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Chapter 17: Problem 114

The osmotic pressure of a saturated solution of strontium sulfate at \(25^{\circ} \mathrm{C}\) is 21 torr. What is the solubility product of this salt at \(25^{\circ} \mathrm{C} ?\)

Short Answer

Expert verified
The solubility product constant (Kₛₚ) of strontium sulfate at 25°C is approximately 1.23 × 10⁻⁶.

Step by step solution

01

Write down the expression for osmotic pressure

The osmotic pressure (π) of a solution can be determined using the formula: π = (n/V)RT where n is the amount of solute in moles, V is the volume of the solution in liters, R is the ideal gas constant (0.08206 L atm mol⁻¹ K⁻¹) and T is the temperature in Kelvin.
02

Convert the given osmotic pressure to atm

We are given the osmotic pressure of 21 torr. Since the gas constant R is given in atm, we need to convert the pressure to atm: 1 atm = 760 torr So, 21 torr = (21/760) atm ≈ 0.02763 atm
03

Calculate the molar concentration of the solution

We know π = (n/V)RT. Therefore, n/V (molar concentration) can be calculated as: n/V = π / RT We are given the temperature 25°C, which is 298.15 K in Kelvin. Therefore, n/V can be calculated as: n/V = 0.02763 atm / (0.08206 L atm mol⁻¹ K⁻¹ × 298.15 K) ≈ 0.00111 mol/L
04

Write the solubility product expression for strontium sulfate

Strontium sulfate (SrSO₄) dissociates in water as follows: SrSO₄(s) ⇌ Sr²⁺(aq) + SO₄²⁻(aq) The solubility product constant (Kₛₚ) can be written as: Kₛₚ = [Sr²⁺][SO₄²⁻]
05

Calculate the solubility product constant (Kₛₚ)

Since the saturated solution is at equilibrium, the concentrations of Sr²⁺ and SO₄²⁻ are equal (0.00111 mol/L). Therefore, we can calculate the solubility product constant: Kₛₚ = (0.00111 mol/L)(0.00111 mol/L) ≈ 1.23 × 10⁻⁶ So, the solubility product of strontium sulfate at 25°C is approximately 1.23 × 10⁻⁶.

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Most popular questions from this chapter

A \(1.00-\mathrm{L}\) solution saturated at \(25^{\circ} \mathrm{C}\) with lead(II) iodide contains \(0.54 \mathrm{~g}\) of \(\mathrm{PbI}_{2} .\) Calculate the solubility-product constant for this salt at \(25^{\circ} \mathrm{C}\).

Predict whether the equivalence point of each of the following titrations is below, above, or at \(\mathrm{pH} 7:\) (a) formic acid titrated with \(\mathrm{NaOH},\) (b) calcium hydroxide titrated with perchloric acid, (c) pyridine titrated with nitric acid.

The solubility product for \(\mathrm{Zn}(\mathrm{OH})_{2}\) is \(3.0 \times 10^{-16} .\) The formation constant for the hydroxo complex, \(\mathrm{Zn}(\mathrm{OH})_{4}^{2-},\) is \(4.6 \times 10^{17}\). What concentration of \(\mathrm{OH}^{-}\) is required to dissolve 0.015 mol of \(\mathrm{Zn}(\mathrm{OH})_{2}\) in a liter of solution?

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