Problem 28 - Analytical Chemistry

Question

Lithium in the blood serum of a manic-depressive patient treated with lithium carbonate is determined by flame emission spectrometry, using a standard additions calibration. One hundred microliters of serum diluted to \(1 \mathrm{~mL}\) gives an emission signal of 6.7 units. A similar solution to which \(10 \mu \mathrm{L}\) of a \(0.010 \mathrm{M}\) solution of \(\mathrm{LiNO}_{3}\) has been added gives a signal of 14.6 units. Assuming linearity between the emission signal and the lithium concentration, what is the concentration of lithium in the serum, in parts per million?

Step-by-Step Solution

Answer

The concentration of lithium in the serum is approximately 0.59 ppm.

Step 1: Understand the Problem

We have a serum sample and a modified sample with a known amount of lithium nitrate. We need to calculate the concentration of lithium in the original serum using the difference in emission signals.

Step 2: Determine initial concentration contributions

The initial serum signal is 6.7 units with an unknown lithium concentration. In the second solution, adding 10 µL of a 0.010 M LiNO3 solution to 1 mL of serum adds a known amount of lithium.

Step 3: Calculate lithium added in molarity

The volume added is 10 µL and concentration is 0.010 M, thus moles of Li added is calculated as:\[ n = 0.010 \, \text{mol/L} \times \frac{10 \, \text{µL} \times 10^{-6} \, \text{L}}{1 \, \text{mL} \times 10^{-3} \, \text{L}} = 0.0001 \, \text{moles/L} \]

Step 4: Understand change in the emission units

The signal increased from 6.7 to 14.6 units, an increase of 7.9 units, due to the added lithium.

Step 5: Relate emission change to concentration

The increase of 7.9 units corresponds to the concentration increase of 0.0001 M. Assuming linearity, 1 unit increase represents 0.0001 M / 7.9.

Step 6: Solve for original lithium concentration in serum

The original concentration of lithium in serum is found using the initial signal of 6.7 units:\[ C_{Li} = 6.7 \, \text{units} \times \frac{0.0001 \, \text{mol/L}}{7.9 \, \text{units}} = 0.00008481 \, \text{mol/L} \]

Step 7: Convert molarity to parts per million (ppm)

Converting from molarity to ppm involves accounting for the molar mass of lithium (6.94 g/mol):\[ \text{ppm} = 0.00008481 \, \text{mol/L} \times 6.94 \, \text{g/mol} \times 10^3 \, \text{mg/g} = 0.5886 \, \text{ppm} \]

Key Concepts

Standard Additions Calibration

Standard additions calibration is a crucial technique often used in analytical chemistry for determining the concentration of an analyte in a complex sample. This method helps overcome matrix effects that may otherwise interfere with the analysis.
In this exercise, we assume that a linear relationship exists between the emission signal produced by flame emission spectrometry and the concentration of lithium.

• First, an initial measurement of the emission signal from the serum is taken.
• Then, a known amount of standard (in this case, lithium nitrate) is added to the serum sample.
• A second measurement of the emission signal is taken after adding the standard.

By observing the change in signal, we calculate the concentration of lithium in the original serum. This method proves useful because the difference in signals is proportional to the amount of lithium present.
Thus, the standard additions calibration provides a path to measure analyte concentration by minimizing systematic errors due to sample matrix.

Lithium Concentration

The main goal in this context is to determine the concentration of lithium within a blood serum sample. Lithium is often prescribed for mood disorders, and its therapeutic range must be carefully monitored to ensure efficacy and safety.
In this particular case, the concentration of lithium in the serum was evaluated using flame emission spectrometry, which analyzes light emitted by atoms in a flame.
The linear relationship assumed means that increasing the lithium concentration by a known amount should increase the measured signal proportionately.

• With an initial emission signal of 6.7 units, the lithium concentration is unknown.
• Adding 10 µL of 0.010 M LiNO3 amplifies the signal significantly.
• Through calculations, this increase quantifies the added lithium, guiding us in establishing the concentration in the original serum.

By accurately quantifying this concentration change, a precise number in ppm (parts per million) can be determined, essential for patient care.

Blood Serum Analysis

Analyzing blood serum is essential for monitoring numerous biochemical substances, critical in both diagnostics and therapeutic interventions. Lithium measurement in blood is especially significant for patients under treatment for bipolar disorder.
Flame emission spectrometry offers a valuable method for such analyses due to its ability to detect metal ions accurately. In this process:

• Serum, a complex biological matrix, can interfere with signal measurements, which is where standard additions help mitigate such interferences.
• The emission signal difference indicates the concentration of lithium in the serum.
• Calculations convert this initial concentration from molarity to ppm, fulfilling a common requirement for such biological assessments.

Furthermore, consistent analysis of lithium levels in blood serum ensures patient safety by maintaining appropriate therapeutic levels, preventing toxicity while ensuring effectiveness.
Thus, mastering this analysis technique provides a robust tool for therapeutic drug monitoring.