# How can known standard additions be used to calculate sample concentrations when using an Ion Selective Electrode (ISE)?

## Document ID

Document ID TE9235

## Published Date

Published Date 11/21/2019
Question
How can known standard additions be used to calculate sample concentrations when using an Ion Selective Electrode (ISE)?
Summary
Explanation of the math used to calculate concentration in a sample with a difficult sample matrix where normal measurement cannot be used.
In some cases there can be sample matrix issues that prevent accurate sample measurements through traditional means due to either interferences in the sample matrix or due to the sample matrix being different enough from the matrix of the standards used for calibration that results are impacted.

To do this a calibration still needs to be performed on electrode with an acceptable slope. Volume measurements are important as the accuracy of the volume measurements greatly impacts the accuracy of the measured result. Temperature is also important to keep consistent between standards and samples, in most cases it's best that the calibration and measurements all be taken at room temperature, and the sample should be stirred during measurement.

Procedure:
1. Calibrate electrode following the normal calibration procedure and note the slope of the calibration.
2. Measure 50 mL of the sample to be measured in put into a beaker. (Note: most sample measurement procedures use 25 mL of sample. In this case we are using more because the larger volume leads to a larger spike volume. This is good because if 25 mL is used, the spike volume would likely be very small and difficult to measure accurately.)
3. Add the correct amount of ISA for the sample volume used and stir. (Note: for most Hach ISE's this would be two ISA powder pillows, but consult the probes user manual to be sure)
4. Take a reading and record the result. For this step it's important to record both the mg/L result (even if it's assumed to be wrong) and the mV result.
5. Calculate the volume of standard to add (see below for calculation steps).
6. Add the calculated volume of standard to the sample.
7. Take and additional reading of the spiked sample and record the mV result.
8. Calculate the final result (see below for calculation steps.
Calculation steps for the volume of standard to add (Step 5)

To perform this calculation the following variables are needed:
Cest= Sample result in mg/L of the un-spiked sample
Cstd= Concentration of the standard to be spiked
Vsmp= The volume of sample

Cest acts as an estimate of the sample concentration used to give us an idea of a starting point, the goal of adding the standard is to roughly double the concentration after the standard is added. You want to use a Cstd that is fairly high because you want the volume to be small but easily measured. This will often be the largest concentration of the calibration set. If following the procedure above Vsmp should be 50 mL. If the result is something difficult to measure you want to round up to the nearest volume that would be easy to measure accurately.

Example:
If the result from step 4 was 4.0 mg/L, and you are going to be spiking using a 1000 mg/L standard

Vstd= (4x50)/1000= 0.2 mL

Calculation steps for the concentration of the sample (Step 8)

To perform this calculation the following variables are needed:
Cstd= Concentration of the standard that was added.
Vsmp= The volume of sample (this is 50 mL when following the procedure above)
Vstd= The volume of standard that was added (this is the result calculated in step 5)
S= Slope of the calibration in mV/decade (this is recorded in step 1)
E1= The sample potential in mV (this is recorded in step 4)
E2= The potential of the spiked sample in mV (this is recorded in step 7)

Example:
Following the procedure above, the sample potential measured in step 4 was -53.9 mV. After adding 0.2 mL of 1000 mg/L standard, the potential measures -72.2 mV. The slope of the current calibration is -58.6 mV/decade.

Csmp= (0.2 x 1000)/((50+0.2) x 10 (-72.2-(-53.9))/-58.6) - 50)
Csmp= (200)/(50.2 x 10 -18.3/-58.6 -50)
Csmp= (200)/(50.2 x 10  0.312 -50)
Csmp= (200)/(50.2 x 2.05 -50)
Csmp= (200)/(103 -50)
Csmp= (200)/(53)
Csmp= 3.8 mg/L