December 2, 2020

Chapter 8

8-1. To use CRW, you must first specify a mixture name – in this case “Homework 6 2018” and

then searching for the chemicals in the database and adding them to the mixture. There can

be some confusion on what exact chemicals to use from the database. In this case, the

Once the mixture has been populated, we then click the Compatibility Chart button at the

top of the program and our compatibility chart is displayed. The result is shown below.

We have 10 possible binary combinations with these 5 chemicals. Five combinations are

incompatible and 4 have cautions. Only one combination is compatible.

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PREDICTED HAZARDS REPORT

--------------------------------------------------

Chemicals and Reactive Groups in this Mixture:

--------------------------------------------------

ACETIC ANHYDRIDE mixed with itself -

INTRINSIC REACTIVE HAZARDS:

CUMENE HYDROPEROXIDE mixed with ACETIC ANHYDRIDE -

PREDICTED HAZARDS:

CUMENE HYDROPEROXIDE mixed with itself -

INTRINSIC REACTIVE HAZARDS:

METHANOL mixed with ACETIC ANHYDRIDE -

PREDICTED HAZARDS:

METHANOL mixed with CUMENE HYDROPEROXIDE -

PREDICTED HAZARDS:

3

METHANOL mixed with itself -

INTRINSIC REACTIVE HAZARDS:

SULFURIC ACID mixed with ACETIC ANHYDRIDE -

PREDICTED HAZARDS:

POTENTIAL GASES:

SULFURIC ACID mixed with CUMENE HYDROPEROXIDE -

PREDICTED HAZARDS:

SULFURIC ACID mixed with METHANOL -

PREDICTED HAZARDS:

Nitrogen Oxides

SULFURIC ACID mixed with itself -

INTRINSIC REACTIVE HAZARDS:

WATER mixed with ACETIC ANHYDRIDE -

PREDICTED HAZARDS:

WATER mixed with CUMENE HYDROPEROXIDE -

PREDICTED HAZARDS:

--- END OF HAZARDS FOR THIS MIXTURE PAIR ---

WATER mixed with METHANOL -

PREDICTED HAZARDS:

WATER mixed with SULFURIC ACID -

PREDICTED HAZARDS:

WATER mixed with itself -

INTRINSIC REACTIVE HAZARDS:

1. For the binary combinations that are not compatible, special precautions must be done

to ensure these chemicals are not stored together nor accidently mixed. These

combinations are:

2. For the cautions, we need to be aware of these potential reaction hazards. Note that

several of the cautions are predicted to result in an exothermic reaction:

8-2. It can be easily shown that:

0

/ 1 /

Bx Bx T T T

. Thus, the solution here follows

the solution of Example 8-4 and Figure 8-12 in the textbook.

6

e. Equation 8-21 provides the location of the maximum rate:

0.8211

The actual temperature is computed using Equation 8-14:

8-3. a. The total energy in the liquid is:

0

P

Q mC T T

7

8-4. Start with Equation 8-20:

Differentiate with respect to

:

Set equal to 0 and solve for x. Divide first by

exp

Bx

:

8-5. a. Substituting the numbers provided into Equations 8-17 and 8-18:

b. From Equation 8-21:

8

This can be converted to a temperature using Equation 8-14:

The maximum temperature rate is provided by Equation 8-19:

Substituting into Equation 8-26:

c. We can use Figure 8-2 to determine the time. For

10

and B = 0.75 we get

9

8-6. The data are shown below. Since the data points are not equally spaced, we need to use

the Lagrange derivative method to calculate the slope at each point.

Given the data points:

and we wish to compute the derivative at any arbitrary point x where

0 2

x x x

, then

the derivative at x is given by:

Then

To calculate the derivative at the middle point then

1

x x

and the formulas are

simplified somewhat.

To calculate the derivative at the very first point, then

o

x x

and we get the following

equations:

To calculate the derivative at the very last point, then

2

x x

and we get the following

equations:

The raw data table is shown below:

RSST Data

Time Temp. Pressure Time Temp.

********** Lagrange Derivative **********

(min) (deg. C) (psia) (s) (K) a b c dT/dt -1000/T -1000/RgT (dT/dt)/(Tf-T) ln(col L)

0 12.0 309.6 0 285.15 -1.402 1.9022 -0.4885 0.01122 -3.507 -0.4218 7.017E-05 -9.565E+00

101.2 171.9 332.3 6072 445.05 72.963 -92.8646 17.2973 -2.604295 -2.247 -0.2703 2.140E+02 5.366E+00

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Results from above plot:

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Once we have these results, we can use the theoretical model to compare the theoretical results

with the experiment results. This is always important!

1

RESULTS: OTHER RESULTS:

Calculating temperature from theoretical model

Time step: 0.0003

Tau x dx/dtau Time (s) T (K)

0.009 0.009468 1.111523 3848.9 306.851

0.0093 0.009802 1.115648 3855.8 306.898

0.0096 0.010136 1.119802 3862.7 306.944

0.0099 0.010472 1.123985 3869.6 306.991

0.0102 0.01081 1.128198 3876.5 307.038

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8-7. From Equation 8-20:

Differentiate with respect to

:

The term

exp

Bx

can be dropped out of each term.

Divide by

1

n

x

:

Which is the desired result.

Comparison of Experimental Data with Theoretical model - See calculations below

250

270

290

0 1000 2000 3000 4000 5000 6000

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8-8. Start with Equation 8-21:

Substitute these into Equation 8-21 above:

But the square root term in the bottom equation can be simplified to:

Then,

16

8-9. From Equation 8-34,

Here:

Substituting into Equation 8-34,

This is a typical phi-factor for an ARC.

8-10. a. The maximum energy generation will occur at the maximum self-heat rate. From

Example 8-4, the max. self-heat rate is 104 K/min = 1.73 K/s. The heat release rate is

given by:

Substituting the numbers provided:

Other considerations:

b. Heat capacity of water:

Not much difference.

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8-11. Reactor volume = 10 m3

Specific gravity of liquid mixture = 0.97

Heat of reaction = 67.8 kJ/mol

a. For the fastest reaction, operate at the maximum self-heat rate temperature. For a 2:1

b. Molecular weights:

Methanol, CH3OH: 32

Thus,

c. Maximum cooling duty = 30 MJ/min = 5

5.00 10 J/s

Let

m

= molar addition rate of acetic anhydride

d. Total addition time: 4763 kg acetic anhydride

105.5 min 1.75 hours

45.1 kg/min