Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 3: Problem 86

The important natural sources of boron compounds are the minerals kernite, \(\mathrm{Na}_{2} \mathrm{B}_{4} \mathrm{O}_{7} \cdot 4 \mathrm{H}_{2} \mathrm{O}\) and borax, \(\mathrm{Na}_{2} \mathrm{B}_{4} \mathrm{O}_{7} \cdot 10 \mathrm{H}_{2} \mathrm{O} .\) How much additional mass of mineral must be processed per kilogram of boron obtained if the mineral is borax rather than kernite?

Short Answer

Expert verified
The additional mass of mineral that must be processed per kilogram of boron obtained if the mineral is borax rather than kernite is approximately 0.12 kg.

Step by step solution

01

Determine the Molar Mass of Boron

Firstly, use the periodic table to determine the molar mass of each element in the compounds. Boron (B) is 10.81 g/mol.
02

Calculate the molar mass of Kernite and Borax

Next, calculate the molar mass of kernite \(\mathrm{Na}_{2} \mathrm{B}_{4} \mathrm{O}_{7} \cdot 4 \mathrm{H}_{2} \mathrm{O}\) and borax \(\mathrm{Na}_{2} \mathrm{B}_{4} \mathrm{O}_{7} \cdot 10 \mathrm{H}_{2} \mathrm{O}\). For Kernite, it is (2*22.99) + (4*10.81) + (7*16.00) + (8*1.008) = 381.376 g/mol. For Borax, it is (2*22.99) + (4*10.81) + (7*16.00) + (20*1.008) = 411.376 g/mol.
03

Find the proportion of Boron

Now determine the mass fraction of boron in kernite and borax. The mass of Boron in kernite is \(4*10.81\) = 43.24 g. The mass fraction of boron in kernite is \(43.24 / 381.376\) and for borax is same, but divided by the molar mass of borax: \(43.24 / 411.376\)
04

Compare the mass needed

Finally, we will determine how much more borax is needed to yield the same amount of boron as kernite. If 1 kg of boron is obtained from kernite, the mass of borax needed will be \(1 / (43.24 / 411.376)\) kg. Then subtract the mass of kernite (1kg) to determine the additional mass needed.

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

Nitrogen forms five oxides in which its oxidation states are \(+1,+2,+3,+4,\) and \(+5,\) respectively. Write appropriate formulas for these compounds.

All of the following minerals are semiprecious or precious stones. Determine the mass percent of the indicated element. (a) \(\mathrm{Zr}\) in zircon, \(\mathrm{ZrSiO}_{4}\) (b) Be in beryl (emerald), \(\mathrm{Be}_{3} \mathrm{Al}_{2} \mathrm{Si}_{6} \mathrm{O}_{18}\) (c) Fe in almandine (garnet), \(\mathrm{Fe}_{3} \mathrm{Al}_{2} \mathrm{Si}_{3} \mathrm{O}_{12}\) (d) S in lazurite (lapis lazuli), \(\mathrm{Na}_{4} \mathrm{SSi}_{3} \mathrm{Al}_{3} \mathrm{O}_{12}\)

Three of the following formulas might be either an empirical or a molecular formula. The formula that must be a molecular formula is (a) \(\mathrm{N}_{2} \mathrm{O} ;\) (b) \(\mathrm{N}_{2} \mathrm{H}_{4}\) (c) \(\mathrm{NaCl} ;\) (d) \(\mathrm{NH}_{3}\)

The organic solvent thiophene is a carbon-hydrogensulfur compound that yields \(\mathrm{CO}_{2}, \mathrm{H}_{2} \mathrm{O},\) and \(\mathrm{SO}_{2}\) when burned in an excess of oxygen. When subjected to combustion analysis, a \(1.3020 \mathrm{g}\) sample of thiophene produces \(2.7224 \mathrm{g} \mathrm{CO}_{2}, 0.5575 \mathrm{g} \mathrm{H}_{2} \mathrm{O},\) and \(0.9915 \mathrm{g} \mathrm{SO}_{2} .\) What is the empirical formula of thiophene?

Without per frming detailed calculations, indicate which of the following hydrates has the greatest \% \(\mathrm{H}_{2} \mathrm{O}\) by mass: \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}, \quad \mathrm{Cr}_{2}\left(\mathrm{SO}_{4}\right)_{3} \cdot 18 \mathrm{H}_{2} \mathrm{O}, \quad \mathrm{MgCl}_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O}\) and \(\mathrm{LiC}_{2} \mathrm{H}_{3} \mathrm{O}_{2} \cdot 2 \mathrm{H}_{2} \mathrm{O}\)
See all solutions

Recommended explanations on Chemistry Textbooks

Kinetics

Read Explanation

Chemical Analysis

Read Explanation

Inorganic Chemistry

Read Explanation

Chemical Reactions

Read Explanation

Physical Chemistry

Read Explanation

Chemistry Branches

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