A saline solution is administered intravenously to patients who cannot take fluid orally and are in danger of dehydration. The osmotic pressure of this solution must match that of blood to prevent hemolysis or crenation of blood cells. What mass of sodium chloride (58.44 g/mol) is needed to produce 100.0 mL of saline solution with an osmotic pressure of 7.83 atm at a body temperature of 37 $\circ$ C?
A)0.899 g
B)8.99 g
C)18.0 g
D)1.80 g
E)0.450 g

Question

Quizplus · Accepted Answer

The osmotic pressure ($\Pi$) can be calculated using the formula $\Pi = iMRT$, where $i$ is the van't Hoff factor for NaCl (which is 2, because it dissociates into Na$^+$ and Cl$^-$), $M$ is the molarity of the solution, $R$ is the ideal gas constant (0.0821 L·atm/K·mol), and $T$ is the temperature in Kelvin. Given the osmotic pressure (7.83 atm) and the temperature (37°C, which is 310 K when converted), we can rearrange the formula to solve for $M$, the molarity of the solution. First, convert the temperature to Kelvin: $37°C + 273 = 310 K$.Then, rearrange the formula to solve for $M$: $M = \Pi / (iRT)$.Substitute the given values into the equation: $M = 7.83 / (2 \times 0.0821 \times 310)$.Solving for $M$ gives a molarity of approximately 0.122 M.To find the mass of NaCl needed, use the formula $mass = M \times MW \times volume$, where $MW$ is the molar mass of NaCl (58.44 g/mol) and the volume is in liters (0.100 L for 100.0 mL).$mass = 0.122 \times 58.44 \times 0.100 = 0.899 g$.Therefore, 0.899 g of NaCl is needed to prepare the solution.

A Saline Solution Is Administered Intravenously to Patients Who Cannot ∘\circ∘

A Saline Solution Is Administered Intravenously to Patients Who Cannot $\circ$