###### Question 45 (Textile Technology & Fibre Science)

The molecular weight (M) of a polymer is determined from Mark-Houwink Equation by using coefficient K = 11.5×10^{−3} ml/g and exponent a = 0.73. If the measured intrinsic viscosity [η] of the solution is 6.0×10^{2} ml/g then the value of M×10^{−6}, (rounded off to two decimal places), is __**2.70 to 3.10**__.

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Formula:

=KM^{a} ,where is viscosity , K is coefficient, M is molecular weight of polymer ,a is constant**As given in the question,**

K=11.5×10^{-3} ml/g,a=0.73 and =6.0×10^{2} ml/g

By putting these values in to the formula-

=KM^{a}

6×10^{2}=11.5×10^{-3} xM^{0.73}

52173.913=M^{0.73}

M^{0.73}=52173.913**By taking log both side-**

log_{e}(M)^{0.73}=log_{e}(52173.913)

0.73log_{e}(M)=10.86,

log_{e}(M)=14.88

M=e^{14.88} , (**By logarithm rule, log _{e} m ^{n}=m log_{e} n and log_{e} m=n to m=e^{n}**)

M=2899358.3 ,

M=2.89×10

^{6}

M=2.89/10

^{-6}

**Mx10**(Answer)

^{-6}=2.89###### Frequently Asked Questions | FAQs

**What is Mark-Houwink equation ?**