Considering the following polymer size fractions of a given polymer sample:
Fraction Molecular Weight Number of Chains
1 6,500 400
2 10,000 1000
3 1,000,000 8
(a) Calculate the number-average molecular weight of the polymer.
(b) Calculate the weight-average molecular weight of the polymer.
(c) Which average molecular weight did the 8 chains of molecular weight of 1,000,000 most significantly affect? why?
(d) Calculate the polydispersity index(PI = (Mw/Mn) of the polymer

Answers

Answer 1

Answer:

Explanation:

From the information given:

Molecular weight Mi      Number of chains (Ni)      NiMi

400                                           6500                        2600000

1000                                         10000                       10000000

8                                               1000000                   8000000

[tex]\sum_{Ni} = 1408[/tex]                                                [tex]\sum _{NiMi}[/tex] = 20600000

Thus, the average number of molecular weight = [tex]\dfrac{\sum_{NiMi}}{\sum_{Ni} }[/tex]

[tex]= \dfrac{20600000}{1408}[/tex]

= 14630.68

b)

weight-average molecular weight  = [tex]\dfrac{\sum _{NiMi^2} }{\sum _{NiMi}}[/tex]

[tex]Ni[/tex]                  [tex]Mi[/tex]             [tex]Mi^2[/tex]                     [tex]Ni[/tex] [tex]Mi^2[/tex]

400              6500          42.25 × 10⁶        16.9  × 10⁹

1000             10000        100 × 10⁶            100 × 10⁹

8                   1000000    1 × 10¹²               800 × 10⁹

                                                                [tex]\sum _{NiMi^2} = 916.9 \times 10^9[/tex]

weight-average molecular weight   [tex]=\dfrac{916.9 \times 10^9 }{20.6 \times 10^6}[/tex]

= 44509.71

c)

The number average molecular weight is most significantly affected. This is because the number average molecular weight value is worth more in comparison to the weight-average molecular weight.

d)

The polydispersity index (PI) = [tex]\dfrac{\overline {M_W}}{\overline {M_n}}[/tex]

[tex]PI = \dfrac{44509.71}{14630.68}[/tex]

PI = 3.04


Related Questions

Determine the mass of oxygen that is needed to react with 33 grams of phosphorus.
4P + 5 O2 → 2 P205
A
27.3 grams O2
B
1.33 grams O2
С
213 grams 02
D
42.6 grams 02

Answers

Answer:

D =  42.6 g

Explanation:

Given data:

Mass of oxygen needed = ?

Mass of phosphorus react = 33 g

Solution:

Chemical equation:

4P + 5O₂     →      2P₂O₅

Number of moles of phosphorus:

Number of moles = mass/molar mass

Number of moles = 33 g/ 30.97 g/mol

Number of moles = 1.065 mol

now we will compare the moles of P and oxygen.

                P         :       O₂

                4         :        5

          1.065        :        5/4×1.065 = 1.33mol

Mass of oxygen needed:

Mass = number of moles × molar mass

Mass = 1.33 mol × 32 g/mol

Mass = 42.6 g

The weight loss of an aluminum alloy corroding in a solution of hydrochloric acid was observed to be 0.250 g/cm2 after an 8 h immersion period [13]. What is the corresponding anodic current density in milliamperes per square centimeter, assuming that all the corrosion is due to the following anodic half-cell reaction:

Answers

This question is incomplete, the complete question is;

The weight loss of an aluminum alloy corroding in a solution of hydrochloric acid was observed to be 0.250 g/cm² after an 8 h immersion period [13]. What is the corresponding anodic current density in milliamperes per square centimeter, assuming that all the corrosion is due to the following anodic half-cell reaction:

Al → Al³⁺ + 3e⁻

The atomic weight is 58.7 g/mol

Answer:

Current density in milliamperes per square centimeter is 45.81 mA/cm²

Explanation:

Given the data in the question;

we know that Faradays law of electrolysis states that;

amount of substance produced at each electrode is directly proportional to the quantity of charge flowing through the cell.

so

m = ( Q/F) (M/z)

where m is the mass of substance liberated at an electrode( 0.250 g/cm²)

