Determination of Cadmium Release from Ceramic Ware by Atomic Absorption Spectrometry

This is the example A5 of the EURACHEM / CITAC Guide "Quantifying Uncertainty in Analytical Measurement", Second Edition.

The amount of released cadmium from ceramic ware is determined using atomic absorption spectrometry. The procedure employed is the empirical method BS 6748.

The item to be tested is filled with a 4 % v/v acetid acid solution for a given lenght of time, the amount of cadmium released from the item is then calculated from the measured cadmium concentration in the leach solution and the volume of the leach solution. Parameters such as leaching time, temperature, acid concentration etc. are specified in the empirical method.

Model Equation:

{calculation of the uncertainty of volume VL}

VL = VL nominal * fVL-filling * fVL-temperature * fVL-reading * fVL-calibration;

{calculation of the uncertainty of the surfache area}

aV = aV nominal * faV-length1 *faV-lenght2 * faV-area;

{calculation of the mass of cadmium leached}

r = c0 * VL / aV * d * facid * ftime * ftemperature;

List of Quantities:

Quantity Unit Definition
VL L Volume of the leachate
VL nominal L Nominal volume of the leachate
fVL-filling   Uncertainty contribution of VL due to filling of the vessel
fVL-temperature   Uncertainty contribution of VL due to temperature variation
fVL-reading   Uncertainty contribution of VL due to reading of the measuring cylinder
fVL-calibration   Uncertainty contribution of VL due to calibration of the measuring cylinder
aV dm2 Surface area of the vessel
aV nominal dm2 Nominal surface area of the vessel
faV-length1   Uncertainty contribution to aV of first length measurement (i.e. height)
faV-lenght2   Uncertainty contribution to aV of second length measurement (i.e. lenght)
faV-area   Uncertainty contribution to aV due to imperfect geometry
r mg/dm2 Mass of cadmium leached per unit area
c0 mg/L Content of cadmium in the extraction solution
d   Dilution factor (if used)
facid   Influence of the acid concentration
ftime   Influence of the duration
ftemperature   Influence of the temperature

VL nominal: Constant
Value: 0.332 L
The nominal volume is not associated with any uncertainties. Four different factors contribute to the uncertainty of the real volume, filling, temperature, reading and calibration. These are introduced in the uncertainy budget through the factors fVL-filling, fVL-temperature, fVL-reading and fVL-calibration.

fVL-filling: Type B triangular distribution
Value: 0.995
Halfwidth of Limits: 0.005
The method requires the vessel to be filled 'to within 1mm from the brim'. For a typical drinking or kitchen utensil, this represents about 1% of the total height. The vessel will therefore be 99.5% ± 0.5% filled.

fVL-temperature: Type B rectangular distribution
Value: 1
Halfwidth of Limits: =2.1e-4*2
The temperature of the acetic acid has to be 22 ±2°C, according to the method. This range leads to an uncertainty in the measured volume, due to a considerably larger volume expansion of the liquid compared to the vessel. The coefficient of volume expansion for water is 2.1·10-4°C-1. This leads to a possible volume variation of ±(332 · 2 · 2.1·10-4) mL. A rectangular distribution is assumed for the temperature variation of the volume. Since fVL-temperature is a multiplicative factor to the nominal volume, which is only used to introduce the temperature uncertainty, it has the value 1. Its uncertainty is calculated as the possible volume variation divided by the volume.

fVL-reading: Type B triangular distribution
Value: 1
Halfwidth of Limits: 0.01
fVL-calibration: Type B triangular distribution
Value: 1
Halfwidth of Limits: =2.5/332
The volume is calibrated within ±2.5 mL for a 500 mL measuring cylinder. No further statement is made about the level of confidence or the underlying distribution. An assumption is necessary to work with this uncertainty statement. In this case a triangular distribution is assumed. Since fVL-calibration is a multiplicative factor to the nominal volume, which is only used to introduce the calibration uncertainty, it has the value 1. The halfwidth of limits corresponds to the relative uncertainty as stated by the manufacturer (i.e. 2.5 mL / 332 mL).

aV nominal: Constant
Value: 2.37 dm2
The nominal surface are is not associated with any uncertainties. Three different factors contribute to the uncertainty of the real surface area, that are the two length measurements required to calculate the surface area, and an area-factor, covering the imperfect geometry of any real vessel.

faV-length1: Type B normal distribution
Value: 1
Expanded Uncertainty: =0.01/1.45
Coverage Factor: 1
Typically, two length measurements are required to calculate the surface area of a vessel. In this case, the item was approximated by a cylindrical geometry. Typical dimensions are between 1.0 and 2.0 dm, leading to an estimated uncertainty of 1 mm. The two length measurements required for this vessel were 1.45 and 1.64 dm.

faV-lenght2: Type B normal distribution
Value: 1
Expanded Uncertainty: =0.01/1.64
Coverage Factor: 1
Typically, two length measurements are required to calculate the surface area of a vessel. In this case, the item was approximated by a cylindrical geometry. Typical dimensions are between 1.0 and 2.0 dm, leading to an estimated uncertainty of 1 mm. The two length measurements required for this vessel were 1.45 and 1.64 dm.

