Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 20: Problem 29

Slaked lime, \(\mathrm{Ca}(\mathrm{OH})_{2},\) is used to soften hard water by removing calcium ions from hard water through the reaction $$ \begin{array}{r}{\mathrm{Ca}(\mathrm{OH})_{2}(a q)+\mathrm{Ca}^{2+}(a q)+2 \mathrm{HCO}_{3}^{-}(a q) \rightarrow} \\ {2 \mathrm{CaCO}_{3}(s)+2 \mathrm{H}_{2} \mathrm{O}(l)}\end{array} $$ Although \(\mathrm{CaCO}_{3}(s)\) is considered insoluble, some of it does dissolve in aqueous solutions. Calculate the molar solubility of \(\mathrm{CaCO}_{3}\) in water $\left(K_{\mathrm{sp}}=8.7 \times 10^{-9}\right) .$

Short Answer

Expert verified
The molar solubility of \(\mathrm{CaCO}_{3}\) in water is approximately \(2.95 \times 10^{-5}\) M, using the given \(K_{\mathrm{sp}} = 8.7 \times 10^{-9}\) and solving for \(s\).

Step by step solution

01

Write the dissociation reaction and \(K_{\mathrm{sp}}\) expression for \(\mathrm{CaCO}_{3}\).

Dissolving \(\mathrm{CaCO}_{3}\) in water, we have: \[ \mathrm{CaCO}_{3}(s) \rightleftharpoons \mathrm{Ca^{2+}}(aq) + \mathrm{CO}_{3}^{2-}(aq) \] Let \(s\) be the molar solubility of \(\mathrm{CaCO}_{3}\) in water. Then, the concentration of \(\mathrm{Ca^{2+}}\) and \(\mathrm{CO}_{3}^{2-}\) will both be \(s\). The \(K_{\mathrm{sp}}\) expression for the dissociation is: \[K_{\mathrm{sp}} = [\mathrm{Ca^{2+}}][\mathrm{CO}_{3}^{2-}] = (s)(s) = s^2\] Now, we are given \(K_{\mathrm{sp}} = 8.7 \times 10^{-9}\). We will use this information to solve for \(s\).
02

Solve for the molar solubility (\(s\)).

To find the molar solubility, we set up the following equation: \[ K_{\mathrm{sp}} = s^2 \] Substitute the given value of \(K_{\mathrm{sp}}\): \[ 8.7 \times 10^{-9} = s^2 \] Now, solve for \(s\): \[ s = \sqrt{8.7 \times 10^{-9}} \] Calculating this value gives: \[ s \approx 2.95 \times 10^{-5} \] Hence, the molar solubility of \(\mathrm{CaCO}_{3}\) in water is approximately \(2.95 \times 10^{-5}\) 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

What trade-offs must be made between kinetics and thermodynamics in the Haber process for the production of ammonia? How did the discovery of an appropriate catalyst make the process feasible?

What is the hybridization of the central atom in each of the following molecules? a. \(\mathrm{SF}_{6}\) b. \(\mathrm{ClF}_{3}\) c. \(\mathrm{GeCl}_{4}\) d. \(\mathrm{XeF}_{4}\)

Although nitrogen trifluoride \(\left(\mathrm{NF}_{3}\right)\) is a thermally stable compound, nitrogen triiodide (NI \(_{3} )\) is known to be a highly explosive material. \(\mathrm{NI}_{3}\) can be synthesized according to the equation $$ \mathrm{BN}(s)+3 \mathrm{IF}(g) \longrightarrow \mathrm{BF}_{3}(g)+\mathrm{NI}_{3}(g) $$ a. What is the enthalpy of formation for \(\mathrm{NI}_{3}(s)\) given the enthalpy of reaction \((-307 \mathrm{kJ})\) and the enthalpies of formation for $\mathrm{BN}(s)(-254 \mathrm{kJ} / \mathrm{mol}), \mathrm{IF}(g)(-96 \mathrm{kJ} / \mathrm{mol})\( and \)\mathrm{BF}_{3}(g)(-1136 \mathrm{kJ} / \mathrm{mol}) ?$ b. It is reported that when the synthesis of \(\mathrm{NI}_{3}\) is conducted using 4 moles of IF for every 1 mole of \(\mathrm{BN}\) , one of the by-products isolated is $\left[\mathrm{IF}_{2}\right]^{+}\left[\mathrm{BF}_{4}\right]^{-} .$ What are the molecular geometries of the species in this by-product? What are the hybridizations of the central atoms in each species in the by-product?

The heaviest member of the alkaline earth metals is radium (Ra), a naturally radioactive element discovered by Pierre and Marie Curie in \(1898 .\) Radium was initially isolated from the uranium ore pitchblende, in which it is present as approximately 1.0 g per 7.0 metric tons of pitchblende. How many atoms of radium can be isolated from \(1.75 \times 10^{8} \mathrm{g}\) pitch- blende \((1 \text { metric ton }=1000 \mathrm{kg})\) ? One of the early uses of radium was as an additive to paint so that watch dials coated with this paint would glow in the dark. The longest-lived isotope of radium has a half-life of \(1.60 \times 10^{3}\) years. If an antique watch, manufactured in \(1925,\) contains 15.0 \(\mathrm{mg}\) radium, how many atoms of radium will remain in 2025\(?\)

Although He is the second most abundant element in the universe, it is very rare on the earth. Why?
See all solutions

Recommended explanations on Chemistry Textbooks

Organic Chemistry

Read Explanation

Chemistry Branches

Read Explanation

Nuclear Chemistry

Read Explanation

Kinetics

Read Explanation

Inorganic Chemistry

Read Explanation

Physical 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