Question

Every year, oral rehydration therapy (ORT)-the feeding of an electrolyte solution-saves the lives of countless children worldwide who become severely dehydrated as a result of diarrhea. One requirement of the solution used is that it be isotonic with human blood.(a) One definition of an isotonic solution given in the text is that it have the same osmotic pressure as \(0.92 \% \mathrm{NaCl}(\mathrm{aq})\) (mass/volume). Another definition is that the solution have a freezing point of \(-0.52^{\circ} \mathrm{C}\) Show that these two definitions are in reasonably close agreement given that we are using solution concentrations rather than activities.(b) Use the freezing-point definition from part (a) to show that an ORT solution containing \(3.5 \mathrm{g} \mathrm{NaCl}\) \(1.5 \mathrm{g} \mathrm{KCl}, 2.9 \mathrm{g} \mathrm{Na}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}\) (sodium citrate), and \(20.0 \mathrm{g} \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) (glucose) per liter meets the requirement of being isotonic. [Hint: Which of the solutes are nonelectrolytes, and which are strong electrolytes?]

Short answer

To determine whether the solution is isotonic we need, first, to understand the isotonicity definitions and identify whether compounds are electrolytes or nonelectrolytes. Then, we calculate the molality using freezing-point depression for the solution and check if the total freezing depression of the ORT solution equals that of the isotonic solution (-0.52 degrees Celsius). If they are equal, then the solution is isotonic.

Step-by-step solution

Understand the Definitions of Isotonicity

Isotonicity can be defined in two ways: 1) a solution having the same osmotic pressure as a 0.92% NaCl (aq) solution, and 2) a solution having a freezing point of -0.52 degrees Celsius. This step does not involve calculations, but it establishes the criteria that will be used in the following steps.

Identify the Type of Compound

We need to identify whether the compounds are electrolytes or nonelectrolytes. Sodium chloride (NaCl) and potassium chloride (KCl) are strong electrolytes because they completely disassociate into ions in aqueous solution. Sodium citrate (Na3C6H5O7) is also a strong electrolyte. Glucose (C6H12O6) is a nonelectrolyte, because it does not form ions in solution.

Calculate the Molality using Freezing-Point Depression

We can use the freezing-point depression definition to calculate the molality of the required solution. The freezing point depression is given by the equation ΔTf = Kf * m * i, where ΔTf is the freezing point depression, Kf is the freezing point depression constant, m is the molality, and i is the van't Hoff factor. Since we know ΔTf (-0.52 degrees Celsius for an isotonic solution), Kf (1.86 degrees Celsius/molal for water), and i (which is 1 for nonelectrolytes and the number of ions for electrolytes), we can rearrange the equation to solve for m: m = ΔTf / (Kf * i)

Check if ORT Solution is Isotonic

Lastly, we determine if the ORT solution is isotonic. Calculate the total freezing point depression of the ORT solution using the properties of each solute in the solution. If the total freezing point depression of the ORT solution equals that of the isotonic solution (-0.52 degrees Celsius), then the ORT solution is isotonic. If not, it's not isotonic.

Key concepts

Osmotic Pressure Explained

Osmotic pressure is a fundamental concept in understanding how fluids move across semi-permeable membranes, such as those found in human cells. It's the pressure required to prevent the movement of water into a solution through osmosis, which is the process where water moves from a region of lower solute concentration to one of higher concentration.

Osmotic pressure is key in maintaining the balance of fluids in our bodies. If an oral rehydration therapy (ORT) solution does not have the same osmotic pressure as our blood, water may either flood into our cells, causing them to swell and potentially burst, or exit the cells, leading to dehydration. Hence, having an isotonic ORT solution is crucial for safe and effective treatment of conditions like diarrhea that disrupt fluid balance.

Understanding the role of osmotic pressure in solutions leads to better hydration and treatment practices. This is why creating solutions with an osmotic pressure similar to that of body fluids (using the 0.92% NaCl as a standard) is an essential practice in medical treatments.

Interpreting Freezing Point Depression

Freezing point depression occurs when the freezing point of a liquid is lowered by adding another compound to it. This concept is invaluable in designing isotonic solutions because it provides a physical property that can be measured to ensure isotonicity.

When a solute, such as salt, is added to water, it interferes with the formation of ice crystals, lowering the temperature at which the solution freezes. For every solution to be considered isotonic with human blood, its freezing point should be around -0.52°C. This is roughly the same value for a 0.92% NaCl solution, which is used as a benchmark for isotonic solutions.

In an educational context, applying the concept of freezing point depression involves calculations using the formula: \( \Delta T_f = K_f \times m \times i \), where \( \Delta T_f \) is the change in freezing point, \( K_f \) is the cryoscopic constant specific to the solvent, \( m \) is the molality of the solution, and \( i \) is the van’t Hoff factor - which accounts for the number of particles the solute splits into when dissolved. Understanding this scientific principle is critical for students in mastering the necessary skills to control solution properties in medical and industrial applications.

Electrolytes and Nonelectrolytes

Different substances behave differently when dissolved in water, and this is where the categorization into electrolytes and nonelectrolytes becomes significant.

Electrolytes are substances that dissolve in water to produce a solution that conducts electricity. They disassociate into ions, which are charged particles. Examples from the ORT solution include NaCl and KCl, which disassociate into sodium and chloride ions, and potassium ions, respectively. The presence of these ions influences the freezing point depression of a solution, as well as its osmotic pressure.

Nonelectrolytes, like glucose in the ORT solution, do not disassociate into ions when dissolved. They have a different impact on the osmotic pressure and freezing point depression of solutions. When creating an isotonic solution, it's crucial to understand the properties of each solute being added. For medicines like ORT, getting the balance right can mean the difference between a remedy and a complication. By recognizing the distinctions between electrolytes and nonelectrolytes, students and professionals can accurately determine the impact on the solution's properties and ensure its compatibility with human blood.