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Aniline, \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{2}\), when reacted with picric acid gives a derivative with an absorptivity of \(134 \mathrm{~cm}^{-1} \mathrm{~g}^{-1} \mathrm{~L}\) at \(359 \mathrm{nm}\). What would be the absorbance of a \(1.00 \times 10^{-4} M\) solution of reacted aniline in a \(1.00-\mathrm{cm}\) cell?

Short Answer

Expert verified
The absorbance is 0.0134.

Step by step solution

01

Understand the Beer-Lambert Law

The Beer-Lambert Law is given by \( A = \varepsilon \cdot c \cdot l \), where \( A \) is the absorbance, \( \varepsilon \) is the molar absorptivity (or absorptivity in different units), \( c \) is the concentration of the solution, and \( l \) is the path length of the cell (in cm). For this problem, absorptivity refers to \( \varepsilon \) with units \( \text{cm}^{-1} \cdot \text{g}^{-1} \cdot \text{L} \).
02

Identify Given Values

From the problem, we know: - Molar absorptivity (\( \varepsilon \)): 134 \( \text{cm}^{-1} \cdot \text{g}^{-1} \cdot \text{L} \)- Concentration (\( c \)): \(1.00 \times 10^{-4}\, M\)- Path length (\( l \)): \(1.00\, \text{cm}\)
03

Calculate Absorbance Using Beer-Lambert Law

Substitute the given values into the Beer-Lambert Law equation:\[ A = 134 \cdot 1.00 \times 10^{-4} \cdot 1.00 \]Calculate this value to find the absorbance \( A \).
04

Perform Calculation

Perform the multiplication:\[ A = 134 \times 1.00 \times 10^{-4} \]\[ A = 0.0134 \]The absorbance of the solution is 0.0134.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Absorbance Calculation
When dealing with the Beer-Lambert Law, absorbance is a crucial concept. Absorbance measures how much light a sample absorbs at a specific wavelength. In our exercise, you need to calculate the absorbance of a solution at 359 nm. The Beer-Lambert Law formula, \[ A = \varepsilon \cdot c \cdot l \], helps in this calculation.

* \( A \) stands for absorbance, indicating how much light is absorbed. * \( \varepsilon \) represents molar absorptivity, or absorptivity expressed in the units given (cm鈦宦 g鈦宦 L). * \( c \) refers to the concentration of your solution. * \( l \) is the path length through which light travels in the solution.
By multiplying these factors together, you can find the absorbance value. In our problem, the calculation \[ A = 134 \times 1.00 \times 10^{-4} \times 1.00 \] returns an absorbance of 0.0134. Understanding this step by step helps in dissecting problems involving Beer-Lambert Law in spectrophotometric assays.
Molar Absorptivity
Molar absorptivity, or simply absorptivity, refers to how well a substance absorbs light at a particular wavelength. In Beer-Lambert Law, denoted as \( \varepsilon \), it plays a significant role in determining absorbance.

It is essential to understand the units involved in absorptivity. In our example, absorptivity has units of \( \text{cm}^{-1} \cdot \text{g}^{-1} \cdot \text{L} \). These units indicate:
  • How light absorption varies with concentration
  • The inverse of path length (inverse cm)
A higher molar absorptivity means more effective light absorption. This parameter uniquely identifies how aniline derivatives interact with light. In this problem, the given absorptivity is 134, implying substantial absorption efficiency at 359 nm. Being familiar with the concept of molar absorptivity is vital for students working with spectrophotometry.
Aniline Derivatization
Aniline derivatization involves chemically modifying aniline to form a derivative that is more detectable by analytical techniques. In this exercise, aniline reacts with picric acid, resulting in a derivative suitable for spectrophotometric analysis.

Understanding the process of derivatization is key because:
  • It enhances the compound's features for easier detection
  • It often improves the selectivity and sensitivity of the analysis method
By reacting aniline with picric acid, a compound is formed with measurable absorptivity at a specific wavelength. In spectrophotometry, this enhanced feature helps in quantifying the concentration of the compound in a solution. So, mastering the concepts behind derivatization can improve your analytical skills and your ability to apply them in practical scenarios.
Spectrophotometry
Spectrophotometry is an analytical technique used to measure the amount of light absorbed by a substance at various wavelengths. It is a critical tool in chemical analysis for quantifying the concentration of analytes.

Key aspects of spectrophotometry include:
  • Utilizing cuvettes to hold the solution, with a known path length (\( l \))
  • Employing light sources that can produce a beam across the desired wavelengths
  • Recording the intensity of light before and after it passes through the sample
For students, understanding how spectrophotometry is applied helps in grasping the Beer-Lambert Law's importance in experiments like the one described in the exercise. This technique allows us to determine concentrations accurately by measuring absorbance, linking directly back to both the chemical nature of the analyte and the absorptive properties outlined by its derivatives. By mastering the basics of spectrophotometry, you'll be better equipped to analyze and interpret absorbance data in the lab.

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Most popular questions from this chapter

Amines (weak base) form salts with picric acid (trinitrophenol), and all amine picrates exhibit an absorption maximum at \(359 \mathrm{nm}\) with a molar absorptivity of \(1.25 \times 10^{4} .\) A \(0.200-g\) sample of aniline, \(C_{6} H_{5} N H_{2}\), is dissolved in \(500 \mathrm{~mL}\) water. A 25.0 -mL aliquot is reacted with picric acid in a 250 -mL volumetric flask and diluted to volume. A 10.0 -mL aliquot of this is diluted to \(100 \mathrm{~mL}\) and the absorbance read at \(359: \mathrm{nm}\) in a \(1-\mathrm{cm}\) cell. If the absorbance is 0.425 what is the percent purity of the aniline?

Describe radiation sources and detectors for the ultraviolet, visible, and infrared regions of the spectrum.

Define absorptivity and molar absorptivity.

Convert the wavelength \(4000 \AA\) into frequency (Hz) and into wavenumbers \(\left(\mathrm{cm}^{-1}\right)\)

Iron(II) is determined spectrophotometrically by reacting with 1,10 -phenanthroline to produce a complex that absorbs strongly at \(510 \mathrm{nm}\). A stock standard iron(II) solution is prepared by dissolving 0.0702 g ferrous ammonium sulfate, \(\mathrm{Fe}\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4} \cdot 6 \mathrm{H}_{2} \mathrm{O}\), in water in a 1-L volumetric flask, adding \(2.5 \mathrm{~mL}\) \(\mathrm{H}_{2} \mathrm{SO}_{4}\), and diluting to volume. A series of working standards is prepared by transferring \(1.00-, 2.00-, 5.00-,\) and \(10.00-\mathrm{mL}\) aliquots of the stock solution to separate \(100-\mathrm{mL}\) volumetric flasks and adding hydroxylammonium chloride solution to reduce any iron(III) to iron(II), followed by phenanthroline solution and then dilution to volume with water. A sample is added to a 100 -mL volumetric flask and treated in the same way. A blank is prepared by adding the same amount of reagents to a 100 -mL volumetric flask and diluting to volume. If the following absorbance readings measured against the blank are obtained at \(510 \mathrm{nm}\), how many milligrams iron are in the sample? (Table)

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