Question

Solutions introduced directly into the bloodstream have to be "isotonic" with blood; that is, they must have the same osmotic pressure as blood. An aqueous \(\mathrm{NaCl}\) solution has to be \(0.90 \%\) by mass to be isotonic with blood. What is the molarity of sodium ions in solution? Take the density of the solution to be \(1.00 \mathrm{~g} / \mathrm{mL}\).

Short answer

Answer: The molarity of sodium ions in the isotonic NaCl solution is 0.154 M.

Step-by-step solution

Convert mass percentage of NaCl into grams

Since the solution is 0.90% by mass, this means that there are 0.90 grams of NaCl in 100 grams of the solution.

Calculate the number of moles of NaCl

Next, we need to find the number of moles of NaCl. The molar mass of NaCl is 58.44 g/mol. Therefore, the number of moles of NaCl is: moles of NaCl = mass of NaCl / molar mass of NaCl moles of NaCl = 0.90 g / 58.44 g/mol ≈ 0.0154 mol

Calculate the volume of the solution in liters

We are given the density of the solution as 1.00 g/mL. Since there are 100 grams of the solution, and the density is the mass per unit volume, we can find the volume: volume of solution = mass of solution / density volume of solution = 100 g / (1.00 g/mL) = 100 mL Next, convert the volume from milliliters to liters: volume of solution = 100 mL × (1 L / 1000 mL) = 0.100 L

Determine the molarity of NaCl in the solution

The molarity (M) is defined as the number of moles of solute per liter of solution. In this case, the solute is NaCl, and the solution is 0.100 L. Therefore, the molarity of NaCl is: molarity of NaCl = moles of NaCl / volume of solution molarity of NaCl = 0.0154 mol / 0.100 L = 0.154 M

Determine the molarity of sodium ions in the solution

Since NaCl dissociates completely into sodium ions (Na+) and chloride ions (Cl-), the molarity of sodium ions in the solution is equal to the molarity of NaCl. Therefore, the molarity of sodium ions in the isotonic NaCl solution is: molarity of sodium ions = 0.154 M

Key concepts

Osmotic Pressure

Osmotic pressure is a fundamental concept in understanding how fluids and their solutes move across semi-permeable membranes, a process vital to biological systems like our blood. In the context of medical treatments, solutions administered intravenously must mimic the osmotic pressure of blood to prevent damage to blood cells and tissue. Isotonic solutions, which have the same osmotic pressure as blood, do not cause net movement of water into or out of blood cells. This equilibrium is critical to maintaining cell size and function.

For example, a saline solution that is isotonic with human blood contains approximately 0.9% sodium chloride (NaCl) by mass. If the concentration were higher (hypertonic) or lower (hypotonic), it would result in water moving into or out of blood cells, leading to cell damage or dysfunction.

Molarity Calculation

Molarity is a way to express the concentration of a solution, defined as the number of moles of solute per liter of solution. It's a crucial concept in preparing isotonic solutions and in many areas of chemistry. The formula for molarity (M) is:
\[ M = \frac{\text{{moles of solute}}}{\text{{liters of solution}}} \]

To calculate the molarity, one must know the mass of the solute (in this case NaCl), its molar mass, and the volume of the solution. As demonstrated in the exercise, converting mass percentages into grams, calculating moles using molar mass, and then dividing by the volume of the solution in liters allows for the determination of molarity.

Solution Concentration

Understanding solution concentration is central to preparing a solution with the desired properties. In the given exercise, we started with a known mass percentage concentration (0.90%) and converted this into a molarity, a more useful concentration measurement for stoichiometric calculations. The mass percentage tells us how many grams of solute are present in 100 grams of solution, which must be converted into moles to find the molarity. Concentrations can be expressed in various ways, including molarity, molality, mass percentage, and parts per million (ppm), each serving different purposes depending on the scenario.

Stoichiometry

Stoichiometry is the section of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It's based on the conservation of mass and the concept of mole ratios as dictated by the balanced chemical equations. In the case of preparing an isotonic NaCl solution, stoichiometry comes into play when we determine the number of moles of solute from the given mass. It's essential to recognize that NaCl dissociates into two ions: one Na+ and one Cl-. Therefore, the molarity of Na+ ions will be the same as that of the NaCl since the stoichiometry of the dissociation is 1:1.