Essentials Of Materials Science And Engineering
Essentials Of Materials Science And Engineering
4th Edition
ISBN: 9781337670845
Author: ASKELAND
Publisher: Cengage
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Chapter 15, Problem 15.37P
Interpretation Introduction

Interpretation:

The amount of BaO that can be added to 1 kg of SiO2 under given conditions should be determined and comparison should be done with addition of Li2O in SiO2.

Concept Introduction:

While glass formation it is important to study chemical, structural and other factors that decide the limits within any type of material that can exist. During the manufacturing of glass the parameters mandatory are the stability of glass, physical nature of glass, inorganic elements and compounds, viscosity, etc. even parameters like rate of cooling, crystallization are very important.

Expert Solution & Answer
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Answer to Problem 15.37P

The amount of BaO that is 1257 g is more than Li2O that is 245 g for 1000 g of SiO2 for making glass.

Explanation of Solution

Given:

Ratio of O:S = 2.5

  OSi=(1O ionsBaO)(fn)+(2O ions SiO2)(1-fn)(1Si ion SiO2)(1-fn)

Where,

fn = mole fraction of BaO

  (1fn) = mole fraction of SiO2

2.5 = (1O ionsBaO)(fn)+(2O ions SiO2)(1-fn)(1Si ion SiO2)(1-fn)

  fn=0.33

The molecular weight of

Silica = 60.08 g/mol

BaO = 137.3 g/mol+16g/mol

=153.3 g/mol

Glass to be produce with

BaO <_ 33.0 mol%

Weight of % BaO is

Weight % BaO =

  =(fn)(153.3)(fn)(153.3)+(1fn)(60.08)×100=(0.33)(153.3)(0.33)(153.3)+(10.33)(60.08)=55.69 %

Amount of BaO required = x grams in 1000 g of SiO2.

Weight of BaO =

  =xx+1000×10055.69100=xx+1000x=1257g

Now, for mole fraction of Li2O

  OSi=(1O ionsLi2O)(fn)+(2O ionsSiO2)(1fn)(1SiionSiO2)(1fn)

2.5= OSi=(1O ionsLi2O)(fn)+(2O ionsSiO2)(1fn)(1SiionSiO2)(1fn)

  fL=0.33

Molecular weight of silica = 60.08 g/mol

And of Li2O=(2×6.94+16) g/mol

= 29.88 g/mol

Adding Li2O<_33.0 mol%

  wt.%Li2O=(fL)(29.88)(fL)(29.88)+(1fL)(60.08)×100

  =(0.33)(29.88)(0.33)(29.88)+(10.33)(60.08)=19.7 %

Let the amount of Li2O require = x g in 1000 g of SiO2.

Amount is

Weight % of Li2O =

  =xx+1000×10019.7100=xx+1000x=245 g

Conclusion

Thus, the amount of BaO that is 1257 g is more than Li2O that is 245 g for 1000 g of SiO2 for making glass.

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