Thepayment sugar beet growers receive is based on the sucrose content of their d

Question

Thepayment sugar beet growers receive is based on the sucrose content of their delivered beets. A sample is taken from each load of beets and the sugar content in the beets is determined by polarimetry of the beet extract. In a typical situation 50 grams of pulverized beet tissue is homogenized with 360ml of dilute aluminum sulfate. The homogenate is filtered and the optical rotation is determined by use of a polarimeter. For one sample, the following observation were noted:

Tube length=4 decimeters

temperature=20 degree celsius

optical rotation (a)= +4.97 degree

total volume of extract=405ml

1. how much sucrose was contained in the 50 gram sample?

2. If the sugar beet grower receives $0.145 for each pound of sugar, what would he receive for one metric ton (1000Kg) of beet?

Explanation / Answer

Homogenate = 50 g/360 ml
[]o = (100)
(l)(c)
[]o = +66.5 deg cm² g-1 for pure sucrose
c = (100)
(l) []o
= 4.97o x 100
40 cm x 66.5 deg cm² g-1
= 0.1868 g/100 ml
Total volume extract = 405 ml
100 ml contained 0.1868 g
50 g sample yielded 405 ml sucrose
405 ml = 0.1868 x (405/100) g
= 0.7565 g

2) 50 g beets produced 0.7565 g of sucrose
1000 kg of beets = 1,000,000 g beets
1 g beets = 0.7565 g sucrose
50
1 metic ton beets = 1,000,000 g beets
1,000,000 g beets = 0.7565 x 1,000,000 g sucrose
50
= 15,130.80 g sucrose
= 15.13 Kg
1 pound = 0.45359 Kg
0.45359 kg sucrose = $0.145
15.13 Kg = $0.145 x 15.13
0.45359
= $4.84



1 pound of sugar = $0.145

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