/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 97 The maximum allowable concentrat... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 13: Problem 97

The maximum allowable concentration of lead in drinking water is 9.0 ppb. (a) Calculate the molarity of lead in a 9.0 ppb solution. (b) How many grams of lead are in a swimming pool containing 9.0 ppb lead in \(60 \mathrm{~m}^{3}\) of water?

Short Answer

Expert verified
(a) Molarity is \(4.34 \times 10^{-8} M\). (b) There are 0.54 grams of lead.

Step by step solution

01

Understanding Parts Per Billion (ppb)

Parts per billion (ppb) is a unit that quantifies the concentration of a substance in a solution. 1 ppb means 1 part of a substance per billion parts of the solution. For water, which is denser enough to assume 1 kg is approximately 1 L, 9.0 ppb of lead suggests there are 9.0 grams of lead in one billion grams of water.
02

Convert ppb to Molarity for Part (a)

To find the molarity, we convert 9.0 grams of lead per billion grams of water to moles per liter. The molar mass of lead (Pb) is 207.2 g/mol. The density of water is assumed to be 1.0 kg/L, so:\[ \text{Moles of Pb} = \frac{9.0\,g}{207.2\,g/mol} = 0.0434\, mol \]Since 1 g of water corresponds to 1 mL, or 1000 g of water correspond to 1 L, then 1 billion grams of water is 1 million liters. Thus:\[ \text{Molarity} = \frac{0.0434\, mol}{1 \times 10^6 \ L} = 4.34 \times 10^{-8} \ M \]
03

Calculate Volume of Water in Liters for Part (b)

The volume of the swimming pool is given as 60 m鲁. Since 1 m鲁 is equivalent to 1000 liters, the volume of the pool in liters is:\[ 60 \ m^3 \times 1000 \ \frac{liters}{m^3} = 60,000 \ liters \]
04

Find Amount of Lead in Grams for Part (b)

Now, calculate the total grams of lead present in 60,000 liters of water at 9.0 ppb. The concentration is 9.0 grams per billion liters (which equates to 1,000,000 liters for 9.0 grams of lead). Therefore,:\[ \text{grams of lead} = \frac{9.0 \ g}{10^9 \ L} \times 60,000 \ L = 0.54 \ grams \]
05

Conclusion of Calculations

For part (a), the molarity of lead in a 9.0 ppb solution is \(4.34 \times 10^{-8} M\). For part (b), there are 0.54 grams of lead in a swimming pool containing 9.0 ppb lead in 60 m鲁 of water.

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Parts Per Billion (ppb)
The term "parts per billion", abbreviated as ppb, is a measure of concentration commonly used in environmental science and chemistry. It denotes the presence of one part of a substance for every billion parts of the total solution.
For example, 9.0 ppb of lead in water implies there are 9.0 grams of lead dispersed in one billion grams of water. Since water can be approximated as having the density of 1 g/mL, this means 9.0 grams in one million liters of water, as 1,000 liters equals 1 cubic meter.
  • This unit of measure is especially useful for detecting trace amounts of pollutants, as it easily expresses minute concentrations.
  • For perspective, one in a billion is equivalent to one second in approximately 32 years.
To convert ppb to other concentration units like molarity, careful attention must be given to the molar mass and volume.
Molar Mass
Molar mass is a fundamental chemical concept that relates to the mass of one mole of a substance. It is expressed in g/mol and can be found by summing the atomic masses of the elements in a compound according to their proportions.
For instance, the molar mass of lead (Pb) is 207.2 g/mol. This means that one mole of lead contains 207.2 grams and Avogadro's number of atoms:
  • To find the number of moles of a substance, divide the mass by the molar mass.
  • Molar mass serves as a conversion factor, bridging mass and mole-based calculations.
Knowing the molar mass is crucial when converting concentrations like ppb into molarity, as it allows for calculation of the moles of solute present.
Solution Concentration
Solution concentration expresses the amount of a solute present in a certain volume of solvent, indicating how dilute or concentrated a solution is. Molarity ( M ), measured in moles of solute per liter of solution, is a common unit for expressing concentration:
  • In molarity calculations, both the number of moles and the volume of the solution are key.
  • For example, to convert ppb to molarity, calculate the moles of solute and divide by the volume in liters.
In the lead example, 9.0 grams per billion grams convert to a molarity of 4.34 脳 10^{-8} M by considering that 1 billion grams is 1 million liters.
Unit Conversion
Unit conversion is the process of converting one unit of measure to another, ensuring that all units in a calculation are consistent. Proper unit conversion is essential in chemistry to allow calculations using different units to communicate accurately.
In converting from ppb to molarity, it's important to:
  • Convert mass to moles using molar mass.
  • Translate the volume from cubic meters to liters if necessary.
For instance, when calculating the amount of lead in a swimming pool, the pool's volume was given in cubic meters, which required conversion to liters (1 m鲁 = 1000 liters). This consistent use of units ensures that complex problems remain manageable and solutions accurate.

