Question

At 27 °C, \(x \, g\) of \( \text{CaCl}_2 \) was dissolved in 2.5 L of water. The osmotic pressure of the resultant solution is 0.82 atm. What is \(x\) in grams? (Given \(i = 2.5\), \(R = 0.082 \, \text{L atm mol}^{-1} \text{K}^{-1}\))

• A. \(37\)
• B. \(1.85\)
• C. \(3.7\)
• D. \(18.5\)

Hint:

When given an answer, check your units and calculation methods to ensure they align with expected results, particularly in practical chemistry applications.

Answer 1

The Correct Option is C

Step 1: Use the osmotic pressure formula.

The osmotic pressure equation is: \[ \Pi = i M R T \] where: - \( \Pi = 0.82 \) atm (osmotic pressure), - \( i = 2.5 \) (Van't Hoff factor for CaCl\(_2\)), - \( R = 0.082 \) L atm mol\(^{-1}\)K\(^{-1}\), - \( T = 27^\circ C = 273 + 27 = 300 \) K, - \( V = 2.5 \) L.

Step 2: Calculate the molarity (\( M \)).

Rearranging the equation: \[ M = \frac{\Pi}{i R T} \] Substituting the values: \[ M = \frac{0.82}{2.5 \times 0.082 \times 300} \] \[ M = \frac{0.82}{61.5} = 0.0133 \, \text{mol/L} \]

Step 3: Calculate the moles of CaCl\(_2\).

Since \( M = \frac{{\text{moles of solute}}}{{\text{volume in liters}}} \), we get: \[ \text{Moles of CaCl}_2 = 0.0133 \times 2.5 = 0.03325 \, \text{moles} \]

Step 4: Convert moles to grams.

Molar mass of CaCl\(_2\): \[ 40 + 2(35.5) = 111 \, \text{g/mol} \] Mass of CaCl\(_2\) dissolved: \[ x = 0.03325 \times 111 = 3.69 \approx 3.7 \, \text{g} \]

Thus, \( x \) is 3.7 g.

Answer 2

To solve this problem, we need to determine the mass of calcium chloride (CaCl₂) dissolved in 2.5 L of water using the given osmotic pressure.

1. Understanding the Formula for Osmotic Pressure:
The formula for osmotic pressure is: \[ \Pi = i \cdot \frac{n}{V} \cdot R \cdot T \] where: - \( \Pi \) is the osmotic pressure (0.82 atm), - \( i \) is the van't Hoff factor (given as 2.5), - \( n \) is the number of moles of solute (CaCl₂), - \( V \) is the volume of the solution (2.5 L), - \( R \) is the ideal gas constant (0.082 L atm mol⁻¹ K⁻¹), - \( T \) is the temperature in Kelvin (27°C = 300 K). We can rearrange the formula to solve for \( n \): \[ n = \frac{\Pi \cdot V}{i \cdot R \cdot T} \]

2. Substituting Values:
Now, substitute the given values into the equation: \[ n = \frac{0.82 \cdot 2.5}{2.5 \cdot 0.082 \cdot 300} \] \[ n = \frac{2.05}{61.5} = 0.0334 \, \text{mol} \]

3. Finding the Mass of CaCl₂:
Next, we can use the molar mass of CaCl₂ to find the mass. The molar mass of CaCl₂ is: \[ \text{Molar mass of CaCl}_2 = 40 + 2(35.5) = 111 \, \text{g/mol} \] The mass \( x \) is: \[ x = n \cdot \text{molar mass} = 0.0334 \cdot 111 = 3.7 \, \text{g} \]

4. Identifying the Correct Answer:
The mass of CaCl₂ is 3.7 g, which corresponds to Option C.

Final Answer:
The correct answer is Option C: 3.7 g.