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Question: 3.4 g of CaCl₂ is dissolved in 2.5 L of water at 300 K. What is the osmotic pressure of the solution...

3.4 g of CaCl₂ is dissolved in 2.5 L of water at 300 K. What is the osmotic pressure of the solution? van't Hoff factor for CaCl₂ is 2.47.

Answer

0.746 atm

Explanation

Solution

To solve the problem, we use the van't Hoff equation for osmotic pressure: π=iMRT\pi = iMRT where: π\pi is the osmotic pressure ii is the van't Hoff factor MM is the molarity of the solution RR is the ideal gas constant TT is the temperature in Kelvin

Given values: Mass of CaCl₂ = 3.4 g Volume of water = 2.5 L (Assume Volume of solution ≈\approx Volume of water) Temperature, T = 300 K van't Hoff factor, i = 2.47 Molar mass of CaCl₂ = 111 g/mol (Molar mass of Ca ≈\approx 40.08 g/mol, Cl ≈\approx 35.45 g/mol; 40.08+2×35.45=110.9840.08 + 2 \times 35.45 = 110.98 g/mol. Using 111 g/mol as in the similar problem) Ideal gas constant, R = 0.0821 L atm K⁻¹ mol⁻¹

Step 1: Calculate the number of moles of CaCl₂. Number of moles (n)=MassMolar mass=3.4 g111 g/mol\text{Number of moles (n)} = \frac{\text{Mass}}{\text{Molar mass}} = \frac{3.4 \text{ g}}{111 \text{ g/mol}} n≈0.03063 moln \approx 0.03063 \text{ mol}

Step 2: Calculate the molarity of the solution. Molarity (M)=Number of molesVolume of solution (in L)=0.03063 mol2.5 L\text{Molarity (M)} = \frac{\text{Number of moles}}{\text{Volume of solution (in L)}} = \frac{0.03063 \text{ mol}}{2.5 \text{ L}} M≈0.01225 mol/LM \approx 0.01225 \text{ mol/L}

Step 3: Calculate the osmotic pressure using the van't Hoff equation. π=iMRT\pi = iMRT π=2.47×0.01225 mol/L×0.0821 L atm K⁻¹ mol⁻¹×300 K\pi = 2.47 \times 0.01225 \text{ mol/L} \times 0.0821 \text{ L atm K⁻¹ mol⁻¹} \times 300 \text{ K} π≈2.47×0.01225×24.63\pi \approx 2.47 \times 0.01225 \times 24.63 π≈2.47×0.3019875\pi \approx 2.47 \times 0.3019875 π≈0.7459 atm\pi \approx 0.7459 \text{ atm}

Rounding to three significant figures, the osmotic pressure is 0.746 atm.

Explanation of the solution:

  1. Calculate the number of moles of CaCl₂ by dividing the given mass by its molar mass (111 g/mol).
  2. Calculate the molarity of the solution by dividing the number of moles by the volume of water (assumed to be the volume of the solution) in liters.
  3. Use the van't Hoff equation, π=iMRT\pi = iMRT, substituting the calculated molarity (M), given van't Hoff factor (i), ideal gas constant (R = 0.0821 L atm K⁻¹ mol⁻¹), and temperature (T = 300 K) to find the osmotic pressure (π\pi).

Answer: The osmotic pressure of the solution is approximately 0.746 atm.