Analyzing Gravimetric Determination of Pipette Errors

It is crucial with chemical measurements (for example, in titrimetric analysis) that the amount of liquid is measured precisely. This can be done with the use of various measuring vessels. Laboratories currently use all manner of glass measuring vessels, for example, beakers and flasks for measuring larger volumes of liquid and glass pipettes for smaller volumes. Glass pipettes have been used for such measurements since the 1970s.

The measuring value of a “liter” from outside SI set was accepted for official use during the XII Measuring Conference in 1964. A liter [l] represents a cubic decimeter [dm3].

It is much easier to express volume in liters in analytical chemistry, and, as such, it can be used in various documents, norms and publications.

Scientific developments have resulted in developments in metrology. Nowadays, measuring instruments are even more precise and accurate. However, not much has changed in the case of measuring liquids with pipettes. Commonly known as “liquid handling”, most laboratory operators use modern pipettes that can dose volumes as small as a tenth of a microliter [ul].

Volume Measuring Metrology - Pipettes

Appropriate supervision over these instruments is an important issue that applies to all types of measuring instruments in laboratories. Supervision includes calibration and checking of measuring instruments.

Norms and regulations describe the parameters of pipettes just like for any other measuring instrument. EN ISO 8655-2:2003 Piston-operated volumetric apparatus Part 2: Piston pipettes (in content of ISO 8655-2) is the current international standard that refers to pipettes. The norm describes design requirements that are valid for pipettes manufacturers. It also outlines the maximal permissible errors, which constitute as norms for the manufacturers. It is possible to use these as acceptance criteria for pipettes operators.

There are two types of error in the case of piston pipettes: systematic errors and random error.

Laboratories use a weighing method to determine these errors for piston pipettes. This process and the calculations for the means of error are detailed in the norm EN ISO 8655-6:2003 Piston-operated volumetric apparatus – Part 6: Gravimetric methods for the determination of measurement error (in content of ISO 8655-6).

The amount of liquid that is purged from a piston pipette into a specific vessel is specified by the gravimetric method for the determination of measurement. The analytical balance is converted from mass unit into volumetric unit, which is a microliter or milliliter. The following formula describes this relationship:

(1)

 

Where:

V – denotes volume

m – denotes mass

Z – denotes density

This equation provides a value for the volume that is dependent on the mass and density of a substance. The following formula should be used to determine the volume of the liquid used for checking a piston pipette:

Vi = mi Z (2)

 

Where:

Vi – denotes volume value

mi – denotes mass obtained as a result of weighing purged liquid

Z – denotes corrective coefficient dependent on temperature and air pressure in [l/mg]

Mass is read directly from the measuring instrument, i.e. analytical balance, and the Z coefficient is determined through the formula:

(3)

 

Where:

ρw – denotes water density

ρa – denoted air density

ρb – denotes the density of reference mass used for calibration of the balance (according to R111 OIML stainless steel density ρb is approximately 8000 kg/m3) and is determined for each temperature and pressure value in Attachment A norm ISO 8655-6.

In accordance with ISO 8655-6, the measuring procedure should involve 10 series of measurements from each tested volume and the average volume should be calculated using formula (2). The average value should be calculated according to the relationship:

(4)

 

If the temperature of a weighing room is different from that described in norm ISO 8655-2, then a corrective factor of thermal expansion of a device (pipette) Y should be specified. In this case, formula (2) should be replaced with:

Vi = mi Z Y (5)

 

The corrective factor Y can be estimated through the formula:

Y = 1 - αc(td - td20) (6)

 

Where:

αc – denotes a volumetric expansion coefficient expressed in w °C-1

td – denotes temperature expressed in °C

td20 – denotes constant temperature 20 °C

Y – denotes coefficient value approximately equal to a unit

Error Characteristics of Piston Pipettes

The norm ISO 8655-6 determines the characteristic errors for piston pipettes.

Systematic Error

According to the International Vocabulary of Basic and General Terms of Metrology (VIM), systematic error, (also known as pipette accuracy error) is the difference between the average from infinite quantity of measurements of the same measured value performed under repeatable conditions.

