The solubility of the salt M_xA_y is 1.0 *10^-² mol/L at 25°C. The osmotic pressure exhibited by a solution saturated with M_xA_y at 25°C is 1.22 atm. Determine the values of x and y by assuming ideal behavior. A) x = 1, y =3 B) x = 2, y = 5 C) x = 1, y = 1 D) x = 2, y = 3 E) none of these

Question

Quizplus · Accepted Answer

The van't Hoff factor, i, is equal to the number of particles in solution after dissociation divided by the number of formula units initially dissolved. For the given salt, the dissociation equation is:
MS1U1B1xS1U1B0AS1U1B1yS1U1B0 ⇌ x S1U1B1- + y S1U1B1+ + S1U1B0A-
The number of particles in solution after dissociation is x + y + 1. The osmotic pressure, π, is related to the molar concentration, c, and the van't Hoff factor by the equation:
π = iMRT
where M is the molar concentration in units of mol/L, R is the gas constant, and T is the temperature in units of Kelvin. Rearranging this equation to solve for i, we get:
i = π / MRT
Substituting the given values, we get:
i = (1.22 atm) / (1.0 mol/L)(0.0821 L atm/K mol)(298 K) = 4.95
The van't Hoff factor must be a whole number, so the possible values for x and y are those that make i closest to a whole number. The closest integer to 4.95 is 5, which corresponds to x = 2 and y = 3. Therefore, the answer is choice D.

The Solubility of the Salt MxAy Is 1

The Solubility of the Salt M_xA_y Is 1