Average Molecular Weight Calculation

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson

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

Flashcards

Number-average molecular weight (Mn)

The average molecular weight of a polymer, considering the number of molecules of each molecular weight.

Discrete distribution of molecular weights

A discrete distribution of molecular weights implies that a specific set of molecular weights are present, each with a defined number of molecules.

Equation 5.4: Mn for a discrete distribution

This equation calculates the number-average molecular weight by summing the products of the mole fraction and the molecular weight for each species.

Continuous distribution of molecular weights

A continuous distribution of molecular weights assumes an infinite number of molecular weights within a given range, each with a probability density function.

Signup and view all the flashcards

Equation 5.7: Mn for a continuous distribution

This equation calculates the number-average molecular weight for a continuous distribution by integrating the product of the molecular weight and the probability density function.

Signup and view all the flashcards

Viscosity Average Molecular Weight ($M_v$)

A type of average molecular weight calculated using viscosity measurements. It considers both the molecular weight and the contribution of each molecule to the viscosity.

Signup and view all the flashcards

Exponent 'a' in the $M_v$ equation

The exponent 'a' in the equation for $M_v$ is related to the polymer's shape and how it interacts with the solvent. It's specific to the polymer system studied.

Signup and view all the flashcards

Relationship between $M_v$ and $M_w$ when 'a' is close to 1

When the exponent 'a' approaches 1, the viscosity average molecular weight closely resembles the weight average molecular weight.

Signup and view all the flashcards

Relationship between $M_n$, $M_v$, and $M_w$

The viscosity average molecular weight is usually between the number average ($M_n$) and the weight average ($M_w$) molecular weights.

Signup and view all the flashcards

Using Viscosity for Polymer Characterization

Viscosity measurements can be used to determine the average molecular weight of polymers, providing insights into their size and shape.

Signup and view all the flashcards

Molecular weight distribution

A typical polymer sample contains chains with varying lengths, resulting in a range of molecular weights.

Signup and view all the flashcards

End group analysis

End group analysis involves determining the number of end groups in a polymer chain to calculate the average molecular weight.

Signup and view all the flashcards

Weight-average molecular weight (Mw)

The weight-average molecular weight (Mw) is calculated by considering the weight fraction of each molecular weight in a sample.

Signup and view all the flashcards

Colligative properties

Colligative properties are physical properties of a solution that depend on the concentration of solute particles, including molecular weight.

Signup and view all the flashcards

What is osmotic pressure in membrane osmometry?

A semi-permeable membrane allows only the solvent to pass through, separating the polymer solution from pure solvent. The solvent moves from the pure solvent side to the polymer solution side because of the chemical potential difference. This movement can be stopped by applying pressure. At equilibrium, the pressure needed to prevent this flow is equal to the osmotic pressure.

Signup and view all the flashcards

What factors affect osmotic pressure?

Osmotic pressure depends on both the concentration of the solution and the average molecular weight of the polymer. The higher the concentration and the lower the average molecular weight, the higher the osmotic pressure.

Signup and view all the flashcards

How is osmotic pressure calculated?

To calculate osmotic pressure, we use an equation that considers the concentration, temperature, average molecular weight, and virial coefficients. The virial coefficients account for interactions between the polymer and solvent.

Signup and view all the flashcards

How is the equation for osmotic pressure simplified for real-world applications?

In practice, we can simplify the equation for osmotic pressure by neglecting the higher-order terms. This is because their contributions are usually small compared to the first term.

Signup and view all the flashcards

How is membrane osmometry used to determine the average molecular weight?

A plot of osmotic pressure divided by concentration against concentration allows us to determine the average molecular weight of the polymer. At zero concentration, the y-intercept gives us information about the average molecular weight. The slope of the plot is related to the virial coefficient, which reflects interactions between the polymer and solvent.

Signup and view all the flashcards

Number-Average Molecular Weight ($\bar{M}_n$)

A way to represent the average molecular weight of a polymer, taking into account the number of molecules of each size.

Signup and view all the flashcards

Weight-Average Molecular Weight ($\bar{M}_w$)

An average molecular weight that considers the weight fraction of each molecular weight in a sample, giving more weight to larger molecules.

Signup and view all the flashcards

Weight of molecules with molecular weight $M_i$

The total weight of molecules with a specific molecular weight $M_i$, calculated by multiplying the number of molecules $N_i$ by $M_i$.

Signup and view all the flashcards

Influence of polymerization conditions on average molecular weight

The average molecular weight is determined by the specific conditions under which the polymerization reaction occurs. This includes factors like temperature, catalyst, and monomer concentration.

Signup and view all the flashcards

Molecular weight distribution in polymers

A polymer sample is a mixture of molecules with nearly identical structures but varying chain lengths. The distribution of these lengths depends on the polymerization process and its parameters.

Signup and view all the flashcards

Equation 5.4: $\bar{M}_n$ for discrete distributions

A mathematical equation used to calculate the number-average molecular weight, considering the weight fraction of each molecular weight and the total weight.

Signup and view all the flashcards

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

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Quiz Team

More Like This

Use Quizgecko on...
Browser
Open
Browser
Browser