# Internal Standards and LOD

Learning Objectives

Following this activity, students should be able to:

• Explain the purpose of using internal standards
• Use response factors to calculate an unknown concentration based on an internal standard
• Determine the limits of detection (LOD) and quantification of a method

## Internal Standards

An internal standard (I.S.) in analytical chemistry is a substance that is similar to the analyte that is added in a constant amount to the blank, the standards, and the samples. Internal standards are useful to compensate for changes in extraction efficiency, detector response due to sample loss during other sample preparation steps, fluctuations in sample analyzed, or changes in detector response due to different flow rates.  Internal standards are widely used in chromatography because of differences in the reproducibility of sample injected into the chromatograph.  All of these changes should affect the internal standard to the same degree as the analyte so that the ratio of the standard to analyte remains constant.

The equation below will be used to relate the signal of an analyte (Sx) to the signal of the internal standard (SS) of a known concentration [S]. Note that unlike in standard addition, the analyte X and standard S are chemically distinct species.

$\dfrac{S_x}{[X]}=F\dfrac{S_S}{[S]}\nonumber$

A necessary step will be to determine what the response factor F is by analyzing a sample prepared with a known concentration of analyte X and internal standard S. The following problem walks you through an internal standard calculation. But first a little background about an internal standard procedure.

Background

The fatty acid lauric acid is found in cooking oils, which usually contain fatty acids with even numbers of carbon atoms. It can be quantitated by gas chromatography (GC), but because of variability in the small injection volumes used in GC and the volatility of the solvent used to prepare samples, internal standards are necessary to accurately quantify these compounds. Below lauric acid is shown next to nonanoic acid.

Lauric acid (C12H24O2)

Nonanoic acid (C9H19O2)

Example: A standard solution is prepared by combining 2.00 mL of a 0.100 M lauric acid standard and 4.00 mL of a 0.100 M nonanoic acid and diluting the 10.00 mL. The sample is analyzed by GC and a signal of 5467 counts is obtained for the nonanoic acid and 8675 counts for the lauric acid.  4.00 mL of the 0.100 M nonanoic acid was combined with 4.00 mL of a coconut oil sample containing an unknown lauric acid concentration.  The sample was diluted to 10.00 mL and analyzed by GC.  The analysis gave a peak with 7654 counts for nonanoic acid and 7922 counts for lauric acid.

1. Based on the description on the previous page, discuss with your group why nonanoic acid is a good candidate for an internal standard in the analysis of cooking oils?

1. What is the concentration of each acid in the standard solution?

1. Use the signals obtained for the standard solution to determine the response factor F.

1. What is the concentration of the internal standard in the unknown sample?

1. What is the concentration of lauric acid in the injected sample?

1. What is the concentration of lauric acid in the original coconut oil sample?

1. Summarize the process you just completed for this calculation. You will need to be able to make a final determination for the original sample given just the information in the example at the top of the page.

## How low can you go?

Knowing the limits of a method can be just as important as knowing how to use it. Often, we are concerned with how sensitive a method is and this can be used to determine if a method is appropriate for the goals of our analysis. Sensitivity is conveyed using the definitions for the limit of detection (LOD) and the limit of quantification (LOQ).

$LOD \equiv \dfrac{3s}{m} \hspace{40px} LOQ \equiv \dfrac{10s}{m}\nonumber$

In the above equations s is the standard deviation of replicate measurements of the analytical signal of a sample thought to be close to the detection limit (e.g., lowest concentration standard) and m is the slope of the calibration curve.

1. A new electrochemical method relates concentration to current. The slope of the calibration curve is 0.438 nA/µM. Replicate analysis of a low concentration solution gave the following readings: 2.39 nA, 2.45 nA, 2.54 nA, 2.76 nA and 2.58 nA. What is the detection limit?

1. What is the lowest concentration that could be reliably quantified?

1. Why do you think the “bar” is set higher for quantification than detection?

## Summarizing different calibration methods

Summarize the three different types of calibrations that are used and when each is appropriate to use.

Type

Description

Use when…

External Calibration

Internal Standard