility product.

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