Solution Found!
In modeling the effect of an impurity on crystal growth,
Chapter 2, Problem 2.37(choose chapter or problem)
In modeling the effect of an impurity on crystal growth, the following equation was derived: G-Ch Go - G where C is impurity concentration, Ch is a limiting growth rate, Go is the growth rate of the crystal with no impurity present, and KL and m are model parameters. In a particular experiment, Go = 3.00 X 10-3 mm/min. and GL = 1.80 X 10-3 mm/min. Growth rates are measured for several impurity concentrations C (parts per million, or ppm), with the following results: 39 I C (ppm) 50.0 75.0 100.0 125.0 150.0 I I I G(mm/min) X 10 1.90 I 3 2.50 2.20 2.04 1.95 I (For example, when C = 50.0 ppm, G = 2.50 X 10-3 mm/min). (a) Determine KL and m, giving both numerical values and units. (b) A solution is fed to a crystallizer in which the impurity concentration is 475 ppm. Estimate the expected crystal growth rate in (mm/min). Then state why you would be extremely skeptical about this result.
Questions & Answers
QUESTION:
In modeling the effect of an impurity on crystal growth, the following equation was derived: G-Ch Go - G where C is impurity concentration, Ch is a limiting growth rate, Go is the growth rate of the crystal with no impurity present, and KL and m are model parameters. In a particular experiment, Go = 3.00 X 10-3 mm/min. and GL = 1.80 X 10-3 mm/min. Growth rates are measured for several impurity concentrations C (parts per million, or ppm), with the following results: 39 I C (ppm) 50.0 75.0 100.0 125.0 150.0 I I I G(mm/min) X 10 1.90 I 3 2.50 2.20 2.04 1.95 I (For example, when C = 50.0 ppm, G = 2.50 X 10-3 mm/min). (a) Determine KL and m, giving both numerical values and units. (b) A solution is fed to a crystallizer in which the impurity concentration is 475 ppm. Estimate the expected crystal growth rate in (mm/min). Then state why you would be extremely skeptical about this result.
ANSWER:Step 1 of 2
a)
The following expression is used to get a linear relationship.
C = Impurity concentration
Let’s take the logarithm of both sides of the equation.
The data of growth rates at different impurity concentrations are shown in the following table.
From the given,
Let’s calculate the “C” value and 
Now plot the values of 
From the equation of the straight line obtained from plot;
Therefore, the value of 
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