Question

Ibrahim and co-workers developed a new method for the quantitative analysis of hypoxanthine, a natural compound of some nucleic acids. As part of their study they evaluated the method's selectivity for hypoxanthine in the presence of several possible interferents, including ascorbic acid. (a) When analyzing a solution of \(1.12 \times 10^{-6} \mathrm{M}\) hypoxanthine the authors obtained a signal of \(7.45 \times 10^{-5}\) amps. What is the sensitivity for hypoxanthine? You may assume the signal has been corrected for the method blank. (b) When a solution containing \(1.12 \times 10^{-6} \mathrm{M}\) hypoxanthine and \(6.5 \times 10^{-5} \mathrm{M}\) ascorbic acid is analyzed a signal of \(4.04 \times 10^{-5}\) amps is obtained. What is the selectivity coefficient for this method? (c) Is the method more selective for hypoxanthine or for ascorbic acid? (d) What is the largest concentration of ascorbic acid that may be present if a concentration of \(1.12 \times 10^{-6} \mathrm{M}\) hypoxanthine is to be determined within \(1.0 \%\) ?

Short answer

(a) Sensitivity is 66.52 amps/M. (b) Selectivity coefficient is 0.5246. (c) The method is more selective for hypoxanthine. (d) Maximum ascorbic acid concentration is approximately \( 2.135 \times 10^{-8} \mathrm{M} \).

Step-by-step solution

Calculate Sensitivity for Hypoxanthine

Sensitivity is defined as the slope of the calibration curve, which is calculated here as the ratio between the signal and the concentration. For hypoxanthine: \[ \text{Sensitivity} = \frac{\text{Signal}}{\text{Concentration}} = \frac{7.45 \times 10^{-5} \text{ amps}}{1.12 \times 10^{-6} \text{ M}} \]Calculating this gives:\[ \text{Sensitivity} = 66.52 \text{ amps/M} \]

Determine Selectivity Coefficient

Selectivity coefficient is defined by comparing the response of the method to the analyte and the interferent under the same conditions.First, calculate the signal change when ascorbic acid is present:\[ \Delta \text{Signal} = \text{Signal without Ascorbic Acid} - \text{Signal with Ascorbic Acid} = 7.45 \times 10^{-5} - 4.04 \times 10^{-5} = 3.41 \times 10^{-5} \text{ amps} \]The selectivity coefficient, \( k \), is calculated as:\[ k = \frac{\Delta \text{Signal}}{\text{Concentration of Ascorbic Acid}} = \frac{3.41 \times 10^{-5}}{6.5 \times 10^{-5}} \]Calculating this gives:\[ k = 0.5246 \]

Compare Selectivity for Analyte and Interferent

A selectivity coefficient less than 1 indicates a greater selectivity for the analyte (hypoxanthine) than the interferent (ascorbic acid). In this case, the selectivity coefficient is 0.5246, which is less than 1, indicating higher selectivity for hypoxanthine.

Determine Maximum Interferent Concentration for Accurate Measurement

The maximum allowable interferent concentration, \( C_i \), can be calculated using the formula for allowable percentage error:Given that the method allows an error of up to 1%, we calculate using:\[ \frac{C_{i} \times k}{C_{H}} \leq 0.01 \]Solving for \( C_i \):\[ C_i = 0.01 \times C_H \times \frac{1}{k} = 0.01 \times 1.12 \times 10^{-6} \times \frac{1}{0.5246}\]\[ C_i = 2.135 \times 10^{-8} \text{ M} \]

Key concepts

Selectivity Coefficient

In quantitative analysis, the selectivity coefficient is pivotal in determining how well a method can distinguish between the target analyte and potential interferents. It essentially measures the ability of a method to differentiate and provide selective measurement of a target compound in the presence of other substances. For this exercise, it's about how well hypoxanthine is detected in the presence of interferent substances like ascorbic acid.

To calculate the selectivity coefficient, we assess the change in the signal when the interferent is present. The differential signal—expressed in this exercise as the difference in amps—helps us understand the influence of the interferent. The selectivity coefficient (\( k \)) is calculated by dividing this differential signal by the concentration of the interferent.

• When \( k < 1 \), the method is more selective for the target analyte than the interferent.
• When \( k > 1 \), the method struggles to distinguish between the analyte and the interferent as effectively.

Hence, the selectivity coefficient not only quantifies this difference but also ensures that methods are developed to reliably target the intended analytes even with the presence of other substances.

Sensitivity

Sensitivity is a crucial parameter in quantitative analysis, reflecting the ability of a method to detect small changes in analyte concentration, signified by a change in the signal output. For hypoxanthine, sensitivity is determined as the slope of the calibration curve, essentially the ratio of the analytical signal (current, in amps) to the analyte's concentration in molarity.

In the exercise, the sensitivity for hypoxanthine is calculated as:\[\text{Sensitivity} = \frac{\text{Signal (amps)}}{\text{Concentration (M)}} = \frac{7.45 \times 10^{-5}}{1.12 \times 10^{-6}}\]This calculation gives a sensitivity of 66.52 amps/M.

• A higher sensitivity indicates greater efficiency of the method to detect and quantify low concentrations of hypoxanthine.
• Sensitivity directly influences the limit of detection and is essential for discerning small differences between samples.

In practical terms, a sensitive method ensures more accurate and reliable quantitative analysis of compounds like hypoxanthine, especially in biological samples with potentially low concentrations.

Interferents

Interferents are substances that can affect the accuracy of quantitative analysis by introducing signals that overlap or obscure the response from the target analyte. In the context of the exercise, ascorbic acid functions as an interferent to the detection of hypoxanthine.

Understanding and managing interferents is crucial for developing effective analytical methods since they can compromise the method's accuracy and reliability. During analysis, interferents might:

• Contribute additional signals that blend with those generated by the analyte (leading to inaccuracies).
• Cause shifts in the measurement signals, affecting the calibration curve and quantitative results.

To address these challenges, methods such as enhancing selectivity via selectivity coefficients or improving the sensitivity of the detection methods are employed. Accurately determining the concentration of an analyte like hypoxanthine in a mix of other compounds heavily depends on minimizing or accounting for signals from interferents.