Question

How would you prepare \(1.0 \mathrm{~L}\) of an aqueous solution of sodium chloride having an osmotic pressure of \(15 \mathrm{~atm}\) 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 sodium chloride solution with an osmotic pressure of 15 atm at 22°C, calculate the required concentration using the osmotic pressure formula: \(M = \frac{Π}{RT}\). Plug in the given values and find the concentration to be approximately 0.657 mol/L. Then, calculate the mass of sodium chloride needed by multiplying the concentration by the volume and molar mass of NaCl: \(0.657\,\mathrm{mol\,L^{-1}} \times 1.0\,\mathrm{L} \times 58.44\,\frac{\mathrm{g}}{\mathrm{mol}}\), which gives us ≈ 38.36 g. Therefore, 38.36 grams of sodium chloride is required to prepare the solution.

Step-by-step solution

List the given information and the osmotic pressure formula

We are given the following information: - Osmotic pressure (Π) is 15 atm - Temperature (T) is \(22^{\circ}\mathrm{C}\) = 295.15 K (converting to Kelvin) - The volume of the solution is 1.0 L The osmotic pressure formula is: \(Π = MRT\) Where: Π = osmotic pressure, M = concentration (in moles per liter), R = the gas constant (0.0821 L atm/mol K), and T = temperature (in Kelvin)

Solve the formula for concentration

In order to find the concentration (M), we Rearrange the osmotic pressure formula to solve for M: \(M = \frac{Π}{RT}\) Next, plug in the given values for osmotic pressure Π, gas constant R, and temperature T. \(M = \frac{15\,\mathrm{atm}}{(0.0821\,\frac{\mathrm{L\, atm}}{\mathrm{mol\, K}})(295.15\,\mathrm{K})}\) Now, calculate the concentration.

Calculate the concentration

Calculate the concentration (M) using the given information: \(M = \frac{15}{(0.0821)(295.15)}\) \(M \approx 0.657\,\mathrm{mol\,L^{-1}}\) This means that we need a concentration of 0.657 mol/L of sodium chloride (NaCl) in the solution.

Calculate the mass of sodium chloride

As we have found the required concentration, now we need to calculate how much sodium chloride (NaCl) we should add to prepare 1.0 L of the solution. We use the formula: Mass of NaCl = Concentration × Volume × Molar Mass of NaCl The molar mass of NaCl is 58.44 g/mol. Calculate the mass of NaCl needed: Mass of NaCl = \(0.657\,\mathrm{mol\,L^{-1}} \times 1.0\,\mathrm{L} \times 58.44\,\frac{\mathrm{g}}{\mathrm{mol}}\)

Determine the mass of sodium chloride required

Calculate the mass of sodium chloride needed: Mass of NaCl = \(0.657 \times 1.0 \times 58.44\) Mass of NaCl ≈ 38.36 g Therefore, we need 38.36 grams of sodium chloride to prepare 1.0 L of an aqueous solution with an osmotic pressure of 15 atm at 22°C.

Key concepts

Aqueous Solution Preparation

Preparing an aqueous solution involves dissolving a certain amount of solute in a solvent, usually water. The process is fundamental in chemistry and vital for experiments that require a precise concentration of a substance. In our specific scenario, we must dissolve the appropriate mass of sodium chloride into water to achieve a desired osmotic pressure.

The steps for preparing an aqueous solution of a given osmotic pressure include calculating the molarity, which is a measurement of the concentration of solute per volume of solution, and then determining the corresponding mass of solute needed. Molarity (M) is given by the moles of solute divided by the liters of solution. Furthermore, the mass of solute can be found using the molar mass, the molarity, and the volume of the solution.

Accuracy in Measurement

It's crucial to measure the volume of water and mass of sodium chloride precisely. Imbalances can lead to inaccuracies in the solution's concentration, affecting the osmotic pressure.

Sodium Chloride

Sodium chloride, commonly known as table salt, is widely utilized in solutions for its properties as an ionic compound composed of sodium (Na⁺) and chloride (Cl^-) ions. When dissolved, it dissociates into its constituent ions and interacts with the solvent molecules.

In the laboratory, it is essential to use a pure form of sodium chloride without impurities to ensure that the prepared solution has the intended properties and osmotic pressure. Sodium chloride's solubility and ability to dissociate in water make it ideal for experiments involving osmotic pressure calculations.

Impact of Dissociation

When considering the colligative properties of sodium chloride solutions, the complete dissociation into Na⁺ and Cl^- ions must be accounted for, as each ion exerts its own effect on properties like osmotic pressure.

Colligative Properties

Colligative properties are characteristics of a solution that depend solely on the number of dissolved particles in the solution, regardless of their chemical identity. Osmotic pressure is one of the colligative properties, along with boiling point elevation, freezing point depression, and vapor pressure lowering.

Osmotic pressure is particularly significant as it is the pressure necessary to prevent solvent movement across a semi-permeable membrane due to osmosis. It can be influenced by factors such as temperature, solute concentration, and the nature of the solute. Calculations of osmotic pressure assume ideal behavior, which includes the complete dissociation of ionic compounds such as sodium chloride. The contribution of each ion in the solution must be contemplated.

Van't Hoff Factor

The Van't Hoff factor (i) is a dimensionless quantity used in colligative property calculations to accommodate the effects of a substance's dissociation or ionization in solution. For sodium chloride, which dissociates into two ions, the Van't Hoff factor is often considered to be approximately 2. Thus, in our calculation, we would use this factor to account for the presence of two types of particles contributing to the osmotic pressure.