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The Beer-Lambert law relates the absorbance A of a

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 9E Chapter 3.4

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 9E

The Beer-Lambert law relates the absorbance A of a solution to the concentration C of a species in solution by A = MLC, where L is the path length and M is the molar absorption coefficient. Assume that C = 1.25 ± 0.03 mol/cm3, L = 1.2 ± 0.1 cm, and A = 1.30 ± 0.05.

a. Estimate M and find the uncertainty in the estimate.

b. Which would provide a greater reduction in the uncertainty in M: reducing the uncertainty in C to 0.01 mol/cm3, reducing the uncertainty in L to 0.05 cm, or reducing the uncertainty in A to 0.01?

Step-by-Step Solution:
Step 1 of 3

Solution 9E

Step1 of 3:

We have Beer-Lambert law in that A be the absorbance of  a solution to the concentration C of a species and Let A = MLC.

Where,

L = Path length.

   = 1.2 ± 0.1 cm.

M = the molar absorption coefficient.

C = 1.25 ± 0.03 mol/cm3.

A = 1.30 ± 0.05.

Here our goal is:

a).We need to estimate M and find the uncertainty in the estimate.

b).We need to check Which would provide a greater reduction in the uncertainty in M: reducing the uncertainty in C to 0.01 mol/cm3, reducing the uncertainty in L to 0.05 cm, or reducing the uncertainty in A to 0.01?

Step2 of 3:

a).

We have C = 1.25, L = 1.2, A = 1.30 and

Let

   A = MLC

M =

             =

      =

       = 0.8667

Hence, M = 0.8667.

1).Consider,

M =

Differentiate above equation with respect to “A” then

   

             =

       =(1)

          =

  =

     = 0.6667

Hence, = 0.6667.

 

2).Consider,

M =

 Differentiate above equation with respect to “L” then

   

             =

               =

                  =

             =()

 

         =

                  =

        =

       = -0.7222

Hence, = -0.7222.

3).Consider,

M =

 Differentiate above equation with respect to “C” then

   

             =

               =

 ...

Step 2 of 3

Chapter 3.4, Problem 9E is Solved
Step 3 of 3

Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

The full step-by-step solution to problem: 9E from chapter: 3.4 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. The answer to “The Beer-Lambert law relates the absorbance A of a solution to the concentration C of a species in solution by A = MLC, where L is the path length and M is the molar absorption coefficient. Assume that C = 1.25 ± 0.03 mol/cm3, L = 1.2 ± 0.1 cm, and A = 1.30 ± 0.05.a. Estimate M and find the uncertainty in the estimate.________________b. Which would provide a greater reduction in the uncertainty in M: reducing the uncertainty in C to 0.01 mol/cm3, reducing the uncertainty in L to 0.05 cm, or reducing the uncertainty in A to 0.01?” is broken down into a number of easy to follow steps, and 100 words. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. Since the solution to 9E from 3.4 chapter was answered, more than 394 students have viewed the full step-by-step answer. This full solution covers the following key subjects: uncertainty, reducing, solution, estimate, mol. This expansive textbook survival guide covers 153 chapters, and 2440 solutions.

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