# Concentration of fluid

The following growth equation was derived for color-dyed rock candy:

(see the attachment for the equation), where R is growth rate in units (mm/min) and C is concentration of dye in parts per million (ppm). Growth rate data was collected for the following concentrations:

(see the attachment for the table)

a) What are the numerical values and units of A and m?

b) For a dye concentration of 400ppm, what is the estimated growth rate? Are you confident in this estimate, why or why not?

Sulfuryl chloride is used in the production of pesticides. The decomposition of sulfuryl chloride, SO_2Cl_2 -> SO_2 + Cl_2 follows a first order rate law such that the concentration of SO_2Cl_2 as a function of time is described by the following exponential function (see the attachment for the function). C_A is the concentration of SO_2Cl_2 at any time (t) and C_A0 is the concentration at time = zero. The reaction was carried out and concentrations measured at various times to obtain the data below.

(see the attachment for the table)

a) What are the units of C_A0 and k?

b) How should you plot the data to obtain a straight line on a plot with rectangular coordinates?

c) Plot the data as you described in part b and determine the numerical values of C_A0 and k.

#### Solution Preview

I have attached the answers in a docx, and xlsx files. I will also paste the answer here, but it is best viewed in the docx file.

3.The given equation is

((R-1.8x?10?^(-3) mm/min))/(3x?10?^(-3) mm/min-R)=1/(AC^m )

Where R is in mm/min and C in ppm. Values of C and the corresponding R are given in the table, here reproduced.

C (ppm) 50 75 100 125 150

R (mm/min) 0.0025 0.0022 0.00204 0.00195 0.0019

In order to find the values A and m that they ask for, we need to use two given values of C and corresponding values of R. Any two would work. For example, if we use the first two:

When C = 50 ppm and R = 0.0025 mm/min, we plug these in the equation to get

((.0025-1.8x?10?^(-3) mm/min))/(3x?10?^(-3) mm/min-.0025)=1/(A?50?^m )

This reduces to

1.4=1/(A ?50?^m )

Which we can rewrite as:

A=1/(1.4 ?50?^m )

We get another equation from using the second values of C and R:

C = 75 ...

#### Solution Summary

The full working Solution is given to the growth equation questions for color-dyed rock candy and sulfuryl chloride.