The y-intercept obtained from the plot of viscosity of a series of polymer solutions against the concentration is 0.05. The proportionality constant K and exponent a for this polymer – solvent pair are 5 ×10^-5 and 0.5, respectively. The molar mass of the polymer in g mol^-1 is

Concept:

Viscosity:

• The viscosity of a fluid is a measure of its resistance to deformation at a given rate. 
• Viscosity is the internal frictional force between adjacent layers of fluid that are in relative motion. Viscosity depends on a fluid's state such as temperature, pressure, and rate of deformation.
• The internal frictional force (F) between adjacent layers can be measured by using the equation:

​\({\rm{F = \eta A}}{{\rm{u}} \over {\rm{y}}}\),  where \(\eta\) is the viscosity of the fluid, A is the area of each plate, \({u \over y}\) is the rate of shear deformation.

The Mark-Houwink equation gives a relationship between intrinsic viscosity \(\left[ \eta \right]\) and molecular weight [M]. The Mark-Houwink equation is 

\(\left[ \eta \right] = K{M^\alpha }\).  Where K is a constant.

Explanation:

The y-intercept obtained from the plot of the viscosity of a series of polymer solutions against the concentration is 0.05. Thus,

 \(\left[ \eta \right]\) = 0.05.

The proportionality constant K is 5 ×10-5 and exponent \(\alpha \) for this polymer–solvent pair is 0.5.

Thus, from the Mark-Houwink equation 

​\(0.05 = 5 \times {10^{ - 5}} \times {[M]^{0.5}}\)

\({[M]^{0.5}} = 1000 \)

\([M] = {10^6} \)

Conclusion:

Hence, the molar mass of the polymer in g mol-1 is 106