Physical Science
Physical Science
11th Edition
ISBN: 9780077862626
Author: Bill Tillery, Stephanie J. Slater, Timothy F. Slater
Publisher: McGraw-Hill Education
bartleby

Concept explainers

bartleby

Videos

Textbook Question
Book Icon
Chapter 17, Problem 10PEB

An ore deposit consisting of chert and hematite occurs in a deposit measuring 2,500 m long by 1.800 m wide by 75 m high. The deposit has an average specific gravity of 4.3. How many tonnes of iron can potentially be obtained from the mine? (Specific gravity can be converted to density by multiplying by the density of water. Assume SGhematite = 5.3, SGchert = 2.5. and g/cm3 = tonne/m3.)

Expert Solution & Answer
Check Mark
To determine

The tonnes of iron can potentially be obtained from the mine, if hematite and chert occurs in a deposit measuring 2500 m long by 1800 m wide by 75 m high.

Answer to Problem 10PEB

Solution:

6.51×108 tonnes

Explanation of Solution

Given data:

Specific gravity of hematite is 5.3.

Specific gravity of deposit is 4.3.

Specific gravity of chert is 2.5.

Length of the deposit is 2500 m.

Width of the deposit is 1800 m.

Height of the deposit is 75 m.

Density of deposit is 4.3 tonnesm3.

Formula used:

Write the percent of hematite:

% hematite=SGdepositSGchertSGhematiteSGchert×100%

Here, SGdeposit is the specific gravity of deposit, SGhematite is the specific gravity of hematite and SGchert is the specific gravity is chert.

Write the formula for density (ρ):

ρ=mV

Here, V is the volume and m is the mass.

Write the formula for volume:

V=L×W×H

Here, L is the length, W is the width and H is the height.

The mass of hematite in the deposit by multiplying the total mass of the deposit by the ore grade:

mhematite=more(ore grade)

The mass of iron by multipling the mass of hematite by the mass percentage of iron in hematite:

mFe=mhematite(%Fehematite)

Explanation:

Recall the percent of hematite:

% hematite=SGdepositSGchertSGhematiteSGchert×100%

Substitute SGdeposit for 4.3, SGhematite for 5.3 and SGchert for 2.5.

% hematite=4.32.55.32.5×100%=1.82.8×100%=64.3%

Recall the formula for density (ρ):

ρ=mV

Rearrange:

V=mρ

Recall the formula for volume:

V=L×W×H

Substitute mρ for V.

mρ=L×W×Hm=ρ(L×W×H)

Substitute 4.3 tonnesm3 for ρ, 2500 m for L, 1800 m for W and 75 m for H.

m=4.3 tonnesm3(2500 m×1800 m×75 m)=1.45×109 tonnes

Recall the mass of hematite in the deposit by multiplying the total mass of the deposit by the ore grade:

mhematite=more(ore grade)

Substitute 1.45×109 tonnes for more and 64.3% for ore grade.

mhematite=(1.45×109 tonnes)(64.3%)=(1.45×109 tonnes)(64.3)(1100)=9.32×108 tonnes

For Hematite:

The formula: Fe2O3.

The formula weight of Hematite:

AtomsAtomic weightTotal2 of Fe2×28.09 u=111.70 u3 of O3×16 u=48.00 uFormula weight=159.70 u

Recall the mass percent of an element in a compound can be found from:

(atomic weight of Fe)(number of atoms of Fe)formulaweight of Fe3O4×100%of Fe3O4=% of Fe

Substitute (55.85 u Fe) for atomic weight of element, (2) for number of atoms and 159.70 u Fe2O3 for formula weight of compound.

(55.85 u Fe)(2)159.70 u Fe2O3×100% Fe2O3=% of Fe% of Fe=(55.85 Fe)(2)159.70×100%=69.9% Fe

Recall the mass of iron by multiplying the mass of hematite by the mass percentage of iron in hematite:

mFe=mhematite(%Fehematite)

Substitute 9.32×108 tonnes for mhematite and 69.9% for %Fehematite.

mFe=9.32×108 tonnes(69.9%)=9.32×108 tonnes(69.9)(1100)=6.51×108 tonnes

Conclusion:

The mass of iron is 6.51×108 tonnes.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
The initial volume and density of drilling mud are 3800 f3, 65 Ib/f. What is the final volume of drilling mud if the density should be increased to (75 Ib/ft3) using Bentonite (150 Ib/f3).
250 200 150 100 50 10 20 30 40 50 VOLUME (cm') While doing laboratory work on density, a group of students collected data on the mineral pyrite. Their final graph is shown above. If a sample of pyrite has a volume of 50 cm3, what would its mass be? 250 g 175 g 200 g 10 g MASS (grams)
A specimen of shale has a mass of 17.25 g dry and 22.24 g wet.  The volume of the specimen is 12.15 cm3.  What is the porosity of the shale?

