A saturated solution of an ionic salt MX exhibits an osmotic pressure of 74.4 mm Hg at 25 °C. Assuming that MX is completely dissociated in solution, what is the value of its Ksp?

검증된 단계별 안내

Step 1: Convert the osmotic pressure from mm Hg to atm. You can use the conversion factor 1 atm = 760 mm Hg.

Step 2: Use the formula for osmotic pressure, which is Π = n/V * R * T, where Π is the osmotic pressure, n is the number of moles of solute, V is the volume of the solution in liters, R is the ideal gas constant (0.0821 L*atm/K*mol), and T is the temperature in Kelvin. Solve this equation for n/V, which gives the molarity of the solution.

Step 3: Since the salt MX is completely dissociated in solution, the molarity of MX is equal to the molarity of M+ and X-. Therefore, the molarity of MX is equal to the square root of the product of the molarities of M+ and X-.

Step 4: The solubility product constant, Ksp, is the product of the molarities of the ions raised to their stoichiometric coefficients. In this case, Ksp = [M+][X-]. Since [M+] = [X-], you can simplify this to Ksp = [MX]^2.

Step 5: Substitute the molarity of MX from step 3 into the equation from step 4 to find the value of Ksp.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Osmotic Pressure

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

Dissociation of Ionic Compounds

Ionic compounds, such as MX, dissociate into their constituent ions when dissolved in water. For a salt MX, which dissociates into M⁺ and X⁻ ions, the van 't Hoff factor (i) is equal to the number of ions produced, which in this case is 2. This dissociation is crucial for calculating the concentration of ions in the solution, which directly affects the osmotic pressure.

Solubility Product Constant (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 dissolution equation. For MX, Ksp can be calculated using the concentrations of M⁺ and X⁻ ions at saturation, which can be derived from the osmotic pressure and the dissociation of the salt.