Question

1) (25 points) The molecular weight of a polymer can be determined from its viscosity by the following relationship where [n] is the intrinsic viscosity of the polymer M, is the viscosity averaged molecular weight, and K and a are constants specific for the polymer. The intrinsic viscosity is determined experimentally be determining the efflux time, or the time it takes for the polymer solution to flow between two etched lines in a capillary viscometer, at several different concentrations of dilute polymer, and extrapolating to infinite dilution. A plot of to _ versus c should yield a straight line, with a y intercept equal to [n]. The concentration of the polymer solution is c, t is the efflux time of the polymer solution, and to is the efflux time of the solvent without polymer. Using the data below of efflux times for dilute solutions of polystyrene in methyl ethyl ketone at 25°C and the constants K 3.9 x 104 and a 0.58, find the molecular weight of the polystyrene sample. Solve it using MATLAB's polyfit. EffluxTime, s Polymer Concentration, g/d O (pure solvent 004 83 89 0.06 0.08 0.10 0.12 0.14 0.16 0.20 95 104 114 126 139 155 191

Answer 1

Consider the given statement from textbook, to determine the molecular weight of polymer from its viscosity. It is given that. Now by using excel to solved this problem is as below. There are various steps to solve this problem. Step1:-write the given data is as below 83 0.04 89 0.06 95 104 0.08 0.1 114 0.12 126 0.14 139 0.16 155 191 0.2 K 3.90E-04 0.58 Step2:-now calcualte the value of in all columns with their related values. In which the value of 6-83. Now use the formula (B35BS2-1)/A3 in all cells to find value (t/t0-1)/c 83 0.04 89 1.80723 0.06 952.40964 104 3.16265 0.08 114 3.73494 0.12 126 4.31727 0.14 0.16 139 4.81928 155 5.42169 0.2 191 6.50602 K 3.90E-04 0.58

Step3:- Now calculate the value of molecular weight by using the formula (INTERCEPT(C3:C10,A3:A10)/B12)A(1/B13) is as below, t(t/t0-1)/c 83 0.04 891.80723 0.06 95 2.40964 0.08 0.1 104 3.16265 114 3.73494 0.12 126 4.31727 0.14 1394.81928 0.16 155 5.42169 0.2 1916.50602 K 3.90E-04 0.58 M 433273 Step4 now Go to INSERT option and then select Scattered plot is as below Seriesi 0 0.1 0.2 0 0.05 0.15 0.25

Step5:-Now Double click on the plotted point and then select as Add to Trendline is as below AA Series 6 Delete 4 翼 こ Reset to Match Style ab Change Series Chart Type.. Se riest Select Data 3-D Rotation. Add Data Labels Add Trendline 0 Format Data Series... 0.1 0

Step6:- After clicking there is a window opened. Then there tick on the Linear also clicked on Display equation on chart value and tick Display on R2 value on chart is as below Format Trendline Trendine Optons Trendline Options Trend/Regression Type Line Color Line Style Exponential Shadow Linear Glow and Soft Edges Polynomial Orer: 2 Power Moving Average Period: 2 Trendline Name , Automatic : Linear (Senesi) Custom: Forecast Forward: 0.0 periods Backward: 0.0 periods ロSet Intercept- 10.0 Display Equation on chart Display R-squared value on chart Close

Step7:- After click on Close button then the value is dispalyed as given below, y 29.309x 0.7251 Seriesi Linear (Series1) 0 0.05 0 015 0.0.25 2m Hence, the molecular weight is and the best fit equation is mole y29.309x+0.7251and the R2 value is 0.9976

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