Question

Which of these statements comparing a \(0.5 \mathrm{~m} \mathrm{NaCl}\) solution and a \(1.0 \mathrm{~m}\) glucose solution is true? a. They have the same osmolality. b. They have the same osmotic pressure. c. They are isotonic to each other. d. All of these are true.

Short answer

The short answer to the question is: (d) All of these are true. This is because both the $0.5\mathrm{~m} \mathrm{NaCl}$ and $1.0\mathrm{~m}$ glucose solutions have the same osmolality (1 osmol), the same osmotic pressure, and are isotonic to each other.

Step-by-step solution

In order to determine osmolality, we need to consider the number of dissolved particles in each solution. For the 0.5 m NaCl solution, NaCl dissociates into two particles (Na+ and Cl-) when dissolved. Therefore, the osmolality is 0.5 mol * 2 = 1 osmol. For the 1.0 m glucose solution, glucose (C6H12O6) does not dissociate in water, so the osmolality is 1 osmol. #Step 2: Compare osmolalities#

From Step 1, we can see that the osmolalities of the two solutions are the same (1 osmol). This confirms statement (a) to be true. #Step 3: Determine if the solutions are isotonic#

Since both solutions have the same osmolality, they will have the same osmotic pressure. This confirms statements (b) and (c) to be true, as isotonic solutions are those with the same osmotic pressure at the same temperature. #Step 4: Conclude whether all statements are true#

Since we've determined that statements (a), (b), and (c) are all true, we can conclude that statement (d) is also true, meaning all the given statements are true.

Key concepts

Osmolality Calculation

Understanding osmolality is crucial for many scientific and medical applications, as it reflects the concentration of solute particles in a solution. The calculation of osmolality can determine how a solution will interact with cells and tissues. Specifically, osmolality is the total number of osmoles of solute per kilogram of solvent. To calculate this, one should consider both the molarity (moles of solute per liter of solution) and the number of particles the solute dissociates into when in solution.

For example, a salt such as NaCl dissociates into two ions, Na+ and Cl-, so a 0.5 molar (0.5 M) solution of NaCl has an osmolality of 1 osmol (0.5 M × 2 ions). In contrast, a non-dissociating substance like glucose does not break down into smaller particles, so a 1.0 M glucose solution has an osmolality of 1 osmol. Hence, both the 0.5 M NaCl solution and the 1.0 M glucose solution have identical osmolalities, demonstrating how different substances with different molarities can yield the same osmolality.

Isotonicity in Solutions

The concept of isotonicity is pivotal in biology and pharmacology, particularly when it comes to creating solutions that are compatible with the human body. Isotonic solutions are those that have an equal concentration of solute particles as another solution, preventing the net movement of water across a semipermeable membrane - a phenomenon regulated by osmotic pressure.

For two solutions to be isotonic, their osmolalities must match. In the case of our textbook problem, both the 0.5 M NaCl and the 1.0 M glucose solutions have the same osmolality, which implies that they are isotonic to one another. As isotonic solutions, if these were separated by a semipermeable membrane, there would be no net water movement, thus no cell would shrink or swell in such environments. This property is especially crucial when administering intravenous fluids, as isotonic solutions ensure the stability of cells by preventing any undesirable osmotic effects.

Osmotic Pressure

Osmotic pressure is a measure of the tendency for osmosis to occur, driven by the disparity in solute concentrations across a semipermeable membrane. It can be quantified using the formula \( \Pi = iMRT \), where \( \Pi \) is the osmotic pressure, \( i \) is the van't Hoff factor (number of particles the substance dissociates into), \( M \) is the molarity, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin.

In practical terms, osmotic pressure must be carefully considered when preparing solutions to be in contact with living cells. When the osmotic pressure is different across a cell membrane, water will move such that the pressure is equalized. This is why having matching osmotic pressures, as observed in isotonic solutions, is vital for maintaining cellular integrity. Thus, in the context of our problem, since the 0.5 M NaCl solution and the 1.0 M glucose solution have the same osmolality, they also exert the same osmotic pressure when separated by a semipermeable membrane.