Norm EN ISO 8655-1:2003 Piston-operated volumetric apparatus – Part 1: Terminology, general requirements and user recommendations defines this error for piston pipettes as a difference between the volumetric measurement value and a nominal or selected value of the tested pipette.

Systematic error is expressed in volumetric units, microliters [ul] and percentages [%]. It is marked with the symbol es and can be calculated through the following formula if the error is expressed in microliters:

(7)

 

and through this formula if the error is expressed in percentages:

(8)

 

Where:

Vs – denotes value of tested volume.

For pipettes with a constant volume, the tested volume Vs is also the nominal volume V0 and, as such, can be replaced in formula (8).

Random Error

According to the definition from International Vocabulary of Basic and General Terms of Metrology (VIM), random error (also known as pipette repeatability error) is a difference between the measurement result and the average from infinite quantity of measurements of the same measured value performed in repeatable conditions.

In practice, however, it is only possible to perform a finite quantity of measurements and, as such, it is only possible to estimate the value of random error.

The norm EN ISO 8655-1:2003 Piston-operated volumetric apparatus – Part 1: Terminology, general requirements and user recommendations defines the error for pipettes as the dispersion between the measuring result of volume around the average value of volume.

If an assumption is made that in both cases the measure is defined as standard deviation, then both methods are correct.

Random error is expressed in volumetric units: microliters [l] and percentages [%], and marked with the CV symbol. Standard deviation can be used to calculate the measure of random error, standard deviation:

(9)

 

Where:

n – denotes quantity of repetitions, in this case 10 series of repetitions.

Random error can also be expressed in terms of percentages. In this case, the following formula can be used:

(10)

 

Gravimetric Method of Measuring Process

It is necessary to have adequate measuring equipment to adhere to the procedure of gravimetric calibration of a piston pipette in accordance with the metrological requirements as defined by the norm ISO 8655-6.

Analytical Balance

An analytical balance is the most important measuring instrument for the process of calibration of piston pipettes. Pipette volume is taken into consideration when this is selected. Norm ISO 8655-6 precisely defines the requirements for applicable balances:

Chart 1. Minimal requirements for balances (according to ISO 8655-5). Source: Radwag Balances & Scales

Tested volume V Reading unit d mg Repeatability and linearity mg Standard measurement uncertainty mg
1 ul V < 10 ul 0,001 0,002 0,002
10 ul < V < 100 ul 0,01 0,02 0,02
100 ul < V < 1000 ul 0,1 0,2 0,2
1 ml < V < 10 ml 0,1 0,2 0,2
10 ml < V < 200 ml 1 2 2

 

Where the standard measurement for the uncertainty of the liquid weighing process is known (for example from a balance calibration certificate), then this should be used as an acceptance criterion rather than repeatability and linearity parameters. An assumption should be made that the standard deviation is no bigger than two or threefold of the reading unit d.

A balance used for calibration of pipettes should have a valid calibration certificate at the time of carrying out the measurements to maintain measuring coherence.

A balance designed for pipette calibration should first be appropriately prepared in accordance with manufacturer recommendations. Recommendations on balance installation at a workstation are usually outlined in the user manual. Dependent on the design of the balance, an adjustment should be made to the operational conditions in the weighing room, for example, adjustment to gravitational acceleration force:

  • With appropriately selected standard mass, class and nominal weight of the standard mass are outlined by the manufacturer of the balance.
  • With an automatic internal calibration system, there is a built-in reference mass, which is an integral part of the balance.

To make a balance adjustment, the mass of standard or the reference mass (internal or external) should be compared with the mass that is saved in the balance’s memory. It is possible to select three kinds of calibration when balances are equipped with an automatic internal calibration system:

  • Start-up calibration, which automatically begins when a balance is plugged into the mains and automatically compensates the errors by sourcing differences in gravitational acceleration force from the manufacturers site and the users site
  • Temperature calibration, which will automatically begin if a balance sensor detects a change in temperature inside the balance mechanism that exceeds the temperature thresholds set in the service menu of the balance
  • Time calibration is automatically started after a set amount of time as outlined in the service menu of the balance.

