The mathematics of sugar

Biology Level pending

If dehydration synthesis is used to join 35 fructose molecules, 26 glucose molecules, and 54 galactose molecules into a polysaccharide chain in any particular order, the chemical formula of the polysaccharide will be C a H b O c \text{C}_{a}\text{H}_{b}\text{O}_{c} . Find the value of a + b + c a+b+c .


The answer is 2418.

Hobart Pao by Hobart Pao , 23, USA

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1 solution

Hobart Pao
Feb 25, 2016

There will be 115 total hexose (6-C) monosaccharides in the polysaccharide chain. To join them, a total of 114 water molecules will be taken out. Keep in mind that the chemical composition of water is H 2 O \text{H}_{2}\text{O} .

C 6 ⋅ 115 H 6 ⋅ 115 − 114 ⋅ 2 O 6 ⋅ 115 − 114 = C 690 H 1152 O 576 \text{C}_{6 \cdot 115} \, \text{H}_{6 \cdot 115 - 114 \cdot 2} \, \text{O}_{6 \cdot 115 - 114} = \text{C}_{690}\text{H}_{1152}\text{O}_{576}

Finally, what was required was a + b + c a+b+c which equals 690 + 1152 + 576 = 2418 690 + 1152 + 576 = \boxed{2418} .

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