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

Consider water and glycerol, \(\mathrm{CH}_{2}(\mathrm{OH}) \mathrm{CH}(\mathrm{OH}) \mathrm{CH}_{2} \mathrm{OH}\). (a) Would you expect them to be miscible in all proportions? (b) List the intermolecular attractions that occur between a water molecule and a glycerol molecule.

Proteins can be precipitated out of aqueous solution by the addition of an electrolyte; this process is called "salting out" the protein. (a) Do you think that all proteins would be precipitated out to the same extent by the same concentration of the same electrolyte? (b) If a protein has been salted out, are the protein-protein interactions stronger or weaker than they were before the electrolyte was added? (c) A friend of yours who is taking a biochemistry class says that salting out works because the waters of hydration that surround the protein prefer to surround the electrolyte as the electrolyte is added; therefore, the protein's hydration shell is stripped away, leading to protein precipitation. Another friend of yours in the same biochemistry class says that salting out works because the incoming ions adsorb tightly to the protein, making ion pairs on the protein surface, which end up giving the protein a zero net charge in water and therefore leading to precipitation. Discuss these two hypotheses. What kind of measurements would you need to make to distinguish between these two hypotheses?

Compounds like sodium stearate, called "surfactants" in general, can form structures known as micelles in water, once the solution concentration reaches the value known as the critical micelle concentration (cmc). Micelles contain dozens to hundreds of molecules. The cmc depends on the substance, the solvent, and the temperature. At and above the \(\mathrm{cmc}\), the properties of the solution vary drastically. (a) The turbidity (the amount of light scattering) of solutions increases dramatically at the \(\mathrm{cmc}\). Suggest an explanation. (b) The ionic conductivity of the solution dramatically changes at the cmc. Suggest an explanation. (c) Chemists have developed fluorescent dyes that glow brightly only when the dye molecules are in a hydrophobic environment. Predict how the intensity of such fluorescence would relate to the concentration of sodium stearate as the sodium stearate concentration approaches and then increases past the \(\mathrm{cmc}\)

Which of the following in each pair is likely to be more soluble in water: \((\mathbf{a})\) cyclohexane \(\left(\mathrm{C}_{6} \mathrm{H}_{12}\right)\) or glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right),\) (b) propionic acid \(\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COOH}\right)\) or sodium propionate \(\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COONa}\right)\) (c) HCl or ethyl chloride ( \(\left.\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{Cl}\right)\) ? Explain in each case.

(a) Calculate the mass percentage of \(\mathrm{NaNO}_{3}\) in a solution containing \(13.6 \mathrm{~g}\) of \(\mathrm{NaNO}_{3}\) in \(834 \mathrm{~g}\) of water. (b) An alloy contains \(2.86 \mathrm{~g}\) of chromium per \(100 \mathrm{~kg}\) of alloy. What is the concentration of chromium in ppm?
See all solutions

Recommended explanations on Chemistry Textbooks

Kinetics

Read Explanation

Inorganic Chemistry

Read Explanation

Nuclear Chemistry

Read Explanation

Physical Chemistry

Read Explanation

Chemistry Branches

Read Explanation

Making Measurements

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.