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 \(1.00 \mathrm{~g} / \mathrm{mL}\).

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 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.

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 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.