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Chapter 13: Problem 74

Seawater contains \(3.4 \mathrm{~g}\) of salts for every liter of solution. Assuming that the solute consists entirely of \(\mathrm{NaCl}\) (over \(90 \%\) is), calculate the osmotic pressure of seawater at \(20^{\circ} \mathrm{C}\).

Short Answer

Expert verified
The osmotic pressure of seawater at \(20^{\circ} \mathrm{C}\) is approximately \(1.41 \mathrm{atm}\).

Step by step solution

01

Identify the variables and constants

Given variables: - Salt concentration in seawater: \(3.4 \mathrm{g/L}\) - Temperature: \(20^{\circ} \mathrm{C}\) - The molar mass of NaCl: \(58.44 \mathrm{g/mol}\) Constants: - Gas constant (\(R\)): \(0.0821 \mathrm{L \cdot atm / (mol \cdot K)}\)
02

Convert temperature to Kelvin

The temperature must be in Kelvin (K) to use the gas constant. Convert the given Celsius temperature to Kelvin: Temperature, \(T = 20^{\circ} \mathrm{C} + 273.15 = 293.15 \mathrm{K}\)
03

Convert mass concentration to molar concentration

Calculate the molar concentration, \(\mathrm{M}\), using the given mass concentration and the molar mass of NaCl: \(\mathrm{M} = \frac{3.4 \mathrm{g/L}}{58.44 \mathrm{g/mol}} = 0.0582 \mathrm{mol/L}\)
04

Calculate the osmotic pressure using the formula

Use the formula for osmotic pressure derived from the ideal gas law: Osmotic pressure, \(螤 = \mathrm{M} \cdot R \cdot T\) Plug in the values for \(\mathrm{M}, R,\) and \(T\): \( 螤 = (0.0582 \mathrm{mol/L}) \cdot (0.0821 \mathrm{L \cdot atm / (mol \cdot K)}) \cdot (293.15 \mathrm{K}) \)
05

Calculate the osmotic pressure

Solve for the osmotic pressure, \(螤\): \( 螤 \approx 1.41 \mathrm{atm} \) Therefore, the osmotic pressure of seawater at \(20^{\circ} \mathrm{C}\) is approximately \(1.41 \mathrm{atm}\).

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Most popular questions from this chapter

A saturated solution of sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\) is made by dissolving excess table sugar in a flask of water. There are \(50 \mathrm{~g}\) of undissolved sucrose crystals at the bottom of the flask in contact with the saturated solution. The flask is stoppered and set aside. A year later a single large crystal of mass \(50 \mathrm{~g}\) is at the bottom of the flask. Explain how this experiment provides evidence for a dynamic equilibrium between the saturated solution and the undissolved solute.

The density of toluene \(\left(\mathrm{C}_{7} \mathrm{H}_{8}\right)\) is \(0.867 \mathrm{~g} / \mathrm{mL}\), and the density of thiophene \(\left(\mathrm{C}_{4} \mathrm{H}_{4} \mathrm{~S}\right)\) is \(1.065 \mathrm{~g} / \mathrm{mL}\). A solution is made by dissolving \(9.08 \mathrm{~g}\) of thiophene in \(250.0 \mathrm{~mL}\) of toluene. (a) Calculate the mole fraction of thiophene in the solution. (b) Calculate the molality of thiophene in the solution. (c) Assuming that the volumes of the solute and solvent are additive, what is the molarity of thiophene in the solution?

Ascorbic acid (vitamin \(\mathrm{C}\), \(\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6}\) ) is a water-soluble vitamin. A solution containing \(80.5 \mathrm{~g}\) of ascorbic acid dissolved in \(210 \mathrm{~g}\) of water has a density of \(1.22 \mathrm{~g} / \mathrm{mL}\) at \(55^{\circ} \mathrm{C}\). Calculate (a) the mass percentage, (b) the mole fraction, (c) the molality, (d) the molarity of ascorbic acid in this solution.

A textbook on chemical thermodynamics states, "The heat of solution represents the difference between the lattice energy of the crystalline solid and the solvation energy of the gaseous ions." (a) Draw a simple energy diagram to illustrate this statement. (b) A salt such as NaBr is insoluble in most polar nonaqueous solvents such as acetonitrile (CH \(_{3} \mathrm{CN}\) ) or nitromethane \(\left(\mathrm{CH}_{3} \mathrm{NO}_{2}\right)\), but salts of large cations, such as tetramethylammonium bromide \(\left[\left(\mathrm{CH}_{3}\right)_{4} \mathrm{NBr}\right]\), are generally more soluble. Use the thermochemical cycle you drew in part (a) and the factors that determine the lattice energy (Section 8.2) to explain this fact.

What is the osmotic pressure formed by dissolving \(44.2 \mathrm{mg}\) of aspirin \(\left(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\right)\) in \(0.358 \mathrm{~L}\) of water at \(25^{\circ} \mathrm{C} ?\)
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