[Header]
Format=SMU
ver=3
appl=GUMWB32
MR=0
SUR=0
SUP=0
UIP=1
UCR=0
status=2
FUEB=0

[Title]
Title='Standardising a sodium hydroxide solution'
Ref=''
Date='08/29/2007'
Version=''
Author=''
Description=11
Description[0]='This is the example A2 of the EURACHEM /'
Description[1]='CITAC Guide "Quantifying Uncertainty in Analytical Measurement", Second'
Description[2]='Edition.'
Description[3]=''
Description[4]='A'
Description[5]='solution of sodium hydroxide (NaOH) is standardised against the titrimetric'
Description[6]='standard potassium hydrogen phtalate (KHP).'
Description[7]=''
Description[8]='The titrimetric standard KHP is dried and weighed. After the preparation of the'
Description[9]='NaOH solution a'
Description[10]='sample of the KHP is dissolved and then titrated using the NaOH solution.'
PictureCount=1
DCount=1

[Model]
Model=15
Model[0]='{Molar mass of KHP}'
Model[1]=''
Model[2]='M_KHP = 8 * M_C + 5 * M_H + 4 * M_O + M_K;'
Model[3]=''
Model[4]='{Volume delivered by the piston burette, excluding repeatability}'
Model[5]=''
Model[6]='V_T = V_nominal * f_V\minus\calibration * f_V\minus\temperature;'
Model[7]=''
Model[8]='{mass of KHP weighed, excluding repeatability}'
Model[9]=''
Model[10]='m_KHP = m_container\sp\and\sp\KHP - m_container\sp\less\sp\KHP;'
Model[11]=''
Model[12]='{calculation of the concentration of the NaOH solution}'
Model[13]=''
Model[14]='c_NaOH = (k_mL * m_KHP * P_KHP) / (M_KHP * V_T) * f_repeatability;'
CE=1
CTC=1

[Components]
CompOrder=3
Comp=16
Comp[0]=M_KHP_
Comp[1]=M_C_
Comp[2]=M_H_
Comp[3]=M_O_
Comp[4]=M_K_
Comp[5]=V_T_
Comp[6]=V_nominal_
Comp[7]=f_V\minus\calibration_
Comp[8]=f_V\minus\temperature_
Comp[9]=m_KHP_
Comp[10]=m_container\sp\and\sp\KHP_
Comp[11]=m_container\sp\less\sp\KHP_
Comp[12]=c_NaOH_
Comp[13]=k_mL_
Comp[14]=P_KHP_
Comp[15]=f_repeatability_

[COMP 0]
Type=Temp
Definition='Molar mass of KHP'
Unit='g/mol'
Description=0
Fcov=2
NomUnit=
UncUnit=
CovID=1
UncID=0
Vnom=204.2212
Ustd=0.00376530211271287
Neff=10000
HB=0
HC=0
HR=0
IO=0
PictureCount=1
DCount=1

[COMP 1]
Type=TypBRectang
Definition='Atomic weight of carbon'
Unit='g/mol'
Description=3
Description[0]='The atomic weight of carbon and its uncertainty are taken from data listed in'
Description[1]='the latest IUPAC table of atomic weights. The IUPAC quoted data is considered'
Description[2]='to be of rectangular distribution.'
Vnom=12,0107
Hlim=0,0008
PictureCount=1
DCount=1

[COMP 2]
Type=TypBRectang
Definition='Atomic weight of hydrogen'
Unit='g/mol'
Description=3
Description[0]='The atomic weight of hydrogen and its uncertainty are taken from data listed in'
Description[1]='the latest IUPAC table of atomic weights. The IUPAC quoted data is considered'
Description[2]='to be of rectangular distribution.'
Vnom=1,00794
Hlim=0,00007
PictureCount=1
DCount=1

[COMP 3]
Type=TypBRectang
Definition='Atomic weight of oxygen'
Unit='g/mol'
Description=3
Description[0]='The atomic weight of oxigen and its uncertainty are taken from data listed in'
Description[1]='the latest IUPAC table of atomic weights. The IUPAC quoted data is considered'
Description[2]='to be of rectangular distribution.'
Vnom=15,9994
Hlim=0,0003
PictureCount=1
DCount=1

