Problem 27 - Analytical Chemistry

Question

Milardovíc and colleagues used a flow injection analysis method with an amperometric biosensor to determine the concentration of glucose in blood. \(^{26}\) Given that a blood sample that is \(6.93 \mathrm{mM}\) in glucose has a signal of \(7.13 \mathrm{nA}\), what is the concentration of glucose in a sample of blood if its signal is \(11.50 \mathrm{nA}\) ?

Step-by-Step Solution

Answer

The concentration of glucose in the blood sample is 11.18 mM.

Step 1: Verify Given Values

We are provided with the concentration of glucose in one blood sample as \(6.93\, \text{mM}\) with a corresponding signal of \(7.13\, \text{nA}\). We need to find the concentration for another sample with a signal of \(11.50\, \text{nA}\).

Step 2: Set up the Proportionality Relationship

Assume the glucose concentration is proportional to the signal. Thus, we can set up the proportion: \(\frac{6.93\, \text{mM}}{7.13\, \text{nA}} = \frac{x\, \text{mM}}{11.50\, \text{nA}}\), where \(x\) is the concentration of glucose in the second sample.

Step 3: Solve for the Unknown Concentration

Cross multiply to solve for \(x\): \(6.93 \times 11.50 = 7.13 \times x\). This simplifies to \(79.695 = 7.13x\). Divide both sides by 7.13 to find \(x\): \(x = \frac{79.695}{7.13}\).

Step 4: Calculate the Result

Perform the calculation: \(x = 11.18\, \text{mM}\). This is the concentration of glucose in the second blood sample.

Key Concepts

Amperometric Biosensor

An amperometric biosensor is a device used to measure the concentration of a substance, such as glucose, by detecting the electric current generated by a biochemical reaction. Amperometric refers to the measurement of electric current, which is directly proportional to the concentration of the analyte. In the case of glucose monitoring, enzymes like glucose oxidase are used to catalyze a reaction with glucose, generating an electric current that can be measured.
This technique is advantageous because it's sensitive and can provide real-time, continuous monitoring of analyte concentrations. This makes amperometric biosensors valuable in clinical diagnostics, especially for determining glucose levels in blood samples.

Glucose Concentration

Glucose concentration refers to the amount of glucose present in a solution, expressed in terms of molarity (\(\text{mM}\)). Glucose, a simple sugar, is vital for cellular energy and is found in human blood. Monitoring the glucose concentration is crucial for individuals with diabetes, as it helps manage their condition by keeping blood sugar levels within a target range.
In the exercise, the concentration of glucose in different blood samples is determined by measuring the current generated with an amperometric biosensor. The initial sample's known concentration helps to establish a relationship for calculating the unknown glucose concentration in another sample, based on its signal strength.

Proportionality Relationship

The proportionality relationship is central to solving the given exercise. This relationship assumes that the concentration of glucose is directly proportional to the measurement of the electric current. Mathematically, we represent this as \[\frac{\text{Concentration of Sample 1}}{\text{Signal of Sample 1}} = \frac{\text{Concentration of Sample 2}}{\text{Signal of Sample 2}}\]This setup allows for solving the unknown concentration of glucose in the second sample using a simple cross-multiplication technique.
The idea here is straightforward: as glucose concentration increases, the current signal should also increase proportionally, given that other conditions remain constant.

Analytical Chemistry

Analytical chemistry is the branch of chemistry focused on the qualitative and quantitative analysis of material samples. The goal is to determine its composition and quantify its components. Flow injection analysis combined with amperometric biosensors is a technique used within analytical chemistry to achieve this.
Flow injection analysis provides a consistent way of introducing samples into the detector for continuous analysis, while the biosensor component measures the required analyte concentration. In this context, analytical chemistry provides the foundational techniques and principles that allow for the precise analysis and measurement of substances like glucose in blood samples. By understanding the interplay of these techniques, you can appreciate how scientific instruments and methodologies come together to solve real-world analytical problems.