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MMLU-Pro / 4143 / The number average and weight average molecular-weights are defined as M_n=…

Problem

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question

The number average and weight average molecular-weights are defined as M_n= [(\sumN_i M_i) / (\sumN_i)] = [1 / {\sum(w_i/ M_i)}] and M_w = [(\sumW_iM_i) / (\sumW_i)] = [(\sumN_i M^2_i) / (\sumN_i M_i)] = \sumw_iM_i respectively, where M_i = molecular weight of theithspecies N_i = moles of molecules with molecular weight M_i W_i= weight of material with molecular weight M_i w_i= weight fraction of molecules of theithspecies. Derive equations analogous to the ones above for the number average,X_n, and weight average,X_w, degree of polymerization.

category

chemistry

options

  1. X_n= [(\sumN_i X_i) / (\sumN_i)], X_w= [(\sumN_i X^2_i) / (\sumN_i X_i)]
  2. X_n= [(\sumW_i X_i) / (\sumW_i)], X_w= [(\sumN_i X_i^3) / (\sumW_i X_i)]
  3. X_n= [(\sumN_i X_i) / (\sumN_i X_i^0.5)], X_w= [(\sumN_i X_i^1.5) / (\sumN_i)]
  4. X_n= [(\sumw_i X_i) / (\sumw_i)], X_w= [(\sumN_i X_i^0.5) / (\sumN_i)]
  5. X_n= [(\sumN_i X_i) / (\sumN_i X_i^2)], X_w= [(\sumN_i X^2_i) / (\sumN_i X_i^2)]
  6. X_n= [(\sumN_i X_i^2) / (\sumN_i^2 X_i)], X_w= [(\sumN_i X_i) / (\sumN_i^2)]
  7. X_n= [(\sumN_i X_i^3) / (\sumN_i X_i)], X_w= [(\sumN_i X_i) / (\sumN_i X_i^3)]
  8. X_n= [(\sumN_i X^2_i) / (\sumN_i X_i)], X_w= [(\sumN_i X_i) / (\sumN_i)]
  9. X_n= [(\sumN_i X_i^2) / (\sumN_i X_i)], X_w= [(\sumN_i X_i) / (\sumN_i)]
  10. X_n= [(\sumW_i X_i^2) / (\sumN_i X_i)], X_w= [(\sumW_i X_i) / (\sumW_i X_i^2)]

src

stemez-PhysicalChemistry

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Source and history

upstream_id / Original problem ID
4143
task_id
fa4f33a0-1d67-5963-b35b-c7e02af47cb4
task_key
default--test--4143
task_revision_id
1
config / split
default / test

Official source

initial import