[COMP 4]
Type=TypBRectang
Definition='Atomic weight of potassium'
Unit='g/mol'
Description=3
Description[0]='The atomic weight of potassium and its uncertainty are taken from data listed'
Description[1]='in the latest IUPAC table of atomic weights. The IUPAC quoted data is'
Description[2]='considered to be of rectangular distribution.'
Vnom=39,0983
Hlim=0,0001
PictureCount=1
DCount=1

[COMP 5]
Type=Temp
Definition='Volume delivered by piston burette'
Unit='mL'
Description=0
Fcov=2
NomUnit=
UncUnit=
CovID=1
UncID=0
Vnom=18.64
Ustd=0.0127107853415908
Neff=1334
HB=0
HC=0
HR=0
IO=0
PictureCount=1
DCount=1

[COMP 6]
Type=Const
Definition='Volume indicated by burette'
Unit='mL'
Description=14
Description[0]='The nominal volume is not associated with any uncertainties. The uncertainty of'
Description[1]='the real volume of the burette has three components, repeatability, calibration'
Description[2]='and temperature. The latter two are included in the uncertainty budget as'
Description[3]='separate factors. Repeatability of the volume delivery is taken into account'
Description[4]='via the combined repeatability term for the experiment, f_repeatability_.'
Description[5]='Another factor influencing the result of the titration, which can also be'
Description[6]='attributed to the automatic titration system, of which the burette is one part,'
Description[7]='is the bias of the end-point detection. The titration is performed under a'
Description[8]='protective atmosphere (Ar) to prevent absorption of CO_2_, which would bias the'
Description[9]='titration. There are no indications that the end-point determined from the'
Description[10]='shape of the pH-curve does not correspond to the equivalence-point, because a'
Description[11]='strong acid is titrated with a'
Description[12]='strong base. No further uncertainty contributions are introduced to cover the'
Description[13]='bias of the end-point detection.'
Vnom=18,64
PictureCount=1
DCount=1

[COMP 7]
Type=TypBTriangl
Definition='Uncertainty contribution to the volume due to uncertainty in calibration of the burette'
Unit=''
Description=11
Description[0]='The limits of accuracy for a'
Description[1]='20 mL piston burette are indicated by the manufacturer as typically ±0.03 ml.'
Description[2]='No further statement is made about the level of confidence or the underlying'
Description[3]='distribution. An assumption is necessary to work with this uncertainty'
Description[4]='statement. In this case a'
Description[5]='triangular distribution is assumed. Since f_V\minus\calibration is a'
Description[6]='multiplicative factor to the nominal volume, which is only used to introduce'
Description[7]='the calibration uncertainty, it has the value 1. The halfwidth of limits'
Description[8]='corresponds to the relative uncertainty as stated by the manufacturer (i.e.'
Description[9]='0.03 mL /'
Description[10]='20 mL).'
Vnom=1
Hlim=0,0015
PictureCount=1
DCount=1

[COMP 8]
Type=TypBNormal
Definition='Uncertainty contribution to the volume due to temperature variation'
Unit=''
Description=15
Description[0]='The laboratory temperature can vary by ±3°C. The uncertainty of the volume due'
Description[1]='to temperature variations can be calculated from the estimate of the possible'
Description[2]='temperature range and the coefficient of the volume expansion. The volume'
Description[3]='expansion of the liquid is considerably larger than that of the burette, so'
Description[4]='only the volume expansion of the liquid is considered. The coefficient of'
Description[5]='volume expansion for water is 2.1\cdot\10^-4^°C^-1^, which is used here also'
Description[6]='for the NaOH solution. This leads to a'
Description[7]='possible volume variation of ±(19 \cdot\ 3 \cdot\ 2.1\cdot\10^-4^/1.96) mL ='
Description[8]='±0.006 mL. A'
Description[9]='rectangular distribution is assumed for the temperature variation Since'
Description[10]='f_V\minus\temperature is a'
Description[11]='multiplicative factor to the nominal volume, which is only used to introduce'
Description[12]='the temperature uncertainty, it has the value 1. Its uncertainty is calculated'
Description[13]='as 0.006 mL /'
Description[14]='19 mL.'
Vnom=1
Uexp=0,0003
Fcov=1
PictureCount=1
DCount=1

[COMP 9]
Type=Temp
Definition='Mass of KHP weighed'
Unit='g'
Description=0
Fcov=2
NomUnit=
UncUnit=
CovID=1
UncID=0
Vnom=0.3888
Ustd=0.00012247448713916
Neff=10000
HB=0
HC=0
HR=0
IO=0
PictureCount=1
DCount=1

