1. A seed crystal of diameter D (mm) is placed in a solution of dissolved salt,
ID: 700797 • Letter: 1
Question
1. A seed crystal of diameter D (mm) is placed in a solution of dissolved salt, and new crystals are observed to form at a constant rate r (crystals/min). Experiments with seed crystals of different sizes show that the rate of formation varies with the seed crystal diameter as r(crystals/min) = 200D-10D2 a. What are the units of the constants 200 and 10? b. Calculate the formation rate in crystals/s corresponding to a diameter of 0.050". c. Derive a formula for r' (crystals/s) in terms of D (inches)Explanation / Answer
Part a
Units of 200 D are same as units of r
200 D = crystals/min
200 (mm) = crystals/min
200 = crystals/(min-mm)
Similarly
Units of 10 D2 are same as units of r
10 D2 = crystals/min
10 (mm2) = crystals/min
10 = crystals/(min-mm2)
Part b
Convert the given dia in mm
D = 0.050 in x 25.4mm/in = 1.27 mm
r = 200 D - 10 D2
r = [200 crystals/(min-mm)] x 1.27 mm - [10 crystals/(min-mm2)] x (1.27 mm)2
r = 254 - 16.129 = 237.871 crystals/min x 1min/60s
r = 3.965 crystals/s
Part C
r' = 200 (D' in x 25.4mm/in) - 10 (D' in x 25.4mm/in)2
r' = (5080 D' - 6451.6 D'2) crystals/min x 1min/60s
r' (crystals/s) = 84.66 D' - 107.53 D'2
Where D' in inches.
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