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Chapter 11: Problem 84

How would you prepare 1.0 \(\mathrm{L}\) of an aqueous solution of sodium chloride having an osmotic pressure of 15 atm at \(22^{\circ} \mathrm{C} ?\) Assume sodium chloride exists as \(\mathrm{Na}^{+}\) and \(\mathrm{Cl}^{-}\) ions in solution.

Short Answer

Expert verified
To prepare a 1.0 L aqueous solution of sodium chloride with an osmotic pressure of 15 atm at 22°C, first calculate the moles of sodium chloride needed using the Van't Hoff equation. The molar concentration is found to be 0.6574 mol/L, which corresponds to 0.6574 moles in 1.0 L. Calculate the mass of sodium chloride needed (38.39 g) and follow the steps: dissolve 38.39 g of sodium chloride in some distilled water, transfer the solution into a 1.0 L volumetric flask, fill up to the mark, and mix thoroughly.

Step by step solution

01

Understand the Van't Hoff equation

The Van't Hoff equation is given by: \(π = cRT\) where: π = osmotic pressure in atm c = molar concentration of solutes in mol/L R = gas constant = 0.0821 L atm/mol K (Remember to always use the same units throughout the problem) T = temperature in Kelvin (K) In our problem, we have: π = 15 atm T = 22°C = 22 + 273.15 = 295.15 K We need to determine the molar concentration (c) required to produce the desired osmotic pressure.
02

Calculate the molar concentration

Rearrange the Van't Hoff equation to solve for molar concentration (c): \(c = \frac{π}{RT}\) Now, plug in the known values for π, R, and T: \(c = \frac{15\,\text{atm}}{(0.0821\,\text{L atm/mol K})(295.15\,\text{K})}\) Calculate the molar concentration (c): \(c = 0.6574\,\text{mol/L}\)
03

Calculate the moles of sodium chloride

We know the molar concentration (c) and the volume of the solution (V). To find the moles of sodium chloride (n), use the formula: \(n = cV\) Plug in the values of c and V: \(n = (0.6574\,\text{mol/L})(1.0\,\text{L})\) Calculate the moles (n) of sodium chloride: \(n = 0.6574\,\text{mol}\)
04

Calculate the mass of sodium chloride

We now know the moles of sodium chloride needed for the solution. Let's calculate the mass of sodium chloride (m) needed by using the formula: \(m = nM\) where: m = mass of sodium chloride in grams n = moles of sodium chloride M = molar mass of sodium chloride = 58.44 g/mol Plug in the values of n and M: \(m = (0.6574\,\text{mol})(58.44\,\text{g/mol})\) Calculate the mass (m) of sodium chloride: \(m = 38.39\,\text{g}\)
05

Preparing the solution

To prepare the 1.0 L aqueous solution of sodium chloride with an osmotic pressure of 15 atm at 22°C: 1. Weigh 38.39 g of sodium chloride. 2. Dissolve the 38.39 g of sodium chloride in a beaker with some distilled water. 3. Transfer the dissolved solution into a 1.0 L volumetric flask. 4. Fill the volumetric flask with distilled water up to the 1.0 L mark. 5. Mix the solution thoroughly to ensure even distribution of solutes. Now, you have prepared a 1.0 L aqueous solution of sodium chloride with the desired osmotic pressure of 15 atm at 22°C.

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