Balance indication drift in relation to temperature changes, for instance during self heating of a balance.

Figure 1. Balance indication drift in relation to temperature changes, for instance during self heating of a balance. Image Credit: Radwag Balances & Scales

Temperature and time calibration may have a negative impact on the measuring process for such small increments of mass. Values of temperature sensitivity drift estimated as error values are presented in the following table:

Chart 2. Balance temperature errors. Source: Radwag Balances & Scales

Balance model Maximal capacity - Max Reading unit - d Division of balance Max/d Sensitivity drift Temperature error for balance Max capacity Temperature error for Δm = 100 g
[g] [mg] [units] Ppm/ºC [mg] [mg]
MXA 31 31 0,001 31.000.000 2 6,200 0,000068
XA 60/220/X 60 0,01 6.000.000 2 4,80 0,000033

 

An analysis of temperature drifts from the specified temperature range of 18 °C to 30 °C by the manufacturers in ppm/°C (parts per million) led to the conclusion that a balance needs to be calibrated to compensate for any temperature errors. Balances are equipped with systems that enable automatic internal calibration that are dependent on time and temperature.

When balances are used in verifiable conditions in line with legal metrology, then these systems of automatic internal calibration have to be active and the operator should not be granted access to modify the settings. Beginning a calibration process for pipettes can prove to be difficult in procedure realization. The results in chart 3 demonstrate that temperature errors for very small increments of mass do not affect the measuring accuracy.

It is useful to know that balances for checking pipettes are adjusted to automatic parameters of internal time and temperature calibration. As such, the best solution for pipette checking is to apply balances that are not controlled by legal metrology, as this is the only route for allowing the operator to adjust balance parameters in relation to calibration features.

Ambient Conditions for Pipette Calibration

The pipette calibration process should be carried out in a weighing room with stable ambient conditions, free from air. In line with regulations, the weighing room temperature should be maintained at a constant level and differ by no more than ± 0,5 °C during the measuring process. The temperature range should be set between 15 °C and 30 °C, and relative humidity of around 50% should also be maintained.

To carry out a proper pipette calibration, the pipette, tips and distilled water should all be stabilized for temperature in the weighing room. A temperature stabilization period of at least two hours before the weighing process is carried out is specified by norm requirements. The pipette and distilled water temperature should be equivalent to the weighing room temperature.

Continuous monitoring of the weighing room’s ambient conditions is required, particularly the air temperature and air pressure. These are both required for calculations. The humidity and distilled water temperature also need to be known.

In accordance with requirements from norm ISO 8655-6, measuring instruments should be in line with norm requirements about standard uncertainty:

  • Thermometer, with standard uncertainty lower or equaling 0,2 °C
  • Hygrometer, with standard uncertainty lower of equaling 10%
  • Barometer, with standard uncertainty lower or equaling 0.5 kPa

All the above uncertainty parameters are specified for the expansion coefficient k = 1. The distilled water used for pipette calibration needs to be compatible with the requirements of class 3 or should be prepared in accordance with the specifications of international norm ISO 3696 Water for laboratory use – Specification and test methods.

Evaporation

Liquid evaporation during the weighing procedure is an important aspect of pipette calibration.

Evaporation is a natural physical phenomenon where liquid changes its state to gas, in this case, water vapor. This process typically takes place on the surface of liquid. Temperature, humidity and partial pressure all influence the speed of evaporation.

Partial pressure is the pressure created by a selected component of gas mixture if the component occupied the same area of vapor over liquid in a specific temperature. If the vapor pressure and saturated vapor is equivalent at a specific temperature, then the evaporation process does not exist. This status is also expressed as an equilibrium between evaporation and condensation.

The evaporation process is present in any case when it comes to weighing distilled water. It is required by norm ISO 8655-6 that the calculations take into consideration the evaporation process and that measures are taken to decrease the potential risk of measuring errors.

