Ron Larson
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7.1 Linear Patterns

7.1 Linear Patterns
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  • 13. Absorbance of Light Using Blue No. 1

    The figure shows light passing through a glass container that contains a substance. Absorbance is a unitless measure of the amount of light that a substance absorbs as light passes through it.

    data folder

    The table shows the absorbance of light with a wavelenght of 630 nanometers for a solution of the food dye Blue No.1 in a 1-centimeter glass container at various concentrations.

    1. Describe the pattern of the absorbance values
    2. Make a scatter plot of the data.
    3. Predict the next absorbance value in the pattern.

    (See Example 5 and Example 6.)

    • Worked-Out Solution
      1. Each time the concentration increases by 1 milligram per liter, the absorbance increases by 0.164.
      2. A scatter plot of the data is shown using a spreadsheet.

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      1. The next absorbance value in the pattern would be for a concentration of 5 milligrams per liter. The absorbance for this concentration should be

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     __   _     ______  __    __   _    _    _    _   
| || | ||  /_   _// \ \\ / // | || | || | |  | || 
| '--' ||   -| ||-   \ \/ //  | || | || | |/\| || 
| .--. ||   _| ||_    \  //   | \\_/ || |  /\  || 
|_|| |_||  /_____//    \//     \____//  |_// \_|| 
`-`  `-`   `-----`      `       `---`   `-`   `-`
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  • 14. Absorbance of Light Using Green No. 3

    The figure shows light passing through a glass container that contains a substance. Absorbance is a unitless measure of the amount of light that a substance absorbs as light passes through it.

    The table shows the absorbance of light with a wavelength of 625 nanometers for a solution of the food dye Green No. 3 in a 1-centimeter glass container at various concentrations.

    1. Describe the pattern of the absorbance values.
    2. Make a scatter plot of the data.
    3. Predict the next absorbance value in the pattern.

    (See Example 5 and Example 6.)

    data folder

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     _    _    __   __    ______   __   __    ______  
| || | ||  \ \\/ //  /_____//  \ \\/ //  /_   _// 
| || | ||   \ ` //   `____ `    \ ` //   `-| |,-  
| \\_/ ||    | ||    /___//      | ||      | ||   
 \____//     |_||    `__ `       |_||      |_||   
  `---`      `-`'    /_//        `-`'      `-`'   
                     `-`
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  • 15. Absorbance of Light Using Red No. 3

    The figure shows light passing through a glass container that contains a substance. Absorbance is a unitless measure of the amount of light that a substance absorbs as light passes through it.

    The table shows the absorbance of light with a wavelength of 527 nanometers for a solution of the food dye Red No. 3 with a concentration of 4 milligrams per liter in glass containers of various path lengths.

    1. Describe the pattern of the absorbance values.
    2. Make a scatter plot of the data.
    3. Predict the next absorbance value in the pattern.

    (See Example 5 and Example 6.)

    • Worked-Out Solution
      1. Each time the path length increases by 0.2 centimeter, the absorbance increases by 0.088.
      2. A scatter plot of the data is shown using a spreadsheet.

      data folder

      1. The next absorbance value in the pattern would be for a path length of 1 centimeter. The absorbance for this path length should be

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     _    _    _    _     _  _     _____     _____   
| || | || | || | ||  | \| ||  |  ___||  |__  //  
| || | || | || | ||  |  ' ||  | ||__      / //   
| \\_/ || | \\_/ ||  | .  ||  | ||__     / //__  
 \____//   \____//   |_|\_||  |_____||  /_____|| 
  `---`     `---`    `-` -`   `-----`   `-----`
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  • 16. Absorbance of Light Using Red No. 40

    The figure shows light passing through a glass container that contains a substance. Absorbance is a unitless measure of the amount of light that a substance absorbs as light passes through it.

    The table shows the absorbance of light with a wavelength of 500 nanometers for a solution of the food dye Red No. 40 with a concentration of 5 milligrams per liter in glass containers of various path lengths.

    1. Describe the pattern of the absorbance values.
    2. Make a scatter plot of the data.
    3. Predict the next absorbance value in the pattern.

    (See Example 5 and Example 6.)

    data folder

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     _    _    _    _    ______      ___              
| \  / || | || | || |      \\   / _ \\    ____    
|  \/  || | || | || |  --  //  | / \ ||  |    \\  
| .  . || | \\_/ || |  --  \\  | \_/ ||  | [] ||  
|_|\/|_||  \____//  |______//   \___//   |  __//  
`-`  `-`    `---`   `------`    `---`    |_|`-`   
                                         `-`
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  • 17. Absorbance of Light Using Yellow No. 5

    The figure shows light passing through a glass container that contains a substance. Absorbance is a unitless measure of the amount of light that a substance absorbs as light passes through it.

    data

    The absorbance of light with a wavelength of 428 nanometers for a solution of the food dye Yellow No. 5 in a 1-centimeter glass container is proportional to the concentration of Yellow No. 5. The absorbance of a solution with a concentration of 2 milligrams per liter is 0.106. What is the absorbance of a solution with a concentration of 5 milligrams per liter? (See Example 5 and Example 6.)

    • Worked-Out Solution

      You are given that the absorbance is proportional to the concentration. You also know that

      • when the concentration is 0, the absorbance is 0, and
      • when the concentraiton is 2, the absorbance is 0.106.

      This is enough information to determine that the absorbance increases by 0.053 each time the concentration increases by 1 milligram per liter. The spreadsheet shows that when the concentration is 5 milligrams per liter, the absorbance is 0.265.

      data folder

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     __   __     ___      ____       ___     __   __  
 \ \\/ //   / _ \\   |  _ \\    / _ \\   \ \\/ // 
  \   //   | / \ ||  | |_| ||  | / \ ||   \   //  
  / . \\   | \_/ ||  | .  //   | \_/ ||   / . \\  
 /_//\_\\   \___//   |_|\_\\    \___//   /_//\_\\ 
 `-`  --`   `---`    `-` --`    `---`    `-`  --`
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  • 18. Absorbance of Light Using Yellow No. 6

    The figure shows light passing through a glass container that contains a substance. Absorbance is a unitless measure of the amount of light that a substance absorbs as light passes through it.

    The absorbance of light with a wavelength of 484 nanometers for a solution of the food dye Yellow No. 6 with a concentration of 6 milligrams per liter is proportional to the path length. The absorbance of the solution in a 0.5-centimeter glass container is 0.162. What is the absorbance of the solution in a 1.1-centimeter glass container? (See Example 5 and Example 6.)

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      _____      ___               _    _     ______  
 |__  //    / _ \\    ____    | || | ||  /_____// 
   / //    | / \ ||  |    \\  | || | ||  `____ `  
  / //__   | \_/ ||  | [] ||  | \\_/ ||  /___//   
 /_____||   \___//   |  __//   \____//   `__ `    
 `-----`    `---`    |_|`-`     `---`    /_//     
                     `-`                 `-`
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