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Chapter 13: Problem 78

A 0.86 percent by mass solution of \(\mathrm{NaCl}\) is called "physiological saline" because its osmotic pressure is equal to that of the solution in blood cells. Calculate the osmotic pressure of this solution at normal body temperature \(\left(37^{\circ} \mathrm{C}\right)\). Note that the density of the saline solution is \(1.005 \mathrm{~g} / \mathrm{mL}\).

Short Answer

Expert verified
The osmotic pressure of the given solution at body temperature is 3.78 atm

Step by step solution

01

Convert temperature to Kelvin

First, convert the body temperature from Celsius to Kelvin. The Kelvin temperature is obtained by adding 273.15 to the Celsius temperature. So, \(T = 37 + 273.15 = 310.15 K\)
02

Calculate the mass of NaCl

Given a solution of 0.86 percent by mass, we have 0.86g of NaCl in 100g of solution.
03

Calculate the volume of the solution

Knowing that the density (\(d\)) of the solution is 1.005 g/mL and we have 100g of solution, we calculate the volume (\(V\)) of the solution. Using the formula \(V=m/d\), where \(m\) is the mass, we find that \(V = 100/1.005 = 99.5 mL\).
04

Calculate the molar concentration

The molar concentration (\(c\)) of the solution is calculated by dividing the number of moles of solute by the volume of the solution in liters. The molar mass of NaCl is 58.44 gmol\(^{-1}\), so we have \(0.86/58.44 = 0.0147 mol\) of NaCl. Convert the volume from mL to L: 99.5 mL = 0.0995 L. The molar concentration of NaCl is then \(0.0147/0.0995 = 0.1478 M\).
05

Calculate the osmotic pressure

Substitute the values into the osmotic pressure formula, \(\Pi = icRT\). As NaCl is non-dissociating, the van't Hoff factor (\(i\)) is 1. The ideal gas constant (\(R\)) is 0.0821 L atm mol\(^{-1}\) K\(^{-1}\). So, the osmotic pressure is \(\Pi = 1 * 0.1478 * 0.0821 * 310.15 = 3.78 atm\).

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Most popular questions from this chapter

Concentrated hydrochloric acid is usually available at 37.7 percent by mass. What is its concentration in molarity? (The density of the solution is \(1.19 \mathrm{~g} / \mathrm{mL}\).)

For ideal solutions, the volumes are additive. This means that if \(5 \mathrm{~mL}\) of \(\mathrm{A}\) and \(5 \mathrm{~mL}\) of \(\mathrm{B}\) form an ideal solution, the volume of the solution is \(10 \mathrm{~mL}\). Provide a molecular interpretation for this observation. When \(500 \mathrm{~mL}\) of ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) are mixed with \(500 \mathrm{~mL}\) of water, the final volume is less than \(1000 \mathrm{~mL}\) Why?

A solution of \(6.85 \mathrm{~g}\) of a carbohydrate in \(100.0 \mathrm{~g}\) of water has a density of \(1.024 \mathrm{~g} / \mathrm{mL}\) and an osmotic pressure of 4.61 atm at \(20.0^{\circ} \mathrm{C}\). Calculate the molar mass of the carbohydrate.

Define ion pairs. What effect does ion-pair formation have on the colligative properties of a solution? How does the ease of ion-pair formation depend on (a) charges on the ions, (b) size of the ions, (c) nature of the solvent (polar versus nonpolar), (d) concentration?

A beaker of water is initially saturated with dissolved air. Explain what happens when He gas at \(1 \mathrm{~atm}\) is bubbled through the solution for a long time.
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