Question

How would you prepare 1.0 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

To prepare 1.0 L of an aqueous solution of sodium chloride with an osmotic pressure of 15 atm at 22°C, first, calculate the concentration (c) using the van't Hoff equation: \(c \approx 1.548\,\text{mol/L}\). Then, find the amount of sodium chloride needed in moles: \(1.548\,\text{mol}\). Convert this to grams using the molar mass of sodium chloride: \(90.41\, \text{g}\). Lastly, dissolve approximately 90.41 g of sodium chloride in enough water to make the total volume 1.0 L.

Step-by-step solution

Find the necessary concentration of sodium chloride using the van't Hoff equation

: The van't Hoff equation relates osmotic pressure (Π) to the concentration of the solute (c), and the ideal gas constant (R) and the temperature (T). The equation is given by: \[Π = icRT\] Where: i: van't Hoff factor, the number of particles produced by the solute in the solution c: concentration of the solute (in mol/L) R: ideal gas constant (0.0821 L atm/mol K) T: temperature (in Kelvin) We know that sodium chloride completely dissociates into Na+ and Cl- ions in solution, so the van't Hoff factor (i) is 2. We are given the osmotic pressure (Π) as 15 atm and temperature as 22°C; therefore, we need to convert this to Kelvin: T(K) = T(°C) + 273.15 T(K) = 22 + 273.15 T(K) = 295.15 K Now, we can solve for the concentration (c): 15 atm = 2c × 0.0821 L atm/mol K × 295.15 K

Calculate the concentration of sodium chloride

: Now let's solve the equation to find the concentration (c): \[c = \dfrac{15\,\text{atm}}{2 \times 0.0821\, \text{L atm/mol K} \times 295.15\,\text{K}}\] \[c \approx 1.548\,\text{mol/L}\]

Calculate the amount of sodium chloride to dissolve

: We need to prepare 1.0 L of the aqueous solution, so we can calculate the total amount of sodium chloride needed for this concentration: Amount (mol) = Concentration × Volume Amount (mol) = 1.548 mol/L × 1.0 L Amount (mol) = 1.548 mol

Convert the amount of sodium chloride to grams

: Finally, we will convert the amount of sodium chloride in moles to grams using its molar mass: Molar mass of sodium chloride = 58.44 g/mol Amount (g) = Amount(mol) × Molar mass Amount (g) = 1.548 mol × 58.44 g/mol Amount (g) ≈ 90.41 g

Prepare the 1.0 L aqueous solution of sodium chloride

: To prepare 1.0 L of an aqueous solution of sodium chloride with an osmotic pressure of 15 atm at 22 °C, dissolve approximately 90.41 g of sodium chloride in enough water to make the total volume 1.0 L. That's it! The solution is ready to use.

Key concepts

Van't Hoff Equation

When discussing solutions and their properties, the Van't Hoff equation is essential to understand osmotic pressure. Osmotic pressure is the force exerted by a solution when two solutions of different concentrations are separated by a semi-permeable membrane. To calculate this pressure, we use the Van't Hoff equation, which is:\[\Pi = icRT\]Where:

• \(\Pi\) is the osmotic pressure.
• i is the van't Hoff factor, representing the number of particles the solute dissociates into in a solution.
• c is the molarity or concentration of the solution in mol/L.
• R is the ideal gas constant, equal to 0.0821 L atm/mol K.
• T is the temperature in Kelvin.

Sodium chloride (\(NaCl\)) dissociates completely into \(Na^+\) and \(Cl^-\) ions, resulting in a van't Hoff factor (\(i\)) of 2. This information allows us to calculate the concentration needed to achieve a desired osmotic pressure at a given temperature. For example, to create a solution with an osmotic pressure of 15 atm at 22°C, we need to determine temperature in Kelvin first (\(295.15K\)) and then use this equation to find the concentration.

Sodium Chloride Solution Preparation

Preparing a sodium chloride (NaCl) solution with specific osmotic characteristics requires not only an understanding of the Van't Hoff equation but also knowledge of solute preparation techniques. Here is a step-by-step method to prepare a solution with the desired properties: First, we identify the concentration of NaCl needed, already calculated as approximately 1.548 mol/L using the Van't Hoff equation. Now, our goal is to prepare 1 liter of this solution. To prepare the solution:

• Measure exactly 1.548 moles of NaCl. Since the molar mass of NaCl is 58.44 g/mol, we convert this amount to grams:
  1.548 mol * 58.44 g/mol = 90.41 grams.
• Weigh 90.41 grams of NaCl using a precise balance.
• Dissolve the NaCl in a minimal amount of distilled water to ensure it fully dissolves.
• Transfer this solution into a volumetric flask and add more distilled water until the total volume reaches 1 liter.
• Ensure the solution is well mixed for uniform distribution of ions.

By following this process, you prepare a solution that effectively achieves the desired osmotic pressure of 15 atm at the given conditions.

Molarity Calculation

Molarity, one of the most important concentration units in chemistry, is defined as the number of moles of solute per liter of solution. To find the molarity (c) of a solution, the following formula is used:\[c = \frac{n}{V}\]where:

• n is the number of moles of solute.
• V is the volume of the solution in liters.

In the context of our sodium chloride solution and osmotic pressure problem, we have already determined the necessary concentration using the Van't Hoff equation. For sodium chloride in this exercise, 1.548 moles of NaCl needed to be dissolved in 1 liter of water, giving the solution a molarity of 1.548 mol/L. Knowing how to calculate molarity helps in preparing solutions with precise concentrations, vital for experimental repeatability and achieving specific reaction conditions.