A dilute aqueous solution of CaCl2 contains 0.159 grams of solute per liter of
solution. It is fully dissociated. What is the osmotic pressure of the solution
against a membrane at 20.0 °C?
pi = iMRT
i = 3 for CaCl2
moles = grams/molar mass CaCl2, then M = moles/L
R = 0.08206
T = 20 in kelvin.
To find the osmotic pressure of the solution, we can use the formula:
Π = i * M * R * T
Where:
Π = osmotic pressure
i = van't Hoff factor (indicates the number of particles the solute dissociates into)
M = molar concentration of the solute (in mol/L)
R = ideal gas constant (0.0821 L * atm / (mol * K))
T = temperature in Kelvin (20.0 °C = 293.15 K)
First, we need to find the molar concentration of CaCl2:
Molar mass of CaCl2 = 40.08 g/mol (Ca) + 2 * 35.45 g/mol (Cl) = 110.98 g/mol
Molar concentration (C) = mass / molar mass
C = 0.159 g / 110.98 g/mol = 0.00143 mol/L
The van't Hoff factor (i) for CaCl2 is 3 because it dissociates into three particles (1 Ca2+ ion and 2 Cl- ions).
Plug in the values into the formula:
Π = 3 * 0.00143 mol/L * (0.0821 L * atm / (mol * K)) * 293.15 K
Π = 3 * 0.00143 * 0.0821 * 293.15 atm
Π ≈ 0.328 atm
Therefore, the osmotic pressure of the solution against a membrane at 20.0 °C is approximately 0.328 atm.
To find the osmotic pressure of the solution, we can use the equation:
π = i * M * R * T
Where:
π is the osmotic pressure,
i is the van't Hoff factor,
M is the molarity of the solution,
R is the ideal gas constant (0.0821 L·atm/(K·mol)),
and T is the temperature in Kelvin.
First, we need to determine the van't Hoff factor, i. The CaCl2 is fully dissociated in solution, so it will produce three ions: one Ca2+ ion and two Cl- ions. Therefore, the van't Hoff factor for CaCl2 is 3.
Next, we need to calculate the molarity, M, of the solution. Molarity is defined as moles of solute per liter of solution. Since we are given the mass of solute and given the molar mass of CaCl2, we can calculate the moles of CaCl2.
The molar mass of CaCl2 is:
Ca: 1 * 40.08 g/mol = 40.08 g/mol
Cl: 2 * 35.45 g/mol = 70.90 g/mol
Adding both values gives us a molar mass of 110.98 g/mol for CaCl2.
Now, we can calculate the number of moles of CaCl2:
moles = mass / molar mass
moles = 0.159 g / 110.98 g/mol
Next, we need to convert the moles to molarity. We know that the solution is dilute and the molarity is defined as moles of solute per liter of solution. Since the mass is given in grams per liter, the molarity is the same as the concentration:
Molarity = moles / volume
Molarity = 0.159 g / 1 L
Now, we have determined the value for M, the molarity of the solution.
Finally, we need to convert the temperature to Kelvin. The given temperature is 20.0 °C, and to convert to Kelvin we add 273.15:
T = 20.0 °C + 273.15
Now that we have all the necessary values, we can plug them into the osmotic pressure formula:
π = 3 * M * R * T
Simply substitute the values into the equation, and calculate the osmotic pressure.