Problem 21 - Analytical Chemistry

Question

The concentration of \(\mathrm{SO}_{2}\) in a sample of air is determined by the \(p\) -rosaniline method. The \(\mathrm{SO}_{2}\) is collected in a 10.00 -mL solution of \(\mathrm{HgCl}_{4}^{2-},\) where it reacts to form \(\mathrm{Hg}\left(\mathrm{SO}_{3}\right)_{2}^{2-},\) by pulling air through the solution for 75 min at a rate of \(1.6 \mathrm{~L} / \mathrm{min}\). After adding \(p\) -rosaniline and formaldehyde, the colored solution is diluted to \(25 \mathrm{~mL}\) in a volumetric flask. The absorbance is measured at \(569 \mathrm{nm}\) in a \(1-\mathrm{cm}\) cell, yielding a value of \(0.485 .\) A standard sample is prepared by substituting a 1.00 -mL sample of a standard solution that contains the equivalent of \(15.00 \mathrm{ppm} \mathrm{SO}_{2}\) for the air sample. The absorbance of the standard is found to be 0.181 . Report the concentration of \(\mathrm{SO}_{2}\) in the air in \(\mathrm{mg}\) \(\mathrm{SO}_{2} / \mathrm{L}\). The density of air is \(1.18 \mathrm{~g} /\) liter.

Step-by-Step Solution

Answer

The concentration of SO2 in air is approximately 0.838 mg/L.

Step 1: Calculate Volume of Air Sample

First, determine the total volume of air that was passed through the solution in 75 minutes. Given that the air flow rate is \(1.6 \text{ L/minute}\), we multiply this by the number of minutes: \[1.6 \text{ L/minute} \times 75 \text{ minutes} = 120 \text{ L}.\]Thus, the total volume of air is \(120 \text{ L}\).

Step 2: Determine Concentration of SO2 in Solution

Use the absorbance values to find the concentration of \(\text{SO}_2\) in solution using the relationship of the standard solution. The concentration of \(\text{SO}_2\) in the standard solution is given by the absorbance ratio: \[\frac{C_x}{C_s} = \frac{A_x}{A_s},\]where \(C_x\) is the concentration of the unknown, \(C_s\) is the concentration of the standard equivalent (15 ppm), \(A_x\) is the absorbance of the unknown sample (0.485), and \(A_s\) is the absorbance of the standard (0.181). Solving for \(C_x\):\[C_x = \frac{0.485}{0.181} \times 15 \text{ ppm} \approx 40.165 \text{ ppm}.\]

Step 3: Convert Concentration to mg/L in Air

Since 1 ppm is equivalent to 1 mg/L, \(C_x = 40.165 \text{ mg/L in the final solution}\). To find \(\text{mg/L}\) in air, account for the dilutions: the solution was diluted from 10.00 mL to 25 mL. This means the concentration of \(\text{SO}_2\) in the original 10 mL solution was \[C_{original} = \frac{25}{10} \times 40.165 \text{ mg/L} = 100.4125 \text{ mg/L}. \]Thus, the \(\text{mg SO}_2\) per \(\text{L}\) of air sample is \[\frac{100.4125 \text{ mg}}{120 \text{ L}} \approx 0.8376 \text{ mg SO}_2/ \text{L air}\].

Key Concepts

SO2 concentration

Measuring the concentration of sulfur dioxide ( SO_2 ) in the air is crucial for understanding air quality and its potential impact on human health and the environment. SO_2 is a colorless gas that can cause respiratory problems, and its levels need to be monitored accurately in various environments. SO_2 concentration indicates the amount of this gas present in a given volume of air. In analytical chemistry, this is often expressed in terms like parts per million (ppm) or milligrams per liter (mg/L). To find SO_2 concentration, air samples are typically collected and analyzed using different chemical methods. One popular technique involves collecting the SO_2 in a reactive solution that forms a measurable compound, which can then be quantified.

p-rosaniline method

The p-rosaniline method is a well-established procedure for determining SO_2 levels. It's a colorimetric technique, meaning it relies on measuring the color intensity of a solution. In this method, SO_2 from an air sample reacts with a solution containing mercury chloride ( HgCl_4^{2-} ) to form mercury(II) sulfite ( Hg(SO_3)_2^{2-} ). Subsequently, this compound reacts with formal aldehyde and p-rosaniline, forming a colored complex. The intensity of the color relates to the concentration of SO_2. This is then compared to a standard solution to calculate the concentration of SO_2 in the original air sample. This method is popular due to its sensitivity, allowing detection of small changes in SO_2 levels.
It involves simple laboratory equipment, making it accessible for routine air quality monitoring.

absorbance measurement

Absorbance measurement is a central element in analytical chemistry, particularly in colorimetric assays like the p-rosaniline method. Absorbance refers to how much light at a specific wavelength is absorbed by a solution. This technique utilizes a spectrophotometer, which directs light through the sample. As the light passes through the solution containing the colored complex, part of it is absorbed by the sample. The spectrophotometer measures the absorbance, which is directly related to the concentration of the absorbing substance.The Beer-Lambert law formalizes this relationship: \[ A = \, \varepsilon c l \]where A is the absorbance, \varepsilon (epsilon) is the molar absorptivity, c is the concentration of the solution, and l is the path length of the cell (typically 1 cm).By knowing the absorbance of the unknown solution and comparing it to a standard, the concentration of SO_2 is determined. This approach is reliable and provides a quantitative measure of SO_2 concentration.

air sample analysis

Air sample analysis involves a series of steps to ensure the accurate determination of SO_2 concentration in a large volume of air. Initially, air is drawn through an absorbing solution at a controlled rate and time duration. This allows the SO_2 to chemically react and get retained in the solution. For the p-rosaniline method, the collection phase occurs over 75 minutes at a flow rate of 1.6 L/min, leading to efficient capture of SO_2 over time. After collection, the change in reaction mixture is analyzed through color development by adding reagents like formaldehyde and p -rosaniline. Subsequent absorbance measurement further gives the quantitative concentration of SO_2 in the air.

The analysis considers dilution factors.

Ensures quality control by using known standards. By comparing results with standards and correcting for air volume, analysts can accurately report SO_2 levels in mg/L, providing crucial air quality data.