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

[Title]
Title='An acid/base titration'
Ref=''
Date='08/29/2007'
Version=''
Author=''
Description=8
Description[0]='This is the example A3 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 hydrochloric acid (HCl) is standardised against a'
Description[6]='solution of sodium hydroxide (NaOH) with known content. The standardisation of'
Description[7]='the NaOH solution is similar to example A2.'
PictureCount=1
DCount=1

[Model]
Model=19
Model[0]='{calculation of the uncertainty of V_T2}'
Model[1]=''
Model[2]='V_T2 = V_T2\sp\nominal * f_VT2\minus\calibration * f_VT2\minus\temperature;'
Model[3]=''
Model[4]='{calculation of the uncertainty of V_T1}'
Model[5]=''
Model[6]='V_T1 = V_T1\sp\nominal * f_VT1\minus\calibration * f_VT1\minus\temperature;'
Model[7]=''
Model[8]='{calculation of the uncertainty of V_HCl}'
Model[9]=''
Model[10]='V_HCl = V_HCl\sp\nominal * f_VHCl\minus\calibration * f_VHCl\minus\temperature;'
Model[11]=''
Model[12]='{molar mass of KHP}'
Model[13]=''
Model[14]='M_KHP = 8 * M_C + 5 * M_H + 4 * M_O + M_K;'
Model[15]=''
Model[16]='{calculation of the the HCl concentration}'
Model[17]=''
Model[18]='c_HCl = ( k_mL * m_KHP * P_KHP * V_T2) / (V_T1 * M_KHP * V_HCl ) * f_repeatability;'
CE=1
CTC=1

[Components]
CompOrder=3
Comp=22
Comp[0]=V_T2_
Comp[1]=V_T2\sp\nominal_
Comp[2]=f_VT2\minus\calibration_
Comp[3]=f_VT2\minus\temperature_
Comp[4]=V_T1_
Comp[5]=V_T1\sp\nominal_
Comp[6]=f_VT1\minus\calibration_
Comp[7]=f_VT1\minus\temperature_
Comp[8]=V_HCl_
Comp[9]=V_HCl\sp\nominal_
Comp[10]=f_VHCl\minus\calibration_
Comp[11]=f_VHCl\minus\temperature_
Comp[12]=M_KHP_
Comp[13]=M_C_
Comp[14]=M_H_
Comp[15]=M_O_
Comp[16]=M_K_
Comp[17]=c_HCl_
Comp[18]=k_mL_
Comp[19]=m_KHP_
Comp[20]=P_KHP_
Comp[21]=f_repeatability_

[COMP 0]
Type=Temp
Definition='Volume of NaOH for HCl titration'
Unit='mL'
Description=0
Fcov=2
NomUnit=
UncUnit=
CovID=1
UncID=0
Vnom=14.89
Ustd=0.0142178298597219
Neff=10000
HB=0
HC=0
HR=0
IO=0
PictureCount=1
DCount=1

[COMP 1]
Type=Const
Definition='Nominal volume of NaOH for HCl titration'
Unit='mL'
Description=11
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. No further uncertainty contributions are introduced to cover the'
Description[10]='bias of the end-point detection.'
Vnom=14,89
PictureCount=1
DCount=1

[COMP 2]
Type=TypBTriangl
Definition='Uncertainty contribution to V_T2 due to instrument calibration'
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_VT2\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]='14.89 mL).'
Vnom=1
Hlim==0.03/14.89
PictureCount=1
DCount=1

[COMP 3]
Type=TypBRectang
Definition='Uncertainty contribution to V_T2 due to temperature variation'
Unit=''
Description=12
Description[0]='The laboratory temperature can vary by ±4°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^. This leads to a'
Description[6]='possible volume variation of ±(15 \cdot\ 4 \cdot\ 2.1\cdot\10^-4^) mL. A'
Description[7]='rectangular distribution is assumed for the temperature variation Since'
Description[8]='f_VT2\minus\temperature is a'
Description[9]='multiplicative factor to the nominal volume, which is only used to introduce'
Description[10]='the temperature uncertainty, it has the value 1. Its uncertainty is calculated'
Description[11]='as the possible volume variation divided by the volume dispensed.'
Vnom=1
Hlim==2.1e-4*4
PictureCount=1
DCount=1