[COMP 10]
Type=TypBRectang
Definition='Mass of container and KHP'
Unit='g'
Description=10
Description[0]='Repeatability of the wheighing is taken into account via the combined'
Description[1]='repeatability term, f_repeatability_. Any systematic offset across the scale'
Description[2]='will also cancel due to the wheighing by difference. The only contributing'
Description[3]='source of uncertainty is the linearity of the balance. The calibration'
Description[4]='certficate of the balance quotes ±0.15 mg for the linearity. The manufacturer'
Description[5]='recommends using a'
Description[6]='rectangular distribution to convert this linearity contribution into a'
Description[7]='standard uncertatiny. This uncertainty is not correlated with the uncertainty'
Description[8]='of m_container\sp\less\sp\KHP, since they are independent observations and the'
Description[9]='linearity effects are not correlated.'
Vnom=60,5450
Hlim=0,00015
PictureCount=1
DCount=1

[COMP 11]
Type=TypBRectang
Definition='Mass of container less KHP'
Unit='g'
Description=10
Description[0]='Repeatability of the wheighing is taken into account via the combined'
Description[1]='repeatability term, f_repeatability_. Any systematic offset across the scale'
Description[2]='will also cancel due to the wheighing by difference. The only contributing'
Description[3]='source of uncertainty is the linearity of the balance. The calibration'
Description[4]='certficate of the balance quotes ±0.15 mg for the linearity. The manufacturer'
Description[5]='recommends using a'
Description[6]='rectangular distribution to convert this linearity contribution into a'
Description[7]='standard uncertatiny. This uncertainty is not correlated with the uncertainty'
Description[8]='of m_container\sp\and\sp\KHP, since they are independent observations and the'
Description[9]='linearity effects are not correlated.'
Vnom=60,1562
Hlim=0,00015
PictureCount=1
DCount=1

[COMP 12]
Type=Result
Definition='Concentration of the sodium hydroxide solution'
Unit='mol/L'
Description=0
Fcov=2
NomUnit=
UncUnit=
CovID=1
UncID=0
Vnom=0.102136159706791
Ustd=9.67818987998781E-5
Neff=570
HB=1
HC=0
HR=1
IO=0
PictureCount=1
DCount=1

[COMP 13]
Type=Const
Definition='Conversion factor 1000 ml = 1L'
Unit='mL/L'
Description=0
Vnom=1000
PictureCount=0
DCount=0

[COMP 14]
Type=TypBRectang
Definition='Purity of the KHP'
Unit=''
Description=3
Description[0]='In the supplier''s catalogue, the purity of the KHP is given as 1.0000±0.0005.'
Description[1]='No further information concerning the uncertainty is given. Therefore this'
Description[2]='value is assumed to be of rectangular distribution.'
Vnom=1
Hlim=0,0005
PictureCount=1
DCount=1

[COMP 15]
Type=TypBNormal
Definition='Repeatability  of the titration'
Unit=''
Description=9
Description[0]='All uncertainty contributions due to repeatability of one of the operations are'
Description[1]='combined in this factor. It includes at least the repeatability of the'
Description[2]='wheighings and of the volume delivered by the burette. The magnitude of this'
Description[3]='uncertainty contribution is assessed during the method validation stage. The'
Description[4]='data shows that the overall repeatability of the titration experiment is 0.05%.'
Description[5]='Since f_repeatability is a'
Description[6]='multiplicative factor to the result, which is only used to introduce the'
Description[7]='repeatability uncertainty, it has the value 1'
Description[8]='with an uncertainty of 0.0005.'
Vnom=1
Uexp=0,0005
Fcov=1
PictureCount=1
DCount=1

[Correlations]
Description=0

[CalCorr]
CNT=20
R[0,12]=-0.0194574
R[5,12]=-0.7196345
R[9,12]=0.3324335
R[0,1]=0.98134
R[0,3]=0.1840013
R[0,2]=0.053667
R[0,4]=0.0153334
R[5,7]=0.8980265
R[5,8]=0.4399413
R[9,10]=0.7071068
R[9,11]=-0.7071068
R[12,7]=-0.6462509
R[12,15]=0.5276615
R[12,8]=-0.3165969
R[12,14]=0.3046455
R[12,10]=0.235066
R[12,11]=-0.235066
R[12,1]=-0.0190943
R[12,3]=-0.0035802
R[12,2]=-0.0010442