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Chapter 13: Problem 79

The osmotic pressure of \(0.010 M\) solutions of \(\mathrm{CaCl}_{2}\) and urea at \(25^{\circ} \mathrm{C}\) are \(0.605 \mathrm{~atm}\) and \(0.245 \mathrm{~atm},\) respectively. Calculate the van't Hoff factor for the \(\mathrm{CaCl}_{2}\) solution.

Short Answer

Expert verified
The van't Hoff factor for the \(CaCl_2\) solution is approximately 3.

Step by step solution

01

Compute The Osmotic Pressure of Urea Solution

Calculate the osmotic pressure for a 0.010 M solution of urea using the formula \(π = iMRT\). Here, \(i\) is the van't Hoff factor and is 1 for urea since it doesn't dissociate, \(M\) is the molarity (0.010 M), \(R\) is the gas constant (0.0821 L atm/K mol), and \(T\) is the temperature in Kelvin (25°C = 298 K). Thus, the osmotic pressure of the urea solution becomes \(π = (1)(0.010 mol/L)(0.0821 L atm/K mol)(298 K) = 0.245 atm\), which matches the given osmotic pressure of the urea solution. This confirms that we have been using the correct formula and values.
02

Calculate The Expected Osmotic Pressure of \(CaCl_2\) Solution

Assuming that \(CaCl_2\) does not dissociate, calculate the expected osmotic pressure using the same formula and values as in Step 1, but with \(i=1\). This gives us \(π = (1)(0.010 mol/L)(0.0821 L atm/K mol)(298 K) = 0.245 atm\).
03

Compare The Expected and Actual Osmotic Pressure

Compare the calculated osmotic pressure of \(CaCl_2\) from Step 2 (0.245 atm) with the given osmotic pressure (0.605 atm). Since the observed osmotic pressure is greater than the calculated one, it means that \(CaCl_2\) does dissociate in solution.
04

Calculate van't Hoff Factor

Now, the van't Hoff factor \(i\) for \(CaCl_2\) can be calculated using the formula \(i = π_{observed} / π_{calculated}\). By substituting the values obtained from Step 3, we have \(i = 0.605 atm / 0.245 atm = 2.47\) which is approximately 3. The discrepancy could be due to experimental error or approximations in the calculation.

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Most popular questions from this chapter

Which of these two aqueous solutions has (a) the higher boiling point, (b) the higher freezing point, and (c) the lower vapor pressure: \(0.35 \mathrm{~m} \mathrm{CaCl}_{2}\) or \(0.90 \mathrm{~m}\) urea? State your reasons.

Give two exceptions to Henry's law.

Calculate the molalities of these aqueous solutions: (a) \(1.22 M\) sugar \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\) solution (density of solution \(=1.12 \mathrm{~g} / \mathrm{mL}\) ), (b) \(0.87 \mathrm{M} \mathrm{NaOH}\) solution (density of solution \(=1.04 \mathrm{~g} / \mathrm{mL}),(\mathrm{c})\) \(5.24 \mathrm{M} \mathrm{NaHCO}_{3}\) solution (density of solution \(=\) \(1.19 \mathrm{~g} / \mathrm{mL})\)

Define Raoult's law. Define each term in the equation representing Raoult's law, and give its units. What is an ideal solution?

How do the solubilities of most ionic compounds in water change with temperature?
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