Problem 4. Even a very small amount of Xanthan gum can lead to a huge change in
ID: 550866 • Letter: P
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Problem 4. Even a very small amount of Xanthan gum can lead to a huge change in the viscosity. Xanthan gum is a polysaccharide polymer with the chemical formula (C3sHagO2)n, i.e. there are n repeating units of the basic monomer CsH49029 (ii) Typical Xanthan gum that is used in food has a polymer length of 8,000 repeating units. What is the molecular weight of the polymer, in g/mol? (ii) If the size (diameter) of a Xanthan gum monomer is 0.6 nm, what is the size (end-to-end length) of the polymer when it is dissolved in solution? Give your answer in nanometers. (iv) Estimate the volume occupied by one xanthan gum polymer? Enter your answer in ml=cm3 (v) Suppose you make a Xanthan gum solution in one mole of water. If you want the solution to have 3% xanthan gum by weight relative to the weight of water how many grams of the xanthan gum polymer do you need? How many molecules of xanthan gum polymer does the solution contain? (vi) What is the total volume of the xanthan gum polymer in the 3% solution described above? Give your answer in mlcm3 Do you think the xanthan gum polymers will be significantly entangled with each other at this concentration? Draw a sketch of the solution.Explanation / Answer
(i) The repeating unit of Xantham gum is C35 H49 O 29
Atomic weight of C, H and O are 12.0107 amu, 1.00794 amu and 15.999 amu respectively.
Molecular weight of monomer is : (12.0107*35 + 1.00794*49 + 15.999*29) g/ mole = 933.735 g/mole
(ii) Total molecular weight of the polymer = Numbers of repeating unit * Molecular weight of monomer = 8000*933.735 g/ mole = 7469880 g/ mole
(iii) Size of the polymer (end to end) = 8000* 0.6 nm = 4800 nm
(iv) Density of the polymer is : 1.5 g/ cm3
So, 1.5 grams of the polymer occupies 1 cc (cubic centimeter) volume
1.5 grams = (1.5/ 7469880) mole of the polymer = 2*10 -7 mole of the polymer = 2*10 -7 * 6.023 * 1023 no. of polymer molecules = 12.046 * 1016 no of polymer molecules which occupy 1 cc volume
So, each polymer molecule occupies 1/(12.046 * 1016 ) cc = 0.083*10-16 cc volume
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