Q is the total electric charge passed through the substance

F is Faradays constant (96,500 C/mol)

M is the molar mass of the substance( 58.7 g/mol )  and Z is the number of electrons transferred(3)

Also

we know that; Q = It

where I is current and t is time( 8hrs × 60 × 60 = 28800 sec )

we substitute  Q = It  into our equation'

we have;

m = ( It/F) (M/z)

m = ItM / Fz

mFz = ItM

I = mFz / tM

so we substitute

I = [0.250 g/cm² × 96,500 C/mol × 3] / [ 28800 × 58.7 g/mol]

I = 72375 /  1690560

I = 0.04581 A/cm²

we know that; 1 ampere = 1000 milliampere

so

I = 0.04581 × 1000

I = 45.81 mA/cm²

Therefore, current density in milliamperes per square centimeter is 45.81 mA/cm²

Calculate the volume of a box which is 125 cm long, 37 cm wide, and 68 cm high. Report your answer with correct significant figures in cubic centimeters. please use significant figures!

Calculate the volume of a box which is 423 cm long, 12 cm wide, and 25 cm high. have significant figures in cubic centimeters.

Suppose you are measuring the mass of a solid sample on a balance using a weigh boat. You record the data in a table. Mass of weigh boat 1.326 g Mass of weigh boat and sample 7.635 g What is the mass of the solid sample?

A graduated cylinder contains 10.00 mL water. A 14.74 g piece of aluminum is added to the water, and the volume rises to 15.46 mL. What is the density of the aluminum?

A 24.5 g sample of solution has a density of 0.768 g/mL. What is the sample volume (in mL)?

Answers

Answer:

1. Volume of box is 314500 cm³.

2. Volume of box 126900 cm³.

3. Mass of sample is 6.309 g.

4. Density of aluminum is 2.7 g/mL.

5. Volume of sample is 31.9 mL.

Explanation:

1. Determination of the volume of the box

Length (L) = 125 cm

Width (W) = 37 cm

Height (H) = 68 cm

Volume (V) =?

V = L × W × H

V = 125 × 37 × 68

V = 314500 cm³

2. Determination of the volume of the box

Length (L) = 423 cm

Width (W) = 12 cm

Height (H) = 25 cm

Volume (V) =?

V = L × W × H

V = 423 × 12 × 25

V = 126900 cm³

3. Determination of the mass of the sample.

Mass of weigh boat = 1.326 g

Mass of weigh boat + Sample = 7.635 g Mass of the sample =?

Mass of Sample = (Mass of weigh boat + Sample) – (Mass of weigh boat)

Mass of Sample = 7.635 – 1.326

Mass of Sample = 6.309 g

4. Determination of the density of aluminum.

Volume of water = 10 mL

Mass of aluminum = 14.74 g

Volume of water + aluminum = 15.46 mL

Density of aluminum =?

Next, we shall determine the volume of aluminum. This can be obtained as follow:

Volume of water = 10 mL

Volume of water + aluminum = 15.46 mL

Volume of aluminum =?

Volume of aluminum = (Volume of water + aluminum) – (Volume of water)

Volume of aluminum = 15.46 – 10

Volume of aluminum = 5.46 mL

Finally, we shall determine the density of aluminum. This can be obtained as follow:

Mass of aluminum = 14.74 g

Volume of aluminum = 5.46 mL

Density of aluminum =?

Density = mass / volume

Density of aluminum = 14.74 / 5.46

Density of aluminum = 2.7 g/mL

5. Determination of the volume of sample.

Mass of sample = 24.5 g

Density of sample = 0.768 g/mL.

Volume of sample =?

Density = mass / volume

0.768 = 24.5 / volume of sample

Cross multiply

0.768 × Volume of sample = 24.5

Divide both side by 0.768

Volume of sample = 24.5 / 0.768

Volume of sample = 31.9 mL.

The mass of an unidentified rock is 15.5 grams. Students determine the volume of the rock by placing the rock in a cylinder with water. What was the density of the rock that the students should have calculated?

Hint: The graduated cylinder measures volume. Read the difference in water level.

