A physiological saline solution is 0.92% NaCl by mass.What is the osmotic pressure of such a solution at a body temperature of 37 $\degree$C? Assume the density of the solution is 1.0 g/mL.

Question

Quizplus · Accepted Answer

The osmotic pressure of a solution is given by the van't Hoff equation:$$\pi = MRT$$where:* $\pi$ is the osmotic pressure in atm* $M$ is the molarity of the solution in mol/L* $R$ is the ideal gas constant in L·atm/(mol·K)* $T$ is the temperature in KWe are given that the physiological saline solution is 0.92% NaCl by mass. We can use the density of the solution to convert this to a molarity:$$M = \frac{\text{mass of NaCl}}{\text{molar mass of NaCl}} \times \frac{1}{\text{volume of solution}}$$$$M = \frac{0.92 \text{ g}}{58.44 \text{ g/mol}} \times \frac{1}{1000 \text{ mL}} = 0.0158 \text{ mol/L}$$We are also given that the body temperature is 37°C. We need to convert this to Kelvin:$$T = 37°C + 273.15 = 310.15 \text{ K}$$Now we can plug these values into the van't Hoff equation to calculate the osmotic pressure:$$\pi = MRT = (0.0158 \text{ mol/L})(0.0821 \text{ L·atm/(mol·K)})(310.15 \text{ K}) = 3.9 \text{ atm}$$Therefore, the osmotic pressure of the physiological saline solution is 3.9 atm.

A Physiological Saline Solution Is 0 °\degree° C? Assume the Density of the Solution Is 1

A Physiological Saline Solution Is 0 $\degree$ C? Assume the Density of the Solution Is 1