The following data were obtained for solutions of carboxymethylcellulose flowing through a capillary viscometer.
Concentration (g/L)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.8
Time (s)
64.2
68.4
72.7
77.1
81.5
86.1
91.0
100.5
The Mark-Houwink-Sakurada parameters for carboxymethylcellulose are K = 5.37 × 10–5 Lg–1 and a = 0.73. What is the molecular weight of the carboxymethylcellulose in this experiment?
To calculate the molecular weight of carboxymethylcellulose using the Mark-Houwink-Sakurada (MHS) equation, we need to plot a graph of viscosities against concentration, and use the slope of the line as per the MHS equation.
1. First, calculate the viscosities (η) using the equation:
η = ηt - η0
Where ηt is the flow time in seconds for a particular concentration, and η0 is the flow time for pure solvent (0 g/L concentration).
Using the given data:
η0 = 64.2 s
η = [68.4, 72.7, 77.1, 81.5, 86.1, 91.0, 100.5] s
Calculate the viscosities by subtracting η0 from each η value:
η = [68.4-64.2, 72.7-64.2, 77.1-64.2, 81.5-64.2, 86.1-64.2, 91.0-64.2, 100.5-64.2] = [4.2, 8.5, 12.9, 17.3, 21.9, 26.8, 36.3] s
2. Plot a graph of η (y-axis) against concentration (x-axis) using the given concentration values and calculated viscosities.
3. Fit a straight line to the data points on the graph, and calculate the slope (k) of the line.
4. Using the MHS equation:
ln(η) = ln(K) + a * ln[M]
Where K = 5.37 x 10^(-5) Lg^(-1), a = 0.73, and [M] is the concentration in g/L.
Rearrange the equation to solve for ln[M]:
ln[M] = (ln(η) - ln(K)) / a
5. Substitute the ln(η) values obtained from the graph into the equation and calculate ln[M] for each data point.
6. Calculate the average value of ln[M] from the data points.
7. Finally, calculate the molecular weight (Mw) using the equation:
Mw = 10^(average ln[M])
By following these steps, you should be able to determine the molecular weight of carboxymethylcellulose in this experiment.