Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 11: Problem 137

In some regions of the southwest United States, the water is very hard. For example, in Las Cruces, New Mexico, the tap water contains about 560$\mu \mathrm{g}$ of dissolved solids per milliliter. Reverse osmosis units are marketed in this area to soften water. A typical unit exerts a pressure of 8.0 atm and can produce 45 \(\mathrm{L}\) water per day. a. Assuming all of the dissolved solids are \(\mathrm{MgCO}_{3}\) and assuming a temperature of \(27^{\circ} \mathrm{C},\) what total volume of water must be processed to produce 45 L pure water? b. Would the same system work for purifying seawater? (Assume seawater is 0.60\(M \mathrm{NaCl.} )\)

Short Answer

Expert verified
In short, to produce 45 L of pure water, 174.6 L of water must be processed. The same reverse osmosis system would not work for purifying seawater because the osmotic pressure of seawater is much higher than the pressure exerted by the unit.

Step by step solution

01

Calculate the number of moles of MgCO3 in 1L of water

First, we need to find the number of moles of MgCO3 in 1 liter (1000 ml) of water. Moles of MgCO3 = mass of MgCO3 / molar mass of MgCO3 Moles of MgCO3 = (560 * 1000 * 10^{-6} g) / 84.31 g/mol = 6.648 * 10^{-3} moles
02

Determine the concentration of MgCO3

Now, we can calculate the concentration of the MgCO3 in the water by dividing the number of moles of MgCO3 by the volume of water (in liters): Concentration of MgCO3 = (6.648 * 10^{-3} moles) / 1 L = 6.648 * 10^{-3} mol/L #b. Calculate the volume of water processed#
03

Calculate the osmotic pressure of MgCO3

We will use the van 't Hoff equation to calculate the osmotic pressure: Osmotic pressure = i * c * R * T where i is the van 't Hoff factor (MgCO3 doesn't dissociate in water, so i = 1), c is the concentration of MgCO3, R is the gas constant (0.0821 L atm/mol K), and T is the temperature in Kelvin (T = 273 + 27 = 300 K). Osmotic pressure = (1) * (6.648 * 10^{-3} mol/L) * (0.0821 L atm/mol K) * (300 K) = 1.6385 atm
04

Calculate the volume ratio of processed water to pure water

The pressure exerted by the reverse osmosis unit is 8.0 atm. The difference between this pressure and the osmotic pressure is the effective pressure applied for reverse osmosis. Effective pressure = 8.0 atm - 1.6385 atm = 6.3615 atm The volume ratio of processed water to pure water can be calculated using Boyle's law, assuming the dissolved solids have been completely removed: P1 * V1 = P2 * V2 ==> V1 / V2 = P2 / P1 Volume ratio = 6.3615 atm / 1.6385 atm = 3.880
05

Calculate the volume of water processed

Now we can use this volume ratio to find the volume of water that needs to be processed to produce 45 L of pure water: Volume of processed water = Volume of pure water * Volume ratio Volume of processed water = 45 L * 3.880 = 174.6 L #b. Analyze if the same system works for purifying seawater#
06

Determine the osmotic pressure of seawater

We will again use the van 't Hoff equation, but now assume that seawater is 0.60 M NaCl: Osmotic pressure = i * c * R * T Since NaCl dissociates into two ions (Na+ and Cl-), i = 2. Osmotic pressure = (2) * (0.60 mol/L) * (0.0821 L atm/mol K) * (300 K) = 29.587 atm
07

Compare osmotic pressures and analyze if the system would work

The osmotic pressure of seawater is much higher than the osmotic pressure of tap water (29.587 atm vs. 1.6385 atm). Thus, the reverse osmosis unit with a pressure of 8.0 atm wouldn't be effective for purifying seawater since the applied pressure is much lower than the osmotic pressure of seawater. In conclusion, it is necessary to process a total volume of 174.6 L of water in order to produce 45 L of pure water. The same system wouldn't be effective for purifying seawater as its osmotic pressure is much higher than the pressure exerted by the reverse osmosis unit.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The solubility of nitrogen in water is $8.21 \times 10^{-4} \mathrm{mol} / \mathrm{L}\( at \)0^{\circ} \mathrm{C}\( when the \)\mathrm{N}_{2}$ pressure above water is 0.790 \(\mathrm{atm}\) . Calculate the Henry's law constant for \(\mathrm{N}_{2}\) in units of \(\mathrm{mol} / \mathrm{L} \cdot\) atm for Henry's law in the form \(C=k P,\) where \(C\) is the gas concentration in mol/L. Calculate the solubility of \(\mathrm{N}_{2}\) in water when the partial pressure of nitrogen above water is 1.10 atm at \(0^{\circ} \mathrm{C} .\)

Rationalize the trend in water solubility for the following simple alcohols:

In flushing and cleaning columns used in liquid chromatography to remove adsorbed contaminants, a series of solvents is used. Hexane \(\left(\mathrm{C}_{6} \mathrm{H}_{14}\right),\) chloroform \(\left(\mathrm{CHCl}_{3}\right),\) methanol $\left(\mathrm{CH}_{3} \mathrm{OH}\right),$ and water are passed through the column in that order. Rationalize the order in terms of intermolecular forces and the mutual solubility (miscibility) of the solvents.

A solution is prepared by dissolving 52.3 g cesium chloride in 60.0 g water. The volume of the solution is 63.3 \(\mathrm{mL}\) . Calculate the mass percent, molarity, molality, and mole fraction of the CsCl solution.

When pure methanol is mixed with water, the resulting solution feels warm. Would you expect this solution to be ideal? Explain.
See all solutions

Recommended explanations on Chemistry Textbooks

Kinetics

Read Explanation

Chemical Reactions

Read Explanation

The Earths Atmosphere

Read Explanation

Organic Chemistry

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Chemical Analysis

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free