Problem 15 - Analytical Chemistry

Question

The concentration of phenol in a water sample is determined by using steam distillation to separate the phenol from non-volatile impurities, followed by reacting the phenol in the distillate with 4 -aminoantipyrine and \(\mathrm{K}_{3} \mathrm{Fe}(\mathrm{CN})_{6}\) at \(\mathrm{pH} 7.9\) to form a colored antipyrine dye. A phenol standard with a concentration of 4.00 ppm has an absorbance of 0.424 at a wavelength of \(460 \mathrm{nm}\) using a \(1.00 \mathrm{~cm}\) cell. A water sample is steam distilled and a \(50.00-\mathrm{mL}\) aliquot of the distillate is placed in a 100 -mL volumetric flask and diluted to volume with distilled water. The absorbance of this solution is 0.394 . What is the concentration of phenol (in parts per million) in the water sample?

Step-by-Step Solution

Answer

The concentration of phenol in the water sample is 7.434 ppm.

Step 1: Understanding Beer's Law

Beer's Law, or Beer-Lambert Law, states that the absorbance of a solution is directly proportional to the concentration of the absorbing species and the path length of the cell. Mathematically, it can be expressed as \( A = \, \varepsilon \cdot c \cdot l \), where \( A \) is the absorbance, \( \varepsilon \) is the molar absorptivity, \( c \) is the concentration, and \( l \) is the path length.

Step 2: Determine the Molar Absorptivity \(\varepsilon\)

Using the standard phenol solution, we calculate the molar absorptivity. For the standard solution with a concentration of 4.00 ppm, \( A = 0.424 \) and \( l = 1.00 \, \mathrm{cm} \). So, \( \varepsilon = \frac{A}{c \cdot l} = \frac{0.424}{4.00 \, \text{ppm} \cdot 1.00 \, \mathrm{cm}} = 0.106 \, \mathrm{ppm}^{-1} \cdot \mathrm{cm}^{-1} \).

Step 3: Calculate Concentration of the Diluted Sample

For the diluted water sample, \( A = 0.394 \) and \( l = 1.00 \mathrm{~cm} \). Using the molar absorptivity from Step 2, the concentration \( c \) of the diluted solution can be calculated as \( c = \frac{A}{\varepsilon \cdot l} = \frac{0.394}{0.106 \cdot 1.00} = 3.717 \text{ ppm} \).

Step 4: Account for Dilution

The 50.00 mL aliquot of the distillate was diluted to 100 mL in the volumetric flask. Therefore, the concentration in the original distillate (\( c_{\text{original}} \)) is twice that of the diluted solution: \( c_{\text{original}} = 2 \times 3.717 = 7.434 \text{ ppm} \).

Step 5: Calculate Phenol Concentration in the Water Sample

Since only part of the water sample was distilled, the calculated concentration in the distillate represents the concentration of phenol in the original water sample. Thus, the phenol concentration in the water sample is 7.434 ppm.

Key Concepts

Beer-Lambert Law

The Beer-Lambert Law is a fundamental principle in analytical chemistry that relates to how light absorbs as it passes through a solution. It's a simple yet powerful equation:

• Absorbance (A): This is a measure of the amount of light absorbed by the sample. Absorbance itself does not have units.


• Molar Absorptivity (\( \varepsilon \)): This is a constant that indicates how well a substance absorbs light at a particular wavelength. It is specific to each compound and is measured in \( \, \text{L mol}^{-1} \text{cm}^{-1} \).


• Concentration (c): Refers to the amount of solute dissolved in a unit volume of solution, usually expressed in molarity. In this exercise, concentration is given in parts per million (ppm).


• Path length (l): The distance that light travels through the solution, usually measured in centimeters (cm).

The Beer-Lambert Law can be expressed mathematically as:\[A = \varepsilon \cdot c \cdot l\] This equation shows that the absorbance is directly proportional to the concentration of the absorbing species and the path length, making it a useful tool for determining unknown concentrations. In practice, by measuring the absorbance and knowing the path length and molar absorptivity, one can solve for the concentration, which is precisely what is done in the given exercise.

Molar Absorptivity

Molar absorptivity, also known as the molar extinction coefficient, is a key concept for understanding how different substances interact with light. It's a measure that reflects how strongly a substance absorbs light at a specific wavelength.

• The unit for molar absorptivity is usually \( \text{L mol}^{-1} \text{cm}^{-1} \), but in this exercise, it is calculated per parts per million (ppm) for convenience.


• It is unique to each compound and wavelength. This means different substances will have different molar absorptivity values at different wavelengths.

In the exercise, the molar absorptivity for phenol was found using a standard phenol solution with known concentration and absorbance. By rearranging the Beer-Lambert Law, we have:\[\varepsilon = \frac{A}{c \cdot l}\]For the standard phenol solution, absorbance \(A\) of 0.424, concentration \(c\) of 4.00 ppm, and path length \(l\) of 1.00 cm, the molar absorptivity was calculated as:\[\varepsilon = \frac{0.424}{4.00 \, \text{ppm} \times 1.00 \, \text{cm}} = 0.106 \, \text{ppm}^{-1} \cdot \text{cm}^{-1}\]Understanding molar absorptivity is essential for calculating unknown concentrations when using spectrophotometry.

Spectrophotometry

Spectrophotometry is an analytical method used to measure the amount of light absorbed by a solution, which in turn relates to the concentration of a solute within it. It is based on the Beer-Lambert Law, and it helps researchers and scientists make quantitative measurements of chemical concentrations. Here are some essential points about spectrophotometry:

• It uses an apparatus known as a spectrophotometer, which passes a beam of light through a solution and measures the intensity of light passing through.


• The spectrophotometer compares the intensity of light before and after passing through the sample to determine absorbance.


• This technique is valuable in many fields, including chemistry, physics, biology, and biochemical analysis, as it provides accurate data on the concentration of solutes in a solution.

In the context of the exercise, spectrophotometry was employed to determine the absorbance of a phenol solution at 460 nm wavelength. By knowing the absorbance, molar absorptivity, and path length, we used spectrophotometry to calculate the phenol concentration in the water sample. This approach proves to be precise and efficient, especially when dealing with solutions of known characteristics and properties.