Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 17: Problem 97

Lead(II) carbonate, \(\mathrm{PbCO}_{3}\), is one of the components of the passivating layer that forms inside lead pipes. (a) If the \(K_{s p}\) for \(\mathrm{PbCO}_{3}\) is \(7.4 \times 10^{-14}\) what is the molarity of \(\mathrm{Pb}^{2+}\) in a saturated solution of lead(II) carbonate? (b) What is the concentration in ppb of \(\mathrm{Pb}^{2+}\) ions in a saturated solution? (c) Will the solubility of \(\mathrm{PbCO}_{3}\) increase or decrease as the \(\mathrm{pH}\) is lowered? (d) The EPA threshold for acceptable levels of lead ions in water is 15 ppb. Does a saturated solution of lead(II) carbonate produce a solution that exceeds the EPA limit?

Short Answer

Expert verified
(a) The molarity of \(\mathrm{Pb}^{2+}\) ions in a saturated solution of lead(II) carbonate is approximately \(2.72 \times 10^{-7} \, \mathrm{M}\). (b) The concentration of \(\mathrm{Pb}^{2+}\) ions in ppb is 272 ppb. (c) The solubility of \(\mathrm{PbCO}_{3}\) will increase as the pH is lowered. (d) A saturated solution of lead(II) carbonate produces a solution with a lead ion concentration of 272 ppb, which exceeds the EPA limit of 15 ppb.

Step by step solution

01

Write the chemical equation for the dissolution of \(\mathrm{PbCO}_{3}\)

Begin by writing out the balanced chemical equation for the dissolution of \(\mathrm{PbCO}_{3}\) in water: \[\mathrm{PbCO}_3(s) \rightleftharpoons \mathrm{Pb}^{2+}(aq) + \mathrm{CO}_3^{2-}(aq)\]
02

Find the molarity of \(\mathrm{Pb}^{2+}\) in a saturated solution

Let's denote the molarity of \(\mathrm{Pb}^{2+}\) and \(\mathrm{CO}_3^{2-}\) in the saturated solution of \(\mathrm{PbCO}_{3}\) as \(x\). The solubility product constant, \(K_{sp}\), can be written as: \[K_{sp} = [\mathrm{Pb}^{2+}][\mathrm{CO}_3^{2-}] = x^2\] Substitute the given \(K_{sp}\) value of \(7.4 \times 10^{-14}\). and solve for \(x\): \[7.4 \times 10^{-14} = x^2\] \[x = \sqrt{7.4 \times 10^{-14}} \approx 2.72 \times 10^{-7} \, \mathrm{M}\] The molarity of \(\mathrm{Pb}^{2+}\) ions in a saturated solution of lead(II) carbonate is approximately \(2.72 \times 10^{-7} \, \mathrm{M}\).
03

Convert the molarity to ppb

To convert the molarity of \(\mathrm{Pb}^{2+}\) ions to parts per billion (ppb), use the relationship: \[1 \, \mathrm{M} = 10^9 \, \mathrm{ppb}\] So, the concentration of \(\mathrm{Pb}^{2+}\) in ppb is: \[(2.72 \times 10^{-7} \, \mathrm{M}) \times \frac{10^9 \, \mathrm{ppb}}{1 \, \mathrm{M}} = 272 \, \mathrm{ppb}\]
04

Determine the effect of lower pH on \(\mathrm{PbCO}_{3}\) solubility

Decreasing the pH in the solution will cause an increase in the concentration of \(\mathrm{H}^+\) ions. These ions will react with \(\mathrm{CO}_3^{2-}\) ions in the solution to produce \(\mathrm{HCO}_3^-\) (bicarbonate ions), as shown below: \[\mathrm{H}^+ + \mathrm{CO}_3^{2-} \rightleftharpoons \mathrm{HCO}_3^-\] This reaction will cause the \(\mathrm{CO}_3^{2-}\) ion concentration in the solution to decrease, which, in turn, decreases the denominator of the \(K_{sp}\) expression (as seen in Step 2). As the numerator remains constant, the decrease in the denominator will increase the solubility of \(\mathrm{PbCO}_{3}\). Therefore, the solubility of \(\mathrm{PbCO}_{3}\) will increase as the pH is lowered.
05

