Respuesta :
Explanation:
The given data will be as follows.
7 kg of dimethyl terephthalate + 5 kg of Ethylene glycol = 12 kg of product
Formula for weight average number is as follows.
[tex]w_{n} = \sum w_{i} \times M_{i}[/tex]
= [tex]\frac{7}{12} \times M_{DMT} + \frac{5}{12} \times M_{EG}[/tex]
Molecular weight of DMT = 198.21 g/mol
Molecular weight of ET = 62.07 g/mol
Hence, calculate the weight average number as follows.
[tex]\frac{7}{12} \times M_{DMT} + \frac{5}{12} \times M_{EG}[/tex]
= [tex]\frac{7}{12} \times 198.21 g/mol + \frac{5}{12} \times 62.07 g/mol[/tex]
= (115.62 + 25.862) g/mol
= 141.482 g/mol
Since, efficiency is given as 50% = 0.5
0.5 = [tex]\frac{\bar{M_{avg. PET}}}{w_{n}}[/tex]
[tex]\bar{M_{avg. PET}} = 0.5 \times w_{n}[/tex]
= [tex]0.5 \times 141.482 g/mol[/tex]
= 70.741 g/mol
As, [tex]m_{PET} \times \bar{M_{avg. PET}}[/tex] = [tex]m_{DMT} \times M_{DMT} + m_{EG} \times M_{EG}[/tex]
[tex]m_{PET} \times 70.741 g/mol = 7 \times 198.21 g/mol + 5 \times 62.07 g/mol[/tex]
[tex]m_{PET}[/tex] = [tex]\frac{1697.82}{70.741}[/tex]
= 24 g
Thus, we can conclude that the amount of given polymer is 24 g.