faV-area: Type B normal distribution
Value: 1
Expanded Uncertainty: =0.05/1.96
Coverage Factor: 1
The item is not a perfect geometric shape (cylinder in this case). Therefore the real surface area may deviate from the caluclated one. This deviation was estimated to be 5% at 95% confidence level. To obtain the standard uncertainty the possible deviation is divided by 1.96.

c0: Type B normal distribution
Value: 0.26 mg/L
Expanded Uncertainty: 0.018 mg/L
Coverage Factor: 1
The content of cadmium in the extraction solution is calculated using a calibration curve. For the calibration curve five calibration standards were prepared and measured 3 times each. Using a linear least square fit, the slope and intercept of the calibration curve have been calculated. Using this data, the concentration c0 was calculated from a duplicate measurement of the actual leach solution. The calculation of the uncertianty of the least square fit is described in Appendix E3 of the EURACHEM / CITAC Guide. Only the final result of this calculation is used here.

d: Type B normal distribution
Value: 1
Expanded Uncertainty: 0
Coverage Factor: 1
For this sample, no dilution of the leach solution was necessary, therefore no uncertainty needs to be introduced here.

facid: Type B normal distribution
Value: 1
Expanded Uncertainty: =0.008*0.1
Coverage Factor: 1
Data from two study on the effect of acid concentration on lead release was used to estimate this factor. One study showed that lead release was increased by approximately 0.1 when the acid concentration was increased from 4 to 5% v/v. Another study reported a 50% increase of the lead release for a change of acid concentration from 2 to 6% v/v. Assuming a liner effect, on can estimate a change of facid of 0.1 per 1% v/v change of acid concentration. In another experiment the concentration of the acetic acid and its standard uncertainty have been established using titration with standardised NaOH solution, resulting in an acetic acid concentration of 3.996 % v/v with a standard uncertainty of 0.008% v/v. The uncertainty of facid can then be calculated as 0.008 · 0.1.

ftime: Type B rectangular distribution
Value: 1
Halfwidth of Limits: =0.5*0.003
For a relatively slow process such as leaching, the amount leached will be approximately proportional to the leaching time for small changes in that time. In a study, a mean change of concentration over the last six hours of leaching of approximately 1.8 mg · L-1 (=0.3% / h) was found. The leaching time is specified in the method as 24 ±0.5 h, the content of Cd in the extraction solution therefore needs to be corrected by a factor of 1 ±(0.5 · 0.003). A rectangular distribution is assumed for this factor.

ftemperature: Type B rectangular distribution
Value: 1
Halfwidth of Limits: 0.1
A number if studies on the effect of temperature on metal release from ceramic ware have been undertaken. The temperature effect is substantial, and a near-exponential increase in metal release with temperature is observed until limiting values are reached. Nevertheless, only one study gives information for the temperature range 20-25°C. The metal release approximately linear wit temperature in this temperature range, with a gradient of approximately 5% °C-1. For the ±2°C range allowed by the empirical method, this leads to a factor ftemperature of 1 ± 0.1. A rectangular distribution is assumed for this factor.

Interim Results:

Quantity Value Standard
Uncertainty
VL 0.33034 L 1.82·10-3 L
aV 2.3700 dm2 0.0643 dm2

Uncertainty Budgets:

r: Mass of cadmium leached per unit area
Quantity Value Standard
Uncertainty
Distribution Sensitivity
Coefficient
Uncertainty
Contribution
Index
VL nominal 0.332 L          
fVL-filling 0.99500 2.04·10-3 triangular 0.036 74·10-6 mg/dm2 0.0 %
fVL-temperature 1.000000 242·10-6 rectangular 0.036 8.8·10-6 mg/dm2 0.0 %
fVL-reading 1.00000 4.08·10-3 triangular 0.036 150·10-6 mg/dm2 0.2 %
fVL-calibration 1.00000 3.07·10-3 triangular 0.036 110·10-6 mg/dm2 0.1 %
aV nominal 2.37 dm2          
faV-length1 1.00000 6.90·10-3 normal -0.036 -250·10-6 mg/dm2 0.5 %
faV-lenght2 1.00000 6.10·10-3 normal -0.036 -220·10-6 mg/dm2 0.4 %
faV-area 1.0000 0.0255 normal -0.036 -930·10-6 mg/dm2 7.3 %
c0 0.2600 mg/L 0.0180 mg/L normal 0.14 2.5·10-3 mg/dm2 53.9 %
d 1.0 0.0 normal 0.0 0.0 mg/dm2 0.0 %
facid 1.000000 800·10-6 normal 0.036 29·10-6 mg/dm2 0.0 %
ftime 1.000000 866·10-6 rectangular 0.036 31·10-6 mg/dm2 0.0 %
ftemperature 1.0000 0.0577 rectangular 0.036 2.1·10-3 mg/dm2 37.5 %
r 0.03624 mg/dm2 3.42·10-3 mg/dm2

Results:

Quantity Value Expanded
Uncertainty
Coverage
factor
Coverage
r 0.0362 mg/dm2 6.8·10-3 mg/dm2 2.00 95% (t-table 95.45%)

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