For volumes below 50 l, a weighing vessel with a cover is required by the norm, or alternatively, a method, which compensates for this unfavorable phenomenon. The norm also requires that measurements of a single volume should be carried out as quickly as possible, usually over a time period of around 60 seconds. This is because quick and repeatable measurements have a positive influence on the size of the error caused by evaporation.

The stabilization time for the weighing process hugely affects pipette calibration. The longer the weighing time, the greater the influence of ambient conditions, such as air, vibrations and temperature drifts.

Most balances used for pipette calibration allow the operator to adjust parameters corresponding to the weighing process to optimize them for the current ambient conditions.

Every balance on manufacture will be adjusted to a certain set of ambient conditions. It is typically assumed that laboratory conditions are compatible with the manufacturer's requirements for temperature range, humidity or possible disturbances. However, these assumptions do not always hold. For the majority of electronic balances, adjusting them for ambient conditions requires:

  • Selection of different setting for signal filtering processes /stronger or weaker filter setting
  • Selection of different criteria for determination of stable measurement.

Graph indicating stabilization of weighing process.

Figure 2. Graph indicating stabilization of weighing process. Image Credit: Radwag Balances & Scales

For practical reasons the filter settings are described as fast, average, slow and very slow, and the criteria for determining the weighing results stability are described as fast, fast + reliable and reliable.

The general rule is that the bigger the disturbances, the higher the filter settings. Such filter settings usually lengthen the weighing process as a consequence. However, in some cases, this is the only way to obtain the correct weighing result. In reality, the best option is to eliminate the sources of disturbance within the process of pipette calibration.

Measuring Retraceability in Gravimetric Pipette Calibration

Maintaining measuring retraceabiility is one of the most important aspects related to measurements. A feature of the measuring process or reference mass, retraceability can be bound with its references - in most cases with national or international standard masses. The binding is continuous and an element of this binding has its uncertainty determined. The uniqueness of measurements is determined by measuring retraceability.

Retraceability schema.

Figure 3. Retraceability schema. Image Credit: Radwag Balances & Scales

Piston pipette retraceability visualization.

Figure 4. Piston pipette retraceability visualization. Image Credit: Radwag Balances & Scales

The best approach for maintaining retraceability of measurements is to calibrate these instruments and masses within accredited laboratories and to monitor them against an internal timetable for calibration. Selected instruments and reference masses should be used to perform the internal control.

Gravimetric Method Measuring Uncertainty

Measuring uncertainty is associated with testing and/or measuring procedures valid within laboratories. There is no such thing as an accurate measurement. It is only possible to estimate the range in which the obtained result is positioned. The accepted trust level dictates the size of this range. A situation may occur where the accepted result is incorrect, or a correct result may be considered incorrect if an uncertainty budget analysis is performed incorrectly.

In research laboratories and scientific offices, the uncertainty of measurement is undergoing a thorough analysis of testing. Uncertainty of measurement, as defined by the International Vocabulary of Basic and General Terms of Metrology, is a parameter relating to a measuring result that can be characterized by dispersion of indications and assigned to specific measured value.

This is the case, for example, with standard deviation and its multiplication. Standard deviation from a series of measurements is also the uncertainty of measurements.

Dependent on the parameters source, the uncertainty of measurements can be grouped into two types – type A and type B.

Method A is carried out through a static analysis of the observed series. A normal distribution is considered for uncertainty type A, which can be presented graphically as a Gausses curve.

A scientific analysis based on all available information on the changeability of the initial value is used to determine uncertainty type B. Such data is obtained from previously performed measurements, operator’s experience, and characteristic features of measured materials and measuring devices. Data is utilized from manufacturer’s product specification, uncertainty reference data, handbook and manual content and all accessible publications by uncertainty type B. Calibration certificates of measuring instruments, reference masses and sizes from physical objects or any other certificates provide another important source of data.

Using the analytical balance mentioned above, it is possible to determine the components of uncertainty type B. These are:

  • Reading unit d,
  • Repeatability, as determined by the standard deviation set by an operator or during the calibration process,
  • Balance indication error, specified in calibration certificate,
  • Uncertainty while determining an indication error.

More parameters can be found through a more thorough analysis, but dependent on its accuracy, these may not influence a measurement.

