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CBSE Class 12-science Answered

In a polymer sample 30% of molecules have a molecular mass 20,000, 40% have 30,000 and the rest 60,000. What is the weight average molecular mass of the polymer? (1) 40,300, (2) 30,600, (3) 43,333, (4) 50,400

Asked by patra04011965 | 14 May, 2019, 07:55: AM
Expert Answer
The correct option is (3)
Given:
 
n1 = 30
 
n2 = 40
 
n3 = 30
 
M1 = 20000
 
M2 = 30000
 
M3 = 60000
 
We have,
 
stack straight M subscript straight w space with straight _ on top equals space fraction numerator begin display style sum from blank to blank of niMi squared end style over denominator sum from blank to blank of niMi end fraction

space space space space space equals space fraction numerator straight n subscript 1 straight M squared subscript 1 space plus space straight n subscript 2 straight M squared subscript 2 space plus space straight n subscript 3 straight M squared subscript 3 space over denominator straight n subscript 1 straight M subscript 1 space plus space straight n subscript 2 straight M subscript 2 space plus space straight n subscript 3 straight M subscript 3 space end fraction

space space space space space space equals space fraction numerator 30 open parentheses 20000 close parentheses squared plus space 40 open parentheses 30000 close parentheses squared space plus space 30 cross times open parentheses 60000 close parentheses squared over denominator 30 open parentheses 20000 close parentheses plus space 40 open parentheses 30000 close parentheses plus space 30 cross times open parentheses 60000 close parentheses end fraction

space space space space space space equals fraction numerator open parentheses 120 cross times 10 to the power of 8 thin space plus space 360 space cross times 10 to the power of 8 space plus space 1080 cross times 10 to the power of 8 close parentheses over denominator open parentheses 60 cross times 10 to the power of 4 thin space plus space 120 space cross times 10 to the power of 4 plus space 180 cross times 10 to the power of 4 close parentheses end fraction

space space space space space space space equals fraction numerator open parentheses 120 thin space plus space 360 space plus space 1080 close parentheses cross times 10 to the power of 8 over denominator 10 to the power of 4 open parentheses 60 plus 120 plus 180 close parentheses end fraction

space space space space space space space equals fraction numerator 1560 cross times 10 to the power of 4 over denominator 360 end fraction

space stack straight M subscript straight w space with straight _ on top equals space 43333
 
Mass average molecular mass of the polymer is 43333.
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