Respuesta :
Answer:
Mn = 43,783
Mw = 60,000
Mz = 73,333
narrow distribution = 1.37
Explanation:
The molecular weights of these fractions increase from 20,000 to 100,000 in increments of 20,000. This means their Mi is respectively: (The molar weight (Mi) of the fractions)
Fraction 1 : Mi = 20 *10^3
Fraction 2: Mi = 40 *10^3
Fraction 3 : Mi = 60 *10^3
Fraction 4: Mi = 80 *10^3
Fraction 5 : Mi = 100 *10^3
The ΣMi = 300*10^-3
The Wi (mass of the fractions is for all the fractions the same, let's say 1)
So Wi = 1+1+1+1+1 = 5
Since number of moles = mass / Molar mass
The number of moles is respectively: ni = Wi/Mi (x10^5)
Fraction 1 : ni = Wi/Mi = 1/20000 = 5
Fraction 2: ni = 1/40000 = 2.5
Fraction 3 : ni =1/60000 = 1.67
Fraction 4: ni = 1/80000 = 1.25
Fraction 5 : ni= 1/100000 = 1
The Σni = 11.42
Mn = ΣWi/ni = 5/11.42*10^-5 = 43,783
Mw = (ΣWi * Mi)/ΣWi = 300,000 /5 = 60,000
Mz = (ΣWi * Mi²)/ΣWi *Mi = (4*10^8 +16*10^8 +36*10^8 +64*10^8 +100*10^8) /300,000 =73,333
Mz/Mn = narrow distribution =60,000/43,783 = 1.37
Answer:
Mn=43783 g/mol
Mw=60000 g/mol
Mz=73333 g/mol
Explanation:
Hello,
In this case, since the molar masses of the fractions are 20x10³, 40x10³, 60x10³, 80x10³ and 100x10³, the total molar mass is:
[tex]M_T=20x10^3+40x10^3 +60x10^3+80x10^3+100x10^3=300x10^3g/mol[/tex]
Now, assuming each fraction weights 1 gram, the moles of each fraction turns out:
[tex]n_1=\frac{1g}{20x10^3g/mol}=5x10^{-5} mol\\n_2=\frac{1g}{40x10^3g/mol}=2.5x10^{-5} mol\\n_3=\frac{1g}{60x10^3g/mol}=1.7x10^{-5} mol\\n_4=\frac{1g}{80x10^3g/mol}=1.25x10^{-5} mol\\n_5=\frac{1g}{100x10^3g/mol}=1x10^{-5} mol[/tex]
And the total moles:
[tex]n_T=11.42x10^{-5} mol[/tex]
Therefore,
[tex]Mn=\frac{\Sigma W_i}{n_i} =\frac{5g}{11.42x10^{-5} mol}=43783g/mol[/tex]
[tex]Mw=\frac{\Sigma W_iM_i }{\Sigma W_i}=\frac{300x10^{3}g/mol}{5} =60000g/mol[/tex]
[tex]Mz=\frac{\Sigma W_iM_i^{2}}{\Sigma W_iM_i}=\frac{(4x10^8+1.6x10^9+3.6x10^9+6.4x10^9+10x10^9)g^2/mol^2}{300x10^{3}g/mol}=73333g/mol[/tex]
Best regards.