Complex Uncertainty

A connection between uncertainty type A and type B is known as complex uncertainty. There are, however, some scenarios where complete uncertainty analysis is based solely on type B.

Extended Uncertainty

The range of values surrounding the measuring result is described by extended uncertainty. Such a range can cover a huge part of the distribution of value.

In accordance with the Guide to Expression of Uncertainty in Measurements, u denotes match uncertainty, and U denotes the expression of extended uncertainty. A graphical representation of measurement uncertainty is shown on the chart below:

Figure 5. Graphic interpretation of uncertainty of measurement. Image Credit: Radwag Balances & Scales

where:

x – measurement result

xP – measurand

Value x has been obtained as result of value measurement xP. The result of the measurement is not equal to measurand and there are no ideal measurements in the environment. It is only possible to discuss the range in which the measurand is positioned. The range can have a bigger or smaller scope depending on the accuracy of a measuring process and the uncertainty associated with it. The applied measuring device, ambient conditions, the operator, and also a proper analysis of measuring uncertainty all dictate the scope size.

An extension ratio k is a numerically expressed ratio, used as a multiplier of standard complex uncertainty, determined to set extended uncertainty.

The following relationship can be used to express the extended uncertainty:

U = ku(x) (13)

 

Where:

U – extended uncertainty

k – extension ratio

u(x) – complex uncertainty

In the case of piston pipette calibration, it is possible to distinguish between two sources of uncertainty:

  • Uncertainty related to measuring instrument (pipette)
  • Uncertainty related to measuring method (gravimetric method).

In accordance with the Guide to Expression of Uncertainty in Measurements, it is necessary to analyze both sources of uncertainty and take them into account during the estimation of complex uncertainty during the calibration process.

A statement in the norm ISO 8655-6 describes the uncertainty level obtained from a series of gravimetric measurements as low when measuring equipment is used in comparison to results from a measuring process. An assumption is made that instruments used for the measuring procedure (for example, a balance, barometer or thermometer) are used in line with the specification from this norm. This suggests that operators should focus on systematic and random measuring errors resulting from a series of ten repetitions of tested volume measurement for each instrument and ignore uncertainty level in measurements.

It is important to note that the uncertainty evaluation of the gravimetric method is not influenced by systematic measuring error. It is a measuring result characteristic to volume measurement that includes random error.

u = |es|+2 • sr (14)

 

A simplified formula for calculating uncertainty is provided with norm ISO 8655-6, which can be used to evaluate measuring uncertainty in piston pipette calibration with a 95% trust level:

A thorough and correct analysis of the complete measuring process is crucial for a successful evaluation of uncertainty. Measuring uncertainty should be evaluated based on its accuracy, as often some of the uncertainty components may influence the measuring result. As such, in scenarios with very small volumes or where a more thorough analysis is carried out, formula (12) is not applicable. The ISO/TR 20461 document describes in detail the analysis of gravimetric method uncertainty evaluation.

Sources of Errors in the Process of Pipettes Checking

Measurements carried out during the piston pipette calibration process are affected by the potential risk of measuring errors, as demonstrated by test results documented by RADWAG in section 2 in an analysis of norm ISO 8655-6 requirements. The main sources of risk and the influence of these on the measuring result were defined by research carried out by RADWAG Measuring Laboratory. Sources of errors have been observed in:

  • The incompatible balance used for test procedure
  • Incorrect weighing vessel
  • Liquid evaporation process during weighing procedure
  • Incorrect ambient conditions in a weighing room or lack of continuous monitoring
  • Incorrect workstation (vibrations, air)
  • Incorrect liquid used for piston pipette calibration
  • Calculation errors
  • Incorrectly selected pipette tips
  • Inappropriate physiological condition of an operator
  • Non-ergonomic workstation

Most of these error sources have been discussed above. Tests were performed on inappropriate or incorrect ambient conditions in a weighing room, lack of continuous monitoring, vibrations and air, which influence balance operation, incorrect calculation and workstation and ergonomics and all have been discussed in section 3.

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Last updated: Nov 28, 2019 at 6:31 AM

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