Answers

The concept of water by displacement. D=m/v therefore m=15.5 g and volume=5 mL (final - initial) then calculate the density

Which factor can help balance Earth’s temperature?

Answers

Answer:

Clouds

Explanation:

Because I just got it right

PLEASE HELP ASAP I NEED IT HELP PEASEEEEEEEEEEE it’s number 4 (this is science)

Answers

Here you go:
Continent Polar - Cold and Dry
Maritime Polar - Cold and Humid
Arctic - Extremely Cold and Dry
Maritime Tropical- Warm and Humid

Hope this helps:)

Cellular respiration is? (Single choice.)
A. a chemical reaction that converts energy from food molecules by way of oxygen into a usable energy called ATP.
B. a chemical reaction that converts carbon dioxide and water into glucose and oxygen.
C. a chemical reaction that converts that occurs only in animals.
D. a chemical reaction that occurs only in plants.

Answers

The answer would be A

A student is given a sample of an unknown solid and asked to identify it. The student begins by making a list of questions to investigate about the sample.
BRAINLY QUICK!

Which question would be the least useful in helping the student identify the sample?


A) Is the sample soluble in water?

B) What is the weight of the sample?

C) Is the sample attracted to a magnet?

D) What is the melting point of the sample?

Answers

Answer:

B) What is the weight of the sample?

Explanation:

The least useful question for the student to identify the sample is "What is the weight of the sample?"

To identify a sample, it is important to know its solubility (homogenous or heterogenous), chemical properties such as melting and boiling point, and whether sample is attracted towards the magnet or not to know the nature of the sample.

Weights is the least useful characteristic of a sample that can help to identify the sample.

Hence, the correct answer is "B) What is the weight of the sample?".

PLEASE HELP!! PLEASE HELP PLEASE HELP PLEASE HELP PLEASE HELP PLEASE HELP PLEASE HELP PLEASE HELP PLEASE HELP PLEASE HELP PLEASE HELP PLEASE HELP PLEASE HELP

CHEMJSTRY!! LONE PAIRS WILL GIVE BRAINLIEST IF CORRECT!

Answers

Answer:

T

Explanation:

T is what you are looking for

Based on the organization and colors in the periodic table, which
two elements do you think are most similar in terms of their properties:
magnesium (Mg), barium (Ba), and gold (Au)? Explain.

Answers

Answer:

Magnesium (Mg) and Barium (Ba) are most similar in terms of properties.

Explanation:

The periodic table of elements is organized with elements classified by atomic number. Each column in the table represents elements grouped together by protons in the nucleus and as a result of that also charge. The first column of elements have a +1 charge, while the second column have a +2 charge.

Electronegativity, mass and weight can also be determined by the location of elements in the table, with elements becoming more electronegative from left (least amount) to right (most) and more heavy from top to bottom. Because Magnesium and Barium are in the same column, while gold is in a different column (and assigned a different color) it indicates the element gold is not like the other two and has different properties.

Based on the organization of elements in the  periodic table, the two elements that will be similar are magnesium (Mg), barium (Ba).

The periodic table is arranged in rows called periods and columns called groups.

Elements in the same group of the periodic table are chemically similar because they have the same number of electrons in their outermost shell and consequently undergo the same kind of chemical reactions.

Having said that, Barium and magnesium both belong to group 2 of the periodic table hence they have the similar properties because they are all members of the same group.

Learn more: https://brainly.com/question/11155928

A 558 mg of a mixture of fluorene and benzoic acid was weighed out and subjected to an extraction and recrystallization. After this purification was completed the product crystals were dried and analyzed. The purification procedure produced 185 mg of fluorene and 144 mg of benzoic acid. Calculate the percent composition of this mixture.

Answers

Answer:

See explanation

Explanation:

Mass of mixture of  fluorene and benzoic acid = 558 mg

Mass of pure fluorene  after purification = 185 mg of fluorene

Mass of pure  benzoic acid after purification = 144 mg of benzoic acid

Percentage of fluorene int he mixture = 185mg/558mg * 100 = 33.15 %

Percentage of benzoic acid in the mixture = 144mg/558mg * 100 = 25.81 %

Percentage of impurities = 100% - [33.15 + 25.81]

Percentage of impurities = 100 - 58.96

Percentage of impurities = 41.04 %

You are working in the lab and spill some acid on the counter. Because you don't want to get into trouble, you decide to clean it up by yourself. What would be best to reduce the acidity of the spill?

