Determine the amount of CaCl2 (i = 2.47) dissolved in 2.5 litre of water such that its osmotic pressure is 0.75 atm at 27° C.

To find the amount of calcium chloride (CaCl2) needed to achieve a specific osmotic pressure in a solution, we can use the formula for osmotic pressure, which is given by the equation:

Osmotic Pressure Formula

The osmotic pressure (π) can be calculated using the formula:

π = iCRT

• π = osmotic pressure (in atm)
• i = van 't Hoff factor (which accounts for the number of particles the solute dissociates into)
• C = molarity of the solution (in moles per liter)
• R = ideal gas constant (0.0821 L·atm/(K·mol))
• T = temperature in Kelvin (K)

Step-by-Step Calculation

Given the values:

• π = 0.75 atm
• i = 2.47 (for CaCl2)
• T = 27°C = 27 + 273.15 = 300.15 K

We can rearrange the formula to solve for C (molarity):

C = π / (iRT)

Plugging in the Values

Now, substituting the known values into the equation:

C = 0.75 atm / (2.47 * 0.0821 L·atm/(K·mol) * 300.15 K)

Calculating the denominator:

• 2.47 * 0.0821 * 300.15 ≈ 60.83

Now, calculate C:

C = 0.75 / 60.83 ≈ 0.0123 moles/L

Finding the Total Moles Required

Since we need to find the total moles of CaCl2 for 2.5 liters of solution, we can use the molarity:

moles = C * volume

Substituting the values:

moles = 0.0123 moles/L * 2.5 L ≈ 0.03075 moles

Calculating the Mass of CaCl2

To find the mass of CaCl2 needed, we need its molar mass. The molar mass of CaCl2 is approximately:

• Calcium (Ca) = 40.08 g/mol
• Chlorine (Cl) = 35.45 g/mol × 2 = 70.90 g/mol

Thus, the total molar mass of CaCl2 is:

40.08 g/mol + 70.90 g/mol = 110.98 g/mol

Now, we can calculate the mass required:

mass = moles * molar mass

mass = 0.03075 moles * 110.98 g/mol ≈ 3.41 g

Final Result

To achieve an osmotic pressure of 0.75 atm at 27°C in 2.5 liters of water, you would need to dissolve approximately 3.41 grams of CaCl2.