91Ó°ÊÓ

Lin and Brown described a quantitative method for methanol based on its effect on the visible spectrum of methylene blue. \({ }^{23}\) In the absence of methanol, methylene blue has two prominent absorption bands at 610 \(\mathrm{nm}\) and \(663 \mathrm{nm}\), which correspond to the monomer and the dimer, respectively. In the presence of methanol, the intensity of the dimer's absorption band decreases, while that for the monomer increases. For concentrations of methanol between 0 and \(30 \% \mathrm{v} / \mathrm{v},\) the ratio of the two absorbance, \(A_{663} / A_{610}\), is a linear function of the amount of methanol. Use the following standardization data to determine the \(\% \mathrm{v} / \mathrm{v}\) methanol in a sample if \(A_{610}\) is 0.75 and \(A_{663}\) is 1.07 . $$ \begin{array}{cccc} \% \mathrm{v} / \mathrm{v} \text { methanol } & A_{663} / A_{610} & \% \mathrm{v} / \mathrm{v} \text { methanol } & A_{663} / A_{610} \\ \hline 0.0 & 1.21 & 20.0 & 1.62 \\ 5.0 & 1.29 & 25.0 & 1.74 \\ 10.0 & 1.42 & 30.0 & 1.84 \\ 15.0 & 1.52 & & \end{array} $$

Step by step solution

01

Identify Given Values

Given:- \( A_{610} = 0.75 \)- \( A_{663} = 1.07 \)We need to find the methanol concentration, using the ratio \( A_{663} / A_{610} \).

02

Calculate the Absorbance Ratio

Calculate \( \frac{A_{663}}{A_{610}} \) using the provided absorptance values:\[ \frac{A_{663}}{A_{610}} = \frac{1.07}{0.75} \approx 1.427 \]

03

Use Standard Data for Linear Equation

The table provides the linear relationship between methanol concentration and \( \frac{A_{663}}{A_{610}} \). The data are: - 0.0% methanol, \( A_{663} / A_{610} =1.21 \)- 30.0% methanol, \( A_{663} / A_{610} = 1.84 \).

04

Determine the Slope of the Line

The linear relation can be described as \( y = mx + b \), where \( m \) is the slope. Using two points (0, 1.21) and (30, 1.84), we find:\[ m = \frac{1.84 - 1.21}{30 - 0} = \frac{0.63}{30} = 0.021 \]

05

Construct the Linear Equation

Using the standard point (0,1.21) and slope \( 0.021 \):\[ y - 1.21 = 0.021x \\text{Thus,}\]\[ y = 0.021x + 1.21 \]

06

Calculate Methanol Concentration

Let \( y = 1.427 \) from \( \frac{A_{663}}{A_{610}} \).Substitute this ratio into the linear equation:\[ 1.427 = 0.021x + 1.21 \]Solving for \( x \):\[ 1.427 - 1.21 = 0.021x \0.217 = 0.021x \x = \frac{0.217}{0.021} \approx 10.33 \]

07

Conclude Methanol Percentage

The percentage of methanol in the sample is approximately 10.33% \( v/v \).

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Key Concepts

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

Methylene Blue

Methylene blue is a vital organic compound with a distinctive blue hue, commonly used in chemistry and biology.
It serves various purposes, including as a dye and an indicator in analytical chemistry. In the context of spectrophotometry, methylene blue is examined for its interaction with light, especially at specific wavelengths.
The compound exists in two forms in solution: a monomer and a dimer, each absorbing light at different wavelengths. This unique property allows scientists to study chemical interactions and concentrations in solutions.
Methylene blue's monomer absorbs light primarily at a wavelength of 610 nm, while its dimer absorbs at 663 nm.

Absorption Spectrum

The absorption spectrum is a visual representation of the range of wavelengths absorbed by a substance, in this case, methylene blue.
When light passes through a solution containing methylene blue, certain wavelengths are absorbed more significantly than others.
For methylene blue, two distinct absorption bands appear in its spectrum— one at 610 nm and another at 663 nm, corresponding to the monomer and dimer forms, respectively.
Spectrophotometry measures the intensity of these absorption bands, providing insight into the concentration and form of molecules present.

Quantitative Analysis

Quantitative analysis is the process of determining the amount or concentration of a substance in a sample.
In this scenario, the method revolves around measuring the absorbance of methylene blue's dimer in the presence of methanol.
By establishing a linear relationship between methanol concentration and the absorbance ratio of the dimer and monomer ( A_{663} / A_{610} ), it becomes possible to estimate methanol levels accurately.
Given the ratio of absorbance values, a standard curve can be created from known concentrations, which then helps to determine unknown concentrations via interpolation.

Methanol Concentration

Methanol concentration can significantly affect the absorption characteristics of methylene blue.
As the concentration of methanol rises, it shifts the balance between the monomer and dimer forms of methylene blue.
Specifically, an increase in methanol concentration generally results in a greater monomer absorbance and a diminished dimer absorbance, leading to a change in the ratio of A_{663} / A_{610} .
By analyzing this ratio using a previously determined linear relationship, scientists can ascertain the methanol concentration with precision.
In practical applications, it enables the accurate quantification of methanol in various mixtures, which is crucial for both laboratory analyses and industrial applications.