Question

dillell et of polystyrene standards was used to calibrate a GPC column. in times obtained for these standards using THF as eluent and a 1.0 ml/min flow rate are: V (min) 10.83 11.58 12.45 13.66 14.45 15.09 15.96 16.75 18.08 M (g mol-1) 8500000 3040000 1030000 330000 156000 66000 28500 9200 3250 Construct a calibration curve and determine the molecular weight of a polymer sample with elution time V = 13.0 min.

Answer 1

Note that the molecular weight seems to decrease exponentially with increasing elution time. Hence, it will be better to draw a logarithmic calibration curve by taking natural logarithm of Molecular weight in y axis and elution time in x axis.

Hence, the data points we need to plot is

Elution time(min) M(g/mol) In M 10.83 8500000 15.95558 11.58 3040000 14.92737 12.45 1030000 13.84507 13.66 330000 12.70685 14.45 156000 11.95761 15.09 66000 11.09741 15.96 28500 10.25766 16.75 9200 9.126959 18.08 3250 8.08641

Now, plotting ln M vs elution time, we get the following fitted graph

Calibration Curve for elution time vs In M In M y = -1.0859x + 27.543 R2 = 0.9971 11 12 13 16 17 18 19 14 15 Elution time (min)

Hence, the equation of calibration from the graph is

y = -1.0859.+ 27.543

Where y is the natural logarithm of molecular weight and x is the elution time in minutes.

Hence, for a polymer sample with elution time = 13.0 min, we can calculate the molecular weight as follows:

y = -1.0859.7 + 27.543 In M = -1.0859 x 13.0 + 27.543 In M = -14.1167 + 27.543 = 13.4263 = M = €13.4263677591 677600 g/mol

Hence, the molecular weight of the polymer is about 677600 g/mol.

Note: you can simply take the molecular weight in y axis in the plot too but that will result in an exponential plot and is more error prone.