Average Molecular Weight Calculation
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Questions and Answers

What is a characteristic of molecular-weight distribution in a typical synthetic polymer sample?

  • It consists of chains with uniform lengths.
  • It always has a symmetric distribution. (correct)
  • It is independent of the polymerization conditions.
  • It often contains some molecules of very high molecular weight. (correct)

    • How does the breadth of molecular-weight distribution depend on polymerization?

  • It varies according to specific conditions of polymerization. (correct)
  • It is always narrow regardless of conditions.
  • It generally remains constant across all polymerization types.
  • It has no relation to the conditions of polymerization.

    • Which factor can result in extremely broad molecular-weight distributions in polymers?

  • The polymerization process of certain olefins. (correct)
  • The use of only low molecular weight monomers.
  • The exclusion of any catalysts during polymerization.
  • The cooling rate of the polymer solution.

    • What is one method used to analyze the molecular weight of polymers?

    <p>End group analysis. (D)</p> Signup and view all the answers

    Which type of average is NOT commonly associated with measuring molecular weight of polymers?

    <p>Density average. (C)</p> Signup and view all the answers

    What does N represent in the equation for number-average molecular weight?

    <p>The total number of molecular-weight species in the distribution (A)</p> Signup and view all the answers

    Which of the following equations correctly represents the number-average molecular weight for a discrete distribution?

    <p>$ar{M}_n = rac{ ext{Total of } N_i M_i}{ ext{Sum of } N_i}$ (A)</p> Signup and view all the answers

    What does $n_i$ represent in the formula for number-average molecular weight?

    <p>Mole fraction of species i (D)</p> Signup and view all the answers

    In the continuous distribution function for number-average molecular weight, what is the integration variable?

    <p>M (D)</p> Signup and view all the answers

    Which expression correctly represents the weight fraction $w_i$ of species i?

    <p>$w_i = rac{N_i M_i}{ ext{Total Weight}}$ (D)</p> Signup and view all the answers

    What does the viscosity average molar weight $M_v$ approach as α approaches the value of unity?

    <p>$ar{M}_w$ (B)</p> Signup and view all the answers

    Which statement accurately describes the relationship between the viscosity average, weight average, and number average?

    <p>$M_n &lt; ar{M}_v &lt; ar{M}_w$ (C)</p> Signup and view all the answers

    What happens to the viscosity average molar weight $M_v$ when α equals 1?

    <p>$M_v$ equals $ar{M}_w$ (B)</p> Signup and view all the answers

    In the context of viscosity average molar weight, which parameter does $N_i$ represent?

    <p>The number of molecules of component i (A)</p> Signup and view all the answers

    Which equation represents the calculation of the viscosity average molar weight $M_v$?

    <p>$ar{M}_v = rac{ rac{ ext{Sum of } N_i M_i^{1+a}}{ ext{Sum of } N_i M_i}}{N}$ (B)</p> Signup and view all the answers

    What primarily drives the movement of solvent in membrane osmometry?

    <p>Higher chemical potential in the pure solvent (D)</p> Signup and view all the answers

    How is osmotic pressure ($eta$) expressed in terms of polymer concentration?

    <p>$eta = cRT( rac{1}{M_n} + A_2c + A_3c^2)$ (A)</p> Signup and view all the answers

    What does the slope of the plot of $ rac{eta}{c}$ against $c$ correspond to?

    <p>The virial coefficient $A_2$ (B)</p> Signup and view all the answers

    What is typically neglected in calculations of osmotic pressure?

    <p>Higher-order terms like $c^2$ and $c^3$ (B)</p> Signup and view all the answers

    At equilibrium in membrane osmometry, what condition is met?

    <p>The applied pressure equals the osmotic pressure (A)</p> Signup and view all the answers

    What does the distribution of molecular weights in a synthetic polymer typically include?

    <p>Some molecules of very high molecular weight (C)</p> Signup and view all the answers

    What does the average molecular weight $ar{M}_n$ account for in a polymer sample?

    <p>The lengths of all molecules in the sample (C)</p> Signup and view all the answers

    What is the formula for calculating the average molecular weight $ar{M}_n$ based on molecular weights and their quantities?

    <p>$ar{M}_n = rac{ ext{sum of } N_i imes M_i}{ ext{sum of } N_i}$ (A)</p> Signup and view all the answers

    What constitutes the weight, $W_i$, of a molecule with molecular weight $M_i$?

    <p>$W_i = N_i M_i$ (C)</p> Signup and view all the answers

    Which of the following correctly describes the number-average molecular weight $ar{M}_n$?

    <p>It specifically uses a weighting factor of 1. (B)</p> Signup and view all the answers

    How does the breadth of the molecular-weight distribution change during polymerization?

    <p>It depends on specific polymerization conditions. (B)</p> Signup and view all the answers

    Which equation represents the relationship involving weight-average molecular weight $ar{M}_w$?

    <p>$ar{M}_w = rac{ ext{sum of } W_i}{ ext{sum of } (W_i/M_i)}$ (C)</p> Signup and view all the answers

    What is generally true about the molecular-weight distribution of polymer samples?

    <p>It often contains molecules of varying lengths. (D)</p> Signup and view all the answers

    Study Notes

    Average Molecular Weight

    • The number-average molecular weight (Mn) for a discrete distribution of molecular weights is calculated as follows: Mn = Σ (niMi) / Σ ni = Σ (wi) / Σ (wi/Mi)
    • Where N is the total number of molecular-weight species in the distribution.
    • ni: mole fraction of species i, given by ni = Ni / Σ Ni
    • wi: weight fraction of species i, given by wi = NiMi / Σ NiMi

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    Description

    This quiz covers the calculation of the number-average molecular weight (Mn) for a discrete distribution of molecular weights. Participants will explore formulas that incorporate mole fractions and weight fractions to understand how molecular weights are represented in discrete environments.

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