Problem 78 - Chemistry and Chemical Reactivity

Question

The nitrite ion is involved in the biochemical nitrogen cycle. You can determine the nitrite ion content of a sample using spectrophotometry by first using several organic compounds to form a colored compound from the ion. The following data were collected. $$\begin{array}{|c|c|}\hline \begin{array}{c}\mathrm{NO}_{2}^{-} \text {lon } \\\\\text { Concentration }\end{array} & \begin{array}{c}\text { Absorbance of } \\\\\text { Solution at } 550 \mathrm{nm}\end{array} \\\\\hline 2.00 \times 10^{-6} \mathrm{M} & 0.065 \\\6.00 \times 10^{-6} \mathrm{M} & 0.205 \\\10.00 \times 10^{-6} \mathrm{M} & 0.338 \\ 14.00 \times 10^{-6} \mathrm{M} & 0.474 \\\\\hline 18.00 \times 10^{-6} \mathrm{M} & 0.598 \\\\\hline \text { Unknown solution } & 0.402 \\\\\hline\end{array}$$ (a) Construct a calibration plot, and determine the slope and intercept. (b) What is the nitrite ion concentration in the unknown solution?

Step-by-Step Solution

Answer

The nitrite ion concentration in the unknown solution is approximately 12.24 × 10^{-6} M.

Step 1: Plot the Calibration Data

Start by plotting the given data on a graph. Use the nitrite ion concentrations on the x-axis and the absorbance values on the y-axis. Your points will have the following coordinates: - (2.00 × 10^{-6} M, 0.065) - (6.00 × 10^{-6} M, 0.205) - (10.00 × 10^{-6} M, 0.338) - (14.00 × 10^{-6} M, 0.474) - (18.00 × 10^{-6} M, 0.598).

Step 2: Draw the Best Fit Line

Using the plotted points, draw a line that best fits all the data points. This line should be as close as possible to all points and should show a linear relationship between concentration and absorbance.

Step 3: Calculate Slope and Intercept

Using linear regression, determine the equation of the line, which is typically in the form of \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. Calculating using the least squares method or utilizing software/calculators designed for regression can help accurately find these values. For this data, calculations will yield approximately:- Slope \(m = 33.12 \times 10^{6} \, \text{M}^{-1}\)- Intercept \(b = -0.0029\).

Step 4: Use the Calibration Line to Determine Unknown Concentration

To find the concentration of the unknown solution, insert the absorbance value of 0.402 into the linear equation derived from the calibration data. Using the equation from Step 3, rearrange it to solve for concentration \(x\):\[ x = \frac{y - b}{m} \].

Step 5: Calculate the Nitrite Ion Concentration

Substitute the known values into the equation: \[ x = \frac{0.402 + 0.0029}{33.12 \times 10^{6}} \approx 12.24 \times 10^{-6} \, \text{M} \].This result gives the concentration of the nitrite ions in the unknown solution.

Key Concepts

Calibration Plot

A calibration plot is a useful tool in spectrophotometry to determine the concentration of substances, such as nitrite ions. By plotting known concentrations of a sample against their corresponding absorbance values, a visual relationship between concentration and absorbance is created. This plot typically features:

• The concentration of the sample on the x-axis
• The absorbance values on the y-axis

This creates a graph where each point represents a set of known data. Drawing a best fit line helps to identify this linear relationship, enabling us to predict unknown concentrations with precision. Calibration plots are essential when aiming for accurate spectrophotometric analysis as they form the foundation of quantifying unknowns.

Nitrite Ion Concentration

Determining the nitrite ion concentration is crucial in understanding several biochemical processes, particularly the nitrogen cycle. Using spectrophotometric techniques, nitrite ions react to form colored compounds, which absorb light. This absorbance can be measured using a spectrophotometer:

• Known nitrite ion concentrations create measurable absorbance values
• An unknown sample's absorbance value is then matched to determine its concentration

The concentration for an unknown solution can be computed by referring to the calibration plot, where the corresponding absorbance value is compared to the plotted line to find its concentration. This method provides a reliable way to quantify nitrite ions in various samples, impacting environmental and biochemical studies.

Linear Regression

Linear regression is a statistical method used to model the relationship between two variables. In spectrophotometry, it's applied to find the equation of the best fit line on a calibration plot:

• Usually in the form of \(y = mx + b\)
• Where \(m\) is the slope, indicating the change in absorbance per unit change in concentration
• \(b\) is the y-intercept, representing the absorbance when concentration is zero

Calculating these values can be done using methods like the least squares approach, or with software programmed for regression analysis. Once derived, this equation becomes a powerful analytical tool in identifying concentrations in unknown samples by rearranging and substituting known absorbance values.

Biochemical Nitrogen Cycle

The biochemical nitrogen cycle is an essential process in our ecosystem, returning nitrogen to the atmosphere and maintaining soil fertility. Nitrite ions play a key role in this cycle, acting as an intermediary step in the conversion of ammonia to nitrate:

• Nitrite ions result from the nitrification process performed by certain bacteria
• These ions can further transform into either ammonia or nitrate

Understanding the concentration of nitrite ions, therefore, provides insights into the efficiency of nitrogen cycling. Monitoring nitrite levels can aid in assessing soil health, controlling pollution, and managing agricultural practices, highlighting the importance of accurate measurement techniques like spectrophotometry in ecological studies.