Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 5: Problem 7

Determine the concentration of the ion indicated in each solution. (a) \(\left[\mathrm{K}^{+}\right]\) in \(0.238 \mathrm{M} \mathrm{KNO}_{3} ;\) (b) \(\left[\mathrm{NO}_{3}\right]\) in \(0.167 \mathrm{M} \mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2} ;(\mathrm{c})\left[\mathrm{Al}^{3+}\right]\) in \(0.083 \mathrm{M} \mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3};\) (d) \(\left[\mathrm{Na}^{+}\right]\) in \(0.209 \mathrm{M} \mathrm{Na}_{3} \mathrm{PO}_{4}\).

Short Answer

Expert verified
The concentrations are as follows: (a) \([ \mathrm{K}^{+} ]= 0.238 \mathrm{M} \), (b) \([ \mathrm{NO}_{3}^{-} ]= 0.334 \mathrm{M} \), (c) \([ \mathrm{Al}^{3+} ]= 0.166 \mathrm{M} \), (d) \([ \mathrm{Na}^{+} ]= 0.627 \mathrm{M} \)

Step by step solution

01

Understanding Dissociation

For an ionic compound, when it dissolves in water, it dissociates into its ions. The stoichiometry of the reaction will tell how many of each ion are produced.
02

Determine the concentration of \( \mathrm{K}^{+} \) ions in \(0.238 \mathrm{M} \mathrm{KNO}_{3}\)

Potassium nitrate (\( \mathrm{KNO}_{3} \)) dissociates in water to yield potassium (\( \mathrm{K}^{+} \)) and nitrate (\( \mathrm{NO}_{3}^{-} \)) ions in a 1:1 ratio. Therefore, the concentration of \( \mathrm{K}^{+} \) ions will also be \(0.238 \mathrm{M}.\)
03

Determine the concentration of \( \mathrm{NO}_{3}^{-} \) ions in \(0.167 \mathrm{M} \mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}\)

The calcium nitrate (\( \mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2} \)) dissociates in water yielding calcium (\( \mathrm{Ca}^{2+} \)) and nitrate ions (\( \mathrm{NO}_{3}^{-} \)), but due to the subscript '2' in the formula, two nitrate ions are produced per molecule. Therefore, the concentration of \( \mathrm{NO}_{3}^{-} \) ions will be \(2 \times 0.167 = 0.334 \mathrm{M}. \)
04

Determine the concentration of \( \mathrm{Al}^{3+} \) ions in \(0.083 \mathrm{M} \mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\)

The aluminum sulfate (\( \mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3} \)) dissociates in water to give aluminum (\( \mathrm{Al}^{3+} \)) and sulfate (\( \mathrm{SO}_{4}^{2-} \)) ions. There are two aluminum ions for each formula unit in solution. Therefore, the concentration of \( \mathrm{Al}^{3+} \) ions will be \(2 \times 0.083 = 0.166 \mathrm{M}. \)
05

Determine the concentration of \( \mathrm{Na}^{+} \) ions in \(0.209 \mathrm{M} \mathrm{Na}_{3}\mathrm{PO}_{4}\)

The sodium phosphate (\( \mathrm{Na}_{3}\mathrm{PO}_{4} \)) dissociates in water to yield sodium (\( \mathrm{Na}^{+} \)) and phosphate (\( \mathrm{PO}_{4}^{3-} \)) ions. There are three sodium ions for each formula unit dissolved. Therefore, the concentration of \( \mathrm{Na}^{+} \) ions will be \(3 \times 0.209 = 0.627 \mathrm{M}.\)

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

An iron ore sample weighing \(0.9132 \mathrm{g}\) is dissolved in \(\mathrm{HCl}(\mathrm{aq}),\) and the iron is obtained as \(\mathrm{Fe}^{2+}(\mathrm{aq}) .\) This solution is then titrated with \(28.72 \mathrm{mL}\) of \(0.05051 \mathrm{M}\) \(\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7} .\) What is the mass percent Fe in the ore sample? \(6 \mathrm{Fe}^{2+}+14 \mathrm{H}^{+}+\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-} \longrightarrow_{6 \mathrm{Fe}^{3+}}+2 \mathrm{Cr}^{3+}+7 \mathrm{H}_{2} \mathrm{O}\)

