Degree of polymerization (number-average vs weight-average)

What is the DPn and DPw if a sample consists of:
        50g of cellulose polymerized by 100 glucose molecules
        30g of cellulose polymerized by 200 glucose molecules
        20g of cellulose polymerized by 500 glucose molecules


Number-average degree of polymerization (DPn) - weighed by mole fraction (number of moles)
        MW of glucose = (c.a.) 180
        Number of moles should be 50 / (100*180) = 0.00277,  0.000833,  0.000222, respectively.
        DPn = (0.00277*100 + 0.000833*200 + 0.000222*500) / (0.00277+0.000833+0.000222) = 145
        Experimentally, it is determined by measuring the osmotic pressure of polymer.


Weight-average degree of polymerization (DPw) - weighed by weight fraction
        DPw = (50*100 + 30*200 + 20*500) / (50+30+20) = 210
        Experimentally, it is determined using Rayleigh light scattering.

% ionic character of covalent bonding

Among covalent bonding, it is called "ionic bonding" for those that have "% ionic character" greater than 50%.

        % ionic character = [1-exp(-0.25*(Xa-Xb)^2)] *100
        where Xa and Xb are electro-negativity of each element

determination of polarity of a compound

All ionic compounds (e.g., CaCO3) are polar.

To investigate whether a compound is polar, fuse the compound and see if its molten state conducts electricity (e.g., CaCO3 at 900C,  Mg(OH2) at 325C).  A non-polar compound in its molten state does not conduct electricity.

On the determination of polarity,
the electrical properties of polar systems containing giant molecules (like crystals) differ markedly from those in which the dipoles are on small molecules.


General idea for calculation of dipole moments,
In the simplest case, a positive charge +Q and a negative charge -Q separated by a distance R produce a measurable dipole moment(D) equal to (Q×R).
1) find atomic radius of Ca2+ and Mg2+ and ionic radius of OH- and (CO3)2-, and their charges,
2) convert them in esu unit, then apply the formula.

Experimentally try to find suitable solvents for Mg(OH)2 and CaCO3,
dissolve a certain amount of solute in solvents, measure magnetic moment in magnetic field.

Chemical Concentration (M, %, N, m)

Molarity (M) = mole of solute / volume of solvent = mol/L

Percent concentration (%) = mass of solute / mass of solvent *100 = %
(density of solution should be considered converting between M and %.)

Normality (N) = molarity * equivance = mol/L
e.g., 1M H2SO4 = 1N SO42- = 2N H+

Molality (m) = mole of solute / mass of solvent = mol/kg