Determine if the concentration of \(\mathrm{Pb}^{2+}\) exceeds the EPA limit

From Step 3, the concentration of \(\mathrm{Pb}^{2+}\) ions in a saturated solution of lead(II) carbonate is approximately 272 ppb. The EPA threshold for acceptable levels of lead ions in water is 15 ppb. As 272 ppb is greater than the EPA limit of 15 ppb, a saturated solution of lead(II) carbonate produces a solution in which the lead ion concentration exceeds the EPA limit.

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

Suggest how the cations in each of the following solution mixtures can be separated: (a) \(\mathrm{Na}^{+}\) and $\mathrm{Cd}^{2+},(\mathbf{b}) \mathrm{Cu}^{2+}\( and \)\mathrm{Mg}^{2+},(\mathbf{c}) \mathrm{Pb}^{2+}$ and \(\mathrm{Al}^{3+},(\mathbf{d}) \mathrm{Ag}^{+}\) and \(\mathrm{Hg}^{2+} .\)

Assume that \(30.0 \mathrm{~mL}\) of a \(0.10 \mathrm{M}\) solution of a weak base \(\mathrm{B}\) that accepts one proton is titrated with a \(0.10 \mathrm{M}\) solution of the monoprotic strong acid HA. (a) How many moles of HA have been added at the equivalence point? (b) What is the predominant form of B at the equivalence point? (a) Is the \(\mathrm{pH} 7\), less than 7 , or more than 7 at the equivalence point? (d) Which indicator, phenolphthalein or methyl red, is likely to be the better choice for this titration?

Suppose that a 10 -mL sample of a solution is to be tested for \(\mathrm{I}^{-}\) ion by addition of 1 drop \((0.2 \mathrm{~mL})\) of $0.10 \mathrm{M} \mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}$ What is the minimum number of grams of \(\mathrm{I}^{-}\) that must be present for \(\mathrm{PbI}_{2}(s)\) to form?

Equal quantities of \(0.010 \mathrm{M}\) solutions of an acid HA and a base \(\mathrm{B}\) are mixed. The \(\mathrm{pH}\) of the resulting solution is 9.2 . (a) Write the chemical equation and equilibrium-constant expression for the reaction between HA and B. (b) If \(K_{a}\) for HA is \(8.0 \times 10^{-5}\), what is the value of the equilibrium constant for the reaction between HA and B? (c) What is the value of \(K_{b}\) for \(B\) ?

A solution contains three anions with the following concentrations: $0.20 \mathrm{M} \mathrm{CrO}_{4}^{2-}, 0.10 \mathrm{M} \mathrm{CO}_{3}^{2-},$ and \(0.010 \mathrm{M} \mathrm{Cl}^{-}\). If a dilute \(\mathrm{AgNO}_{3}\) solution is slowly added to the solution, what is the first compound to precipitate: $\mathrm{Ag}_{2} \mathrm{CrO}_{4}\left(K_{s p}=1.2 \times 10^{-12}\right), \mathrm{Ag}_{2} \mathrm{CO}_{3}\left(K_{s p}=8.1 \times 10^{-12}\right)$ or \(\operatorname{AgCl}\left(K_{s p}=1.8 \times 10^{-10}\right) ?\)
See all solutions

Recommended explanations on Chemistry Textbooks

Physical Chemistry

Read Explanation

Kinetics

Read Explanation

Nuclear Chemistry

Read Explanation

Chemistry Branches

Read Explanation

The Earths Atmosphere

Read Explanation

Inorganic Chemistry

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