Iron (Fe) is obtained from rock that is extracted from open pit mines and then crushed. The process used to obtain the pure metal from the crushed rock produces solid waste, called tailings, which are stored in disposal areas near the mines. The tailings pose a serious environmental risk because they contain sulfides, such as pyrite ( \(\mathrm{FeS}_{2}\) ), which oxidize in air to produce metal ions and \(\mathrm{H}^{+}\) ions that can enter into surface water or ground water. The oxidation of \(\mathrm{FeS}_{2}\) to \(\mathrm{Fe}^{3+}\) is described by the unbalanced chemical equation below. \(\mathrm{FeS}_{2}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \longrightarrow\) \(\quad \mathrm{Fe}^{3+}(\mathrm{aq})+\mathrm{SO}_{4}^{2-}(\mathrm{aq})+\mathrm{H}^{+}(\mathrm{aq}) \quad(\text { not balanced })\) Thus, the oxidation of pyrite produces \(\mathrm{Fe}^{3+}\) and \(\mathrm{H}^{+}\) ions that can leach into surface or ground water. The leaching of \(\mathrm{H}^{+}\) ions causes the water to become very acidic. To prevent acidification of nearby ground or surface water, limestone \(\left(\mathrm{CaCO}_{3}\right)\) is added to the tailings to neutralize the \(\mathrm{H}^{+}\) ions: \(\mathrm{CaCO}_{3}(\mathrm{s})+2 \mathrm{H}^{+}(\mathrm{aq}) \underset{\mathrm{Ca}^{2+}}{\longrightarrow}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l})+\mathrm{CO}_{2}(\mathrm{g})\) (a) Balance the equation above for the reaction of \(\mathrm{FeS}_{2}\) and \(\mathrm{O}_{2}\). [ Hint: Start with the half-equations \(\mathrm{FeS}_{2}(\mathrm{s}) \rightarrow\) \(\left.\mathrm{Fe}^{3+}(\mathrm{aq})+\mathrm{SO}_{4}^{2-}(\mathrm{aq}) \text { and } \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{H}_{2} \mathrm{O}(1) .\right]\) (b) What is the minimum amount of \(\mathrm{CaCO}_{3}(\mathrm{s})\) required, per kilogram of tailings, to prevent contamination if the tailings contain \(3 \%\) S by mass? Assume that all the sulfur in the tailings is in the form \(\mathrm{FeS}_{2}\).

We want to determine the acetylsalicyclic acid content of a series of aspirin tablets by titration with \(\mathrm{NaOH}(\mathrm{aq})\) Each of the tablets is expected to contain about \(0.32\) \(\mathrm{g}\) of \(\mathrm{HC}_{9} \mathrm{H}_{7} \mathrm{O}_{4} \cdot\) What molarity of \(\mathrm{NaOH}(\mathrm{aq})\) should we use for titration volumes of about \(23\) \(\mathrm{mL}\) ? (This procedure ensures good precision and allows the titration of two samples with the contents of a 50 mL buret.) \(\mathrm{HC}_{9} \mathrm{H}_{7} \mathrm{O}_{4}(\mathrm{aq})+\mathrm{OH}^{-}(\mathrm{aq}) \longrightarrow_{\mathrm{C}_{9} \mathrm{H}_{7} \mathrm{O}_{4}^{-}}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(1)\)

A \(25.00 \mathrm{mL}\) sample of \(0.132 \mathrm{M}\) \(\mathrm{HNO}_{3}\) is mixed with \(10.00 \mathrm{mL}\) of \(0.318 \mathrm{M} \mathrm{KOH} .\) Is the resulting solution acidic, basic, or exactly neutralized?

Phosphorus is essential for plant growth, but an excess of phosphorus can be catastrophic in aqueous ecosystems. Too much phosphorus can cause algae to grow at an explosive rate and this robs the rest of the ecosystem of oxygen. Effluent from sewage treatment plants must be treated before it can be released into lakes or streams because the effluent contains significant amounts of \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\) and \(\mathrm{HPO}_{4}^{2-}\). (Detergents are a major contributor to phosphorus levels in domestic sewage because many detergents contain \(\mathrm{Na}_{2} \mathrm{HPO}_{4}\) ) A simple way to remove \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\) and \(\mathrm{HPO}_{4}^{2-}\) from the effluent is to treat it with lime, \(\mathrm{CaO}\) which produces \(\mathrm{Ca}^{2+}\) and \(\mathrm{OH}^{-}\) ions in water. The \(\mathrm{OH}^{-}\) ions convert \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\) and \(\mathrm{HPO}_{4}^{2-}\) ions into \(\mathrm{PO}_{4}^{3-}\) ions and, finally, \(\mathrm{Ca}^{2+}, \mathrm{OH}^{-}\), and \(\mathrm{PO}_{4}^{3-}\) ions combine to form a precipitate of \(\mathrm{Ca}_{5}\left(\mathrm{PO}_{4}\right)_{3} \mathrm{OH}(\mathrm{s})\) (a) Write balanced chemical equations for the four reactions described above. [Hint: The reactants are \(\mathrm{CaO}\) and \(\mathrm{H}_{2} \mathrm{O} ; \mathrm{H}_{2} \mathrm{PO}_{4}^{-}\) and \(\left.\mathrm{OH}^{-} ; \mathrm{HPO}_{4}^{2-} \text { and } \mathrm{OH}^{-} ; \mathrm{Ca}^{2+}, \mathrm{PO}_{4}^{3-}, \text { and } \mathrm{OH}^{-} .\right]\) (b) How many kilograms of lime are required to remove the phosphorus from a \(1.00 \times 10^{4}\) L holding tank filled with contaminated water, if the water contains \(10.0 \mathrm{mg}\) of phosphorus per liter?
See all solutions

Recommended explanations on Chemistry Textbooks

Organic Chemistry

Read Explanation

Kinetics

Read Explanation

Chemical Reactions

Read Explanation

Chemistry Branches

Read Explanation

Making Measurements

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