Question

An analyst needs to evaluate the potential effect of an interferent, \(I,\) on the quantitative analysis for an analyte, \(A\). She begins by measuring the signal for a sample in which the interferent is absent and the analyte is present with a concentration of 15 ppm, obtaining an average signal of 23.3 (arbitrary units). When she analyzes a sample in which the analyte is absent and the interferent is present with a concentration of \(25 \mathrm{ppm}\), she obtains an average signal of 13.7 . (a) What is the sensitivity for the analyte? (b) What is the sensitivity for the interferent? (c) What is the value of the selectivity coefficient? (d) Is the method more selective for the analyte or the interferent? (e) What is the maximum concentration of interferent relative to that of the analyte if the error in the analysis is to be less than \(1 \% ?\)

Short answer

(a) 1.553 units/ppm. (b) 0.548 units/ppm. (c) 0.353. (d) Method is more selective for analyte. (e) Maximum concentration of interferent is 0.660 ppm.

Step-by-step solution

Determine Sensitivity for Analyte

The sensitivity for the analyte is calculated by taking the signal obtained when only the analyte is present and dividing it by the analyte's concentration. Here, the signal is 23.3 units at a concentration of 15 ppm. Thus:\[ S_A = \frac{23.3}{15} \approx 1.553 \text{ units per ppm} \]

Determine Sensitivity for Interferent

To find the sensitivity for the interferent, use the signal obtained when only the interferent is present and divide it by its concentration. The signal is 13.7 units at a concentration of 25 ppm, so:\[ S_I = \frac{13.7}{25} = 0.548 \text{ units per ppm} \]

Calculate the Selectivity Coefficient

The selectivity coefficient, \( K \), is a measure of the relative response of the method to the interferent compared to the analyte, computed as:\[ K = \frac{S_I}{S_A} = \frac{0.548}{1.553} \approx 0.353 \]

Evaluate Method Selectivity

To determine if the method is more selective for the analyte or interferent, compare the selectivity coefficient to 1. Since \( K = 0.353 < 1 \), the method is more selective for the analyte.

Determine Maximum Interferent Concentration

To ensure the error in the analysis is less than 1%, we use the formula:\[ (\text{Interferent Response}) = K \times C_I \leq 0.01 \times S_A \times C_A \]Substituting known values:\[ 0.353 \times C_I \leq 0.01 \times 1.553 \times 15 \]Solve for \( C_I \):\[ C_I \leq \frac{0.233}{0.353} \approx 0.660 \text{ ppm} \]

Key concepts

Interferer

In quantitative analysis, an interferer is a substance that affects the measurement of the analyte by altering the outcome of the analysis. Imagine you want to measure the concentration of a specific compound, but another compound present muddles your results. This interfering compound is called an interferer.

Interferers are particularly important when they cause a signal similar to the one you're using to detect your analyte. This can lead to errors, causing you to overestimate or underestimate the amount of the analyte present. In the example exercise, the signal in the absence of interferer was 23.3 units for an analyte concentration, and 13.7 units when the interferer was present alone at a different concentration.

• Important to identify and quantify the presence of interferers.
• Essential to adjust methods to minimize their impact on analysis.

This is why understanding and compensating for interferers is a thesis of good quantitative analysis.

Sensitivity

Sensitivity in quantitative analysis refers to the ability of a method to detect small changes in analyte concentration. It is a key parameter because it defines how efficiently an analytical method can measure the presence of the analyte.

Calculating sensitivity involves taking the signal generated by a known analyte concentration and dividing the signal by that concentration. For the analyte here, sensitivity was calculated: \[ S_A = \frac{23.3}{15} \approx 1.553 \text{ units per ppm} \]This tells us that each ppm of the analyte increases the signal by 1.553 units. Similarly, the sensitivity for the interferer was calculated: \[ S_I = \frac{13.7}{25} \approx 0.548 \text{ units per ppm} \]

A higher sensitivity indicates a more efficient detection method for smaller amounts of a substance.

• High sensitivity is ideal for detecting low concentration analytes.
• It allows for precise measurements even in small quantities.

Hence, understanding sensitivity helps optimize analytical methods for better specificity.

Selectivity Coefficient

The selectivity coefficient quantifies how well an analytical method can distinguish between the analyte and an interferer. It compares the method's sensitivity to each == the analyte and interferent.

To compute the selectivity coefficient, divide the sensitivity of the interferer by that of the analyte: \[ K = \frac{S_I}{S_A} = \frac{0.548}{1.553} \approx 0.353 \]A selectivity coefficient less than 1, as in this example, means the method is more selective for analyte detection, making it less prone to interference.

• Low selectivity coefficients indicate better discrimination between analyte and interferent.
• Helps fine-tune methods to prevent inaccurate readings due to interfence.

Thus, a selectivity coefficient is fundamental in understanding how well an analytical method isolates the desired signal from potential noise.

Error Analysis

Error analysis in quantitative chemical analysis ensures the accuracy of the results by checking and correcting for errors introduced by interferents.

In this process, you calculate the maximum allowable concentration of the interferent to keep errors below a certain threshold. For the example provided, the formula: \[(\text{Interferent Response}) = K \times C_I \leq 0.01 \times S_A \times C_A \]was used to determine the maximum safe concentration of the interferent.Solving this, we found: \[ C_I \leq 0.660 \text{ ppm} \]Any higher concentration would introduce more than 1% error, making the analysis unreliable.

• Assures the reliability of quantitative results by minimizing error sources.
• Analyses the impact of different concentration levels of interferents.

Error analysis underscores the importance of method validation and optimization in analytical chemistry.