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Chapter 10: Problem 17

In the DPD colorimetric method for the free chlorine residual, which is reported as \(\mathrm{mg} \mathrm{Cl}_{2} / \mathrm{L},\) the oxidizing power of free chlorine converts the colorless amine \(\mathrm{N}, \mathrm{N}\) -diethyl- \(p\) -phenylenediamine to a colored dye that absorbs strongly over the wavelength range of \(440-580 \mathrm{nm}\). Analysis of a set of calibration standards gave the following results. $$ \begin{array}{cc} \mathrm{mg} \mathrm{Cl}_{2} / \mathrm{L} & \text { absorbance } \\ \hline 0.00 & 0.000 \\ 0.50 & 0.270 \\ 1.00 & 0.543 \\ 1.50 & 0.813 \\ 2.00 & 1.084 \end{array} $$ A sample from a public water supply is analyzed to determine the free chlorine residual, giving an absorbance of \(0.113 .\) What is the free chlorine residual for the sample in \(\mathrm{mg} \mathrm{Cl}_{2} / \mathrm{L}\) ?

Short Answer

Expert verified
The free chlorine residual is approximately 0.208 mg/L.

Step by step solution

01

Understand the Problem

We need to determine the amount of free chlorine residual in a water sample using a colorimetric method. We are given a set of calibration standards with chlorine residual concentrations and their corresponding absorbance values. Our sample shows an absorbance of 0.113, and we need to find its chlorine concentration.
02

Analyze the Calibration Data

Let's examine the provided calibration data: - 0.00 mg/L corresponds to an absorbance of 0.000 - 0.50 mg/L corresponds to an absorbance of 0.270 - 1.00 mg/L corresponds to an absorbance of 0.543 - 1.50 mg/L corresponds to an absorbance of 0.813 - 2.00 mg/L corresponds to an absorbance of 1.084 This data implies a direct relationship between chlorine concentration (mg/L) and absorbance, likely a linear one.
03

Determine the Best Fit Line for the Calibration Data

Since the data appears linear, we can use a linear equation \( y = mx + b \) where \( y \) is absorbance, \( x \) is chlorine concentration,\( m \) is the slope, and \( b \) is the y-intercept.Calculating the slope, \( m = \frac{1.084 - 0.000}{2.00 - 0.00} = 0.542 \).Assuming \( b \) is 0, the best fit line is \( y = 0.542x \).
04

Solve for the Free Chlorine Residual in the Sample

Using the equation from Step 3, substitute the absorbance of the sample (0.113):\(0.113 = 0.542x\).Solve for \( x \):\[x = \frac{0.113}{0.542} \approx 0.208\].Thus, the free chlorine residual in the sample is approximately 0.208 mg/L.

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Key Concepts

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

DPD Colorimetric Method
The DPD Colorimetric Method is a widely used technique to determine the free chlorine residual in water samples. This method relies on the ability of free chlorine to oxidize the colorless compound N,N-diethyl-p-phenylenediamine (DPD) into a pink-colored dye. The intensity of the pink color produced is directly related to the amount of chlorine present in the sample. This color change occurs because the oxidizing power of free chlorine transforms DPD into a dye, which can be quantitatively measured using a colorimeter or spectrophotometer.
The process is simple:
  • First, a water sample is collected, and DPD is added to it.
  • The sample is then placed in a colorimeter, where the intensity of the pink color is measured.
  • The absorbance of the sample at a specific wavelength is recorded, which reflects the chlorine concentration.
This method is favored for its accuracy, simplicity, and rapid results, making it popular in water quality testing for public health and environmental safety.
Calibration Standards
Calibration standards are essential for ensuring the accuracy and reliability of the DPD Colorimetric Method. These standards are prepared solutions with known concentrations of free chlorine. They serve as reference points to establish a relationship between chlorine concentration and absorbance.
When setting up calibration standards:
  • A series of solutions with varying concentrations of chlorine are prepared.
  • The absorbance of each solution is measured using a colorimeter.
  • The data obtained is used to create a calibration curve, plotting absorbance against concentration.
This curve helps to determine the chlorine concentration in unknown samples by comparing their absorbance against the standard curve. Proper calibration is crucial in analytical methods to ensure accuracy and consistency, allowing for precise water quality assessments.
Linear Relationship
A linear relationship between two variables means they are directly proportional. In the context of the DPD Colorimetric Method, the linear relationship exists between the free chlorine concentration and the absorbance of the colored dye. This relationship implies that as the concentration of chlorine increases, the absorbance also increases proportionally.
Mathematically, this is expressed as the equation of a line:\[ y = mx + b \]where:
  • \( y \) is the absorbance.
  • \( x \) is the chlorine concentration in mg/L.
  • \( m \) is the slope of the line, representing the rate of increase in absorbance per unit of concentration.
  • \( b \) is the y-intercept, often zero in perfect calibration.
This equation is critical for calculating unknown chlorine concentrations in water samples by solving for \( x \), the chlorine concentration, when given an observed absorbance.
Absorbance Measurement
Absorbance measurement is a critical step in the DPD Colorimetric Method, as it provides quantitative data on chlorine concentration in water samples. Absorbance is the amount of light absorbed by a solution, and it is directly measured by a colorimeter or spectrophotometer at a specific wavelength that aligns with the absorption spectrum of the created dye.
The steps involved in absorbance measurement include:
  • Calibrating the colorimeter with a blank sample (usually distilled water).
  • Measuring the baseline absorbance to account for any instrument errors.
  • Inserting the test sample after adding DPD reagent.
  • Recording the absorbance value, which shows how much light is absorbed by the pink dye.
This value is then used alongside calibration data to deduce the chlorine concentration in the sample. Accurate absorbance measurements are vital for precise water quality evaluations, aiding in the maintenance of safe drinking water standards.

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Most popular questions from this chapter

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