Problem 25 - Analytical Chemistry

Question

The concentration of chloride in seawater is determined by a flow injection analysis. The analysis of a set of calibration standards gives the following results. $$ \begin{array}{cccc} {\left[\mathrm{Cl}^{-}\right](\mathrm{ppm})} & \text { absorbance } & {\left[\mathrm{Cl}^{-}\right](\mathrm{ppm})} & \text { absorbance } \\ \hline 5.00 & 0.057 & 40.00 & 0.478 \\ 10.00 & 0.099 & 50.00 & 0.594 \\ 20.00 & 0.230 & 75.00 & 0.840 \\ 30.00 & 0.354 & & \end{array} $$ A 1.00-mL sample of seawater is placed in a 500 -mL volumetric flask and diluted to volume with distilled water. When injected into the flow injection analyzer an absorbance of 0.317 is measured. What is the concentration of \(\mathrm{Cl}^{-}\) in the sample?

Step-by-Step Solution

Answer

The concentration of Cl⁻ in the sample is 13,900 ppm.

Step 1: Plot Absorbance vs. Concentration

Plot the given absorbance values against the corresponding chloride concentration to visualize the relationship. This will help in confirming the linearity which is typically expected in such analysis.

Step 2: Determine Linear Regression Equation

Using the values provided, we can perform a linear regression to find the slope (m) and intercept (b) of the line that best fits the data: Absorbance (A) = m [Cl⁻] + b. After calculation, the equation of the line is found to be: A = 0.0112 [Cl⁻] + 0.0058.

Step 3: Find Concentration from Absorbance

Use the linear regression equation to find the concentration from a given absorbance. Plug in A = 0.317 into the equation: 0.317 = 0.0112 [Cl⁻] + 0.0058.

Step 4: Solve for [Cl⁻] in Diluted Solution

Rearrange the equation to solve for [Cl⁻]:\[[\text{Cl}^-] = \frac{0.317 - 0.0058}{0.0112}.\]Calculate to find [Cl⁻] = 27.8 ppm in the diluted solution.

Step 5: Calculate Original [Cl⁻] in Seawater

Since the sample was diluted from 1.00 mL to 500 mL, apply the dilution factor to find the original concentration in the seawater sample:\[\text{Original } [\text{Cl}^-] = 27.8 \, \text{ppm} \times \frac{500}{1} = 13900 \, \text{ppm}.\]

Key Concepts

Chloride Concentration Determination

Determining the concentration of chloride ions (\[\text{Cl}^-\]) in a sample is essential in various fields, especially environmental chemistry. In this exercise, we used flow injection analysis, a common analytical technique that allows for rapid and automated analysis of ions such as chloride. This method is utilized due to its precision and efficiency in processing multiple samples in a short time.The procedure begins with the preparation of a series of chloride standards with known concentrations. These are solutions where the exact amount of chloride ion is specified. By measuring the absorbance of each standard, we establish a relationship between absorbance and concentration. This relationship is often linear due to the Beer-Lambert Law, which describes how light absorption is proportional to the concentration of the absorbing species.**Steps in Concentration Determination Process:**- **Standard Preparation:** Samples are created with chloride concentrations such as 5 ppm, 10 ppm, up to 75 ppm.- **Measure Absorbance:** These standards are analyzed using a spectrophotometer, which measures how much light the sample absorbs.- **Calibration Curve:** By plotting absorbance versus concentration, you can create a calibration curve. This graph shows how absorbance relates to chloride concentration.
Once the calibration curve is established, the absorbance of an unknown sample can be measured and used to infer its concentration.

Absorbance Measurement

Absorbance measurement is a technique that quantifies how much a chemical substance absorbs light. In the context of chloride determination, absorbance helps relate the amount of light absorbed to the concentration of chloride ions in a sample.Using an instrument like a spectrophotometer, we measure absorbance, which is expressed as a unitless number calculated from the ratio of the intensity of the incident light on the sample to the light transmitted through the sample. It utilizes the logarithmic Beer-Lambert Law relationship:\[A = \varepsilon c l\]**Key components of the Absorbance Equation:**- \( A \) is the absorbance.- \( \varepsilon \) is the molar absorptivity, a constant for each substance and wavelength.- \( c \) is the concentration of the substance.- \( l \) is the path length, the distance the light travels through the sample, typically measured in centimeters.The chloride absorbance data allows us to visualize and verify the linearity between absorbance and concentration. By this visualization and understanding, it becomes easier to determine unknown concentrations just by measuring absorbance. In this exercise, a specific absorbance of 0.317 was used to find the concentration of chloride.

Linear Regression in Chemistry

Linear regression is an essential mathematical tool in chemistry for determining the relationship between two variables, in this case, absorbance and chloride concentration. It provides a way to find the best-fit line, represented by the linear equation:\[A = m [\text{Cl}^-] + b\]This equation helps predict the absorbance for a given concentration or vice versa. "m" is the slope of the line, indicating how absorbance changes per unit change in concentration, and "b" is the intercept on the absorbance axis.**Steps in Linear Regression Application:**- **Data Plotting:** Plot the absorbance against concentration for each standard. As seen in the solution, it establishes a clear pattern.- **Line Calculation:** Use statistical methods or software to calculate the slope (m) and intercept (b) of the best-fit line.- **Equation Application:** With the derived equation, you can now determine unknown concentrations by substituting the absorbance into the equation and solving for the concentration.
In our context, linear regression helped translate an absorbance of 0.317 into a chloride concentration using the formula obtained from the standards:\[[\text{Cl}^-] = \frac{0.317 - 0.0058}{0.0112}\]
This powerful technique illustrates the practical application of mathematical concepts in analytical chemistry, along with ensuring accuracy in chemical analysis.