Question

A sample is analyzed to determine the concentration of an analyte. Under the conditions of the analysis the sensitivity is \(17.2 \mathrm{ppm}^{-1}\). What is the analyte's concentration if \(S_{\text {total }}\) is 35.2 and \(S_{\text {reag }}\) is \(0.6 ?\)

Short answer

The analyte's concentration is approximately 2.012 ppm.

Step-by-step solution

Understand the formula for concentration

The formula to calculate the concentration of an analyte is given by:\[ \text{Concentration} = \frac{S_{\text{total}} - S_{\text{reag}}}{\text{sensitivity}} \]where \( S_{\text{total}} \) is the total signal, \( S_{\text{reag}} \) is the reagent signal, and sensitivity is given.

Substitute the values into the formula

Given values: \( S_{\text{total}} = 35.2 \), \( S_{\text{reag}} = 0.6 \), and sensitivity = 17.2 ppm\(^{-1}\).Substitute these into the formula:\[ \text{Concentration} = \frac{35.2 - 0.6}{17.2} \]

Perform the calculation

First, calculate the difference between \( S_{\text{total}} \) and \( S_{\text{reag}} \):\[ 35.2 - 0.6 = 34.6 \]Next, divide the result by the sensitivity:\[ \frac{34.6}{17.2} \approx 2.012 \]

Conclude with the solution

The concentration of the analyte is approximately \( 2.012 \) ppm.

Key concepts

Analyte Concentration

An analyte concentration refers to the amount of a substance within a given sample. It's crucial in analytical chemistry to accurately determine the concentration because it provides valuable information about the sample's composition. When assessing concentration, chemists often use signal measurements, as seen in our exercise.

The formula for determining analyte concentration in this context uses three key elements:

• **Total Signal ( S_{total} ):** This is the overall signal measurement, which includes all contributions from the analyte and other substances in the sample.
• **Reagent Signal ( S_{reag} ):** This portion of the signal comes from substances other than the analyte, such as reagents or impurities.
• **Sensitivity:** This is a known constant value indicating how much the signal changes per unit change in the analyte concentration.

To calculate the analyte concentration, subtract the S_{reag} from S_{total} to solely consider the contribution of the analyte, and then divide by the sensitivity. This gives a clear indication of how much analyte is present in terms of its contribution to the overall signal.

Sensitivity

In the context of analytical chemistry, sensitivity is a measure of how effectively a measurement method can detect changes in analyte concentration. It is essentially the relationship between the signal produced and the concentration of the analyte being measured.

Sensitivity is often expressed in units such as ppm, and it dictates how minute changes in concentration can alter the signal. For example, in our exercise, sensitivity is given as 17.2 ppm⁻¹, meaning for every additional ppm of analyte, the signal increases by that factor.

The sensitivity of a measurement can play a significant role in determining the reliability and precision of the results. Higher sensitivity allows for the detection of smaller changes in concentration, making it an important parameter in experiments where precision is needed. Keep in mind, though, that extremely high sensitivity can sometimes also amplify noise in measurements, so balancing it with specificity and accuracy is key.

Signal Analysis

Signal analysis in analytical chemistry involves interpreting the signals received from instruments to deduce meaningful chemical information about a sample. Signals are quantitative measurements that represent the presence or concentration of an analyte.

In signal analysis, one starts by understanding the components of the signals:

• **Total Signal ( S_{total} ):** This is the combined result from all influencing factors, including the target analyte and background signals.
• **Reagent Signal ( S_{reag} ):** This represents the signal contribution from reagents or any non-analyte sources in the sample.

When analyzing signals, the main goal is to isolate the analyte's contribution ( S_{analyte} ) from these other components using calculations. In the provided exercise, this is done by subtracting the reagent signal from the total signal.

This clean differentiation ensures the resulting calculation accurately reflects the analyte's concentration. Accurate signal analysis is vital for clear results, helping researchers make informed conclusions about their samples.