Answers

Answer:

By adding baking soda

Explanation:

The best way to reduce the acidity of the spill would be to add some amount of baking soda to the spill and then clean it up with a towel or any other appropriate item.

Baking soda is made up of sodium bicarbonate and has the capacity to react with acid to produce a salt and carbonic acid. The carbonic acid readily decomposes to produce carbon dioxide and water. For example, sodium bicarbonate reacts with hydrochloric acid according to the equation below:

  [tex]NaHCO_3 + HCl --> NaCl + H_2CO3[/tex]

   [tex]H_2CO_3 --> H_2O + CO_2[/tex]

One would expect the addition of a base to the spilled acid to work in a way as to neutralize the acid but bases are also corrosive and only a stoichiometrically balanced quantity would completely neutralize the acid. Thus, the quantity might not easily be determinable and one can end up doing more harm than good.

Hence, the best option is to add baking soda to the spilled acid to reduce its acidity before cleaning it off.

What type of charge do ionic compounds have

Answers

Answer:neutral

Explanation:ionic compounds is between a cation and anion so they cancel eachother out

Which conclusion was a direct result of the gold foil experiment?

Answers

led to the conclusion that each atom in the foil was composed mostly of empty space because most alpha particles directed at the foil

To see the number of atoms of an element in a given molecule we need to multiply stoichiometry to the number that is written on the foot of the element that is stoichiometry. Therefore, each atom in the foil was composed mostly of empty space because most alpha particles directed at the foil.

What is atom?

Atom is the smallest particle of any element, molecule or compound. Atom can not be further divided. Atoms contains nucleus in its center and electron that revolve around the atom in fixed orbit.

In the nucleus, proton and neutron are present. Electron has -1 charge while proton has +1 charge. Neutron is neutral that is it has no charge. So overall the charge of nucleus is due to only proton, not by neutron.

Each atom in the foil was composed mostly of empty space because most alpha particles directed at the foil. This conclusion was the direct result of the gold foil experiment.

To know more about atom, here:

https://brainly.com/question/13518322

#SPJ2

A chemist determines by measurements that .060 moles of nitrogen gas participate in a chemical reaction. Calculate the mass of nitrogen gas that participates. Be sure your answer has the correct number of significant digits.

Answers

Answer:

1.7 g N₂

Explanation:

In order to convert moles of nitrogen gas (N₂) to grams, we'll use its molar mass:

Molar mass of N₂ = (Atomic Mass of N)*2 = (14.00 g/mol)*2 = 28.00 g/mol0.060 mol N₂ * 28.00 g/mol = 1.68 g N₂

0.060 only has two significant digits, so the reported answer should have two significant digits as well. Meaning the answer is 1.7 g.

Do the substances that are reactants in a chemical reaction remain the same after the reaction is complete?

Answers

The first answer is nine you are currently correct

23. How many different elements are in the compound sodium carbonate (Na2CO3)? *
a. 1
b. 3
C. 6
d.7​

Answers

Na, C, and O so the answer is c. 3

What is the mass of 4.70 mol H2O? Answer in units of g.

Answers

Answer:

4.70 moles of water have mass of 84.6g

Explanation:

Given data:

Number of moles of water = 4.70 mol

Mass in gram = ?

Solution:

Formula:

Mass = number of moles × molar mass

Molar mass of water is 18 g/mol

Mass = 4.70 mol × 18 g/mol

Mass = 84.6 g

Thus, 4.70 moles of water have mass of 84.6g.

Pls help, science 8th grade question, #11 thx :)

Answers

D, KOH is a concentrated Base and HCL is an acid. D is the only one that has these two.

atomic radius(size)______ from left to right across a period on the periodic table

Answers

Answer:

Decreases

Explanation:

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