Final answer:
To calculate the osmotic pressure of a solution, determine the molarity of the solute after taking dissociation into account, and then use the formula Π = MRT. The osmotic pressure of the 0.292 L solution of CaCl2 at 295 K is approximately 1.31 atm.
Step-by-step explanation:
To calculate the osmotic pressure of a 0.292 L solution containing 0.587g of CaCl2 at 295 K, we first need to determine the molar concentration of the solute in the solution and then apply the formula for osmotic pressure. The formula is Π = MRT, where Π is the osmotic pressure, 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 kelvins.
First, we calculate the number of moles of CaCl2 because CaCl2 dissociates into three ions (Ca2+ and 2 Cl−). Using the molar mass of CaCl2 (110.98 g/mol), we find that there are 0.587g / 110.98 g/mol = 0.00529 moles of CaCl2. Next, since the volume of the solution is 0.292 L, the molarity (M) is 0.00529 moles / 0.292 L = 0.0181 M. However, as CaCl2 provides three particles per formula unit, the effective concentration is 3 * 0.0181 M = 0.0543 M.
By substituting these values into the osmotic pressure formula, we get:
Π = (0.0543 M) (0.0821 L·atm/K·mol) (295 K) = 1.31 atm
Therefore, the osmotic pressure of the solution is approximately 1.31 atm.