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Chapter 11: Problem 80

A water desalination plant is set up near a salt marsh containing water that is \(0.10 M\) NaCl. Calculate the minimum pressure that must be applied at \(20 .{ }^{\circ} \mathrm{C}\) to purify the water by reverse osmosis. Assume \(\mathrm{NaCl}\) is completely dissociated.

Short Answer

Expert verified
Based on the osmotic pressure formula, the minimum pressure required to purify the water is \(π = \frac{nRT}{V}\). With the given concentration of NaCl (\(0.10 M\)), temperature (\(20^{\circ}C\)), and assuming NaCl is completely dissociated, we can calculate the minimum pressure to be approximately \(4.92 atm\).

Step by step solution

01

Recall the formula for osmotic pressure

We will use the osmotic pressure formula to find out the minimum pressure required to purify the water. The formula for osmotic pressure is: \(π = nRT/V\) Where: π = osmotic pressure n = number of moles of solute R = gas constant (0.08206 L atm/mol K) T = temperature in Kelvin V = volume in liters

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Most popular questions from this chapter

At \(25^{\circ} \mathrm{C}\), the vapor in equilibrium with a solution containing carbon disulfide and acetonitrile has a total pressure of 263 torr and is \(85.5\) mole percent carbon disulfide. What is the mole fraction of carbon disulfide in the solution? At \(25^{\circ} \mathrm{C}\), the vapor pressure of carbon disulfide is 375 torr. Assume the solution and vapor exhibit ideal behavior.

At a certain temperature, the vapor pressure of pure benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) is \(0.930\) atm. A solution was prepared by dissolving \(10.0\) \(\mathrm{g}\) of a nondissociating, nonvolatile solute in \(78.11 \mathrm{~g}\) of benzene at that temperature. The vapor pressure of the solution was found to be \(0.900\) atm. Assuming the solution behaves ideally, determine the molar mass of the solute.

A solution is prepared by mixing \(0.0300 \mathrm{~mol} \mathrm{CH}_{2} \mathrm{Cl}_{2}\) and \(0.0500\) \(\mathrm{mol} \mathrm{CH}_{2} \mathrm{Br}_{2}\) at \(25^{\circ} \mathrm{C}\). Assuming the solution is ideal, calculate the composition of the vapor (in terms of mole fractions) at \(25^{\circ} \mathrm{C}\). At \(25^{\circ} \mathrm{C}\), the vapor pressures of pure \(\mathrm{CH}_{2} \mathrm{Cl}_{2}\) and pure \(\mathrm{CH}_{2} \mathrm{Br}_{2}\) are 133 and \(11.4\) torr, respectively.

In lab you need to prepare at least \(100 \mathrm{~mL}\) of each of the following solutions. Explain how you would proceed using the given information. a. \(2.0 \mathrm{~m} \mathrm{KCl}\) in water (density of \(\mathrm{H}_{2} \mathrm{O}=1.00 \mathrm{~g} / \mathrm{cm}^{3}\) ) b. \(15 \% \mathrm{NaOH}\) by mass in water \(\left(d=1.00 \mathrm{~g} / \mathrm{cm}^{3}\right)\) c. \(25 \% \mathrm{NaOH}\) by mass in \(\mathrm{CH}_{3} \mathrm{OH}\left(d=0.79 \mathrm{~g} / \mathrm{cm}^{3}\right)\) d. \(0.10\) mole fraction of \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) in water \(\left(d=1.00 \mathrm{~g} / \mathrm{cm}^{3}\right)\)

Consider a beaker of salt water sitting open in a room. Over time, does the vapor pressure increase, decrease, or stay the same? Explain.
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