Chapter 17 Solutions

Physical Science

Ch. 17 - 11. An aggregation of one or more minerals that...Ch. 17 - 12. Rocks that are formed from molten minerals...Ch. 17 - 13. Igneous rock that slowly cooled deep below...Ch. 17 - 14. The rock that makes up the bulk of Earth’s...Ch. 17 - 15. The rock that makes up the ocean basins and...Ch. 17 - 16. Rocks that are formed from particles of other...Ch. 17 - 17. Accumulations of silt, sand, or other...Ch. 17 - 18. Limestone and dolomite are a. sandstone. b....Ch. 17 - 19. Heat and pressure change rocks into a.igneous...Ch. 17 - 20. The relationship between rocks that are...Ch. 17 - 21. The thin layer that covers Earth’s surface is...Ch. 17 - 22. Based on its abundance in Earth's crust, most...Ch. 17 - 23. The most common rock in Earth's crust is a....Ch. 17 - 24. An intrusive igneous rock will have which type...Ch. 17 - 25. Which igneous rock would have the greatest...Ch. 17 - 26. Which of the following formed from previously...Ch. 17 - 27. Sedimentary rocks are formed by the processes...Ch. 17 - 28. The greatest extent of metamorphic changes has...Ch. 17 - 29. Which type of rock probably existed first,...Ch. 17 - 30. Earth is unique because it has a. CO2 in its...Ch. 17 - 31. The common structural feature of all silicates...Ch. 17 - 32. The one group that is not a subgroup of the...Ch. 17 - 33. The property that is not considered useful in...Ch. 17 - 34. The specific gravity of a mineral depends on...Ch. 17 - 35. Fluorite is a mineral that floats in liquid...Ch. 17 - 36. The group that is not a class of rocks is a....Ch. 17 - 37. The classification of rocks is based on a....Ch. 17 - 38. An example of a sedimentary rock is a....Ch. 17 - 39. The term that does not describe a size of...Ch. 17 - 40. Dissolved rock materials form a. chemical...Ch. 17 - 41. An example of a metamorphic rock is a....Ch. 17 - 42. Extrusive igneous rocks are formed on Earth’s...Ch. 17 - 43. Foliation is found in a. sedimentary rocks. b....Ch. 17 - Prob. 1QFTCh. 17 - Prob. 2QFTCh. 17 - 3. Explain why each mineral has its own unique set...Ch. 17 - 4. Identify at least eight physical properties...Ch. 17 - 5. Explain how the identity of an unknown mineral...Ch. 17 - 6. What is a rock? Ch. 17 - 7. Describe the concept of the rock cycle. Ch. 17 - Prob. 8QFTCh. 17 - 9. Which major kind of rock, based on the way it...Ch. 17 - 10. What is the difference between magma and...Ch. 17 - 11. What is meant by the “texture" of an igneous...Ch. 17 - 12. What are the basic differences between...Ch. 17 - 13. Explain why a cooled and crystallized magma...Ch. 17 - Prob. 14QFTCh. 17 - 15. What are clastic sediments? How are they...Ch. 17 - 16. Briefly describe the rock-forming process...Ch. 17 - 17. What are metamorphic rocks? What limits the...Ch. 17 - 18. Describe what happens to the minerals as shale...Ch. 17 - Prob. 19QFTCh. 17 - 1. What are the significant similarities and...Ch. 17 - 2. Is ice a mineral? Describe reasons to support...Ch. 17 - 3. If ice is a mineral, is a glacier a rock?...Ch. 17 - Prob. 4FFACh. 17 - 1. A sample of the mineral sylvite measures 2.68...Ch. 17 - 2. A rectangular crystal of calcium plagioclase...Ch. 17 - 3. A spherical specimen of the mineral quartz...Ch. 17 - 4. Geologists separate nonferromagnesian silicates...Ch. 17 - 5. Compare the mineral halite (NaCl, hardness of...Ch. 17 - 6. Mica is a sheet silicate while quartz is a...Ch. 17 - 7. Magnesite is a magnesium ore mineral and has...Ch. 17 - 8. Magnetite and hematite are iron ore minerals....Ch. 17 - 9. An iron mine has an ore deposit estimated at...Ch. 17 - 10. An ore deposit consisting of chert and...Ch. 17 - 11. For a given igneous rock type, the proportion...Ch. 17 - 12. Based on Figure 17.13, what is the average...Ch. 17 - 13. A gabbro countertop measuring 4.70 m long by...Ch. 17 - 14. A sandstone building stone measuring 50.0 cm...Ch. 17 - Prob. 15PEB
Knowledge Booster
Background pattern image
Physics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
An Introduction to Physical Science
Physics
ISBN:9781305079137
Author:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres
Publisher:Cengage Learning
Newton's First Law of Motion: Mass and Inertia; Author: Professor Dave explains;https://www.youtube.com/watch?v=1XSyyjcEHo0;License: Standard YouTube License, CC-BY