[COMP 4]
Type=Temp
Definition='Volume of NaOH for KHP titration'
Unit='mL'
Description=0
Fcov=2
NomUnit=
UncUnit=
CovID=1
UncID=0
Vnom=18.64
Ustd=0.0152223567794215
Neff=10000
HB=0
HC=0
HR=0
IO=0
PictureCount=1
DCount=1

[COMP 5]
Type=Const
Definition='Nominal volume of NaOH for KHP titration'
Unit='mL'
Description=11
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. No further uncertainty contributions are introduced to cover the'
Description[10]='bias of the end-point detection.'
Vnom=18,64
PictureCount=1
DCount=1

[COMP 6]
Type=TypBTriangl
Definition='Uncertainty contribution to V_T1 due to instrument calibration'
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_VT1\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]='18.64 mL).'
Vnom=1
Hlim==0.03/18.64
PictureCount=1
DCount=1

[COMP 7]
Type=TypBRectang
Definition='Uncertainty contribution to V_T1 due to temperature variation'
Unit=''
Description=12
Description[0]='The laboratory temperature can vary by ±4°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^. This leads to a'
Description[6]='possible volume variation of ±(19 \cdot\ 4 \cdot\ 2.1\cdot\10^-4^) mL. A'
Description[7]='rectangular distribution is assumed for the temperature variation Since'
Description[8]='f_VT1\minus\temperature is a'
Description[9]='multiplicative factor to the nominal volume, which is only used to introduce'
Description[10]='the temperature uncertainty, it has the value 1. Its uncertainty is calculated'
Description[11]='as the possible volume variation divided by the volume dispensed.'
Vnom=1
Hlim==2.1e-4*4
PictureCount=1
DCount=1

[COMP 8]
Type=Temp
Definition='HCl aliquot for NaOH titration'
Unit='mL'
Description=0
Fcov=2
NomUnit=
UncUnit=
CovID=1
UncID=0
Vnom=15
Ustd=0.0109355688771397
Neff=10000
HB=0
HC=0
HR=0
IO=0
PictureCount=1
DCount=1

[COMP 9]
Type=Const
Definition='Nominal volume of HCl for NaOH titration'
Unit='mL'
Description=5
Description[0]='The nominal volume is not associated with any uncertainties. The uncertainty of'
Description[1]='the real volume of the pipette 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_.'
Vnom=15
PictureCount=1
DCount=1

[COMP 10]
Type=TypBTriangl
Definition='Uncertainty contribution to V_HCl due to pipette calibration'
Unit=''
Description=10
Description[0]='The uncertainty stated by the manufacturer for a'
Description[1]='15 mL pipette is ±0.02 mL. No further statement is made about the level of'
Description[2]='confidence or the underlying distribution. An assumption is necessary to work'
Description[3]='with this uncertainty statement. In this case a'
Description[4]='triangular distribution is assumed. Since f_VHCl\minus\calibration is a'
Description[5]='multiplicative factor to the nominal volume, which is only used to introduce'
Description[6]='the calibration uncertainty, it has the value 1. The halfwidth of limits'
Description[7]='corresponds to the relative uncertainty as stated by the manufacturer (i.e.'
Description[8]='0.02 mL /'
Description[9]='15 mL).'
Vnom=1
Hlim==0.02/15
PictureCount=1
DCount=1

[COMP 11]
Type=TypBRectang
Definition='Uncertainty contribution to V_HCl due to temperature variation'
Unit=''
Description=12
Description[0]='The laboratory temperature can vary by ±4°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 pipette, 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^. This leads to a'
Description[6]='possible volume variation of ±(15 \cdot\ 4 \cdot\ 2.1\cdot\10^-4^) mL. A'
Description[7]='rectangular distribution is assumed for the temperature variation Since'
Description[8]='f_VHCl\minus\temperature is a'
Description[9]='multiplicative factor to the nominal volume, which is only used to introduce'
Description[10]='the temperature uncertainty, it has the value 1. Its uncertainty is calculated'
Description[11]='as the possible volume variation divided by the volume dispensed.'
Vnom=1
Hlim==2.1e-4*4
PictureCount=1
DCount=1

[COMP 12]
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 13]
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 14]
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 15]
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 16]
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 17]
Type=Result
Definition='HCl solution concentration'
Unit='mol/L'
Description=0
Fcov=2
NomUnit=
UncUnit=
CovID=1
UncID=0
Vnom=0.101387161202274
Ustd=0.000183985427330987
Neff=536
HB=1
HC=0
HR=1
IO=0
PictureCount=1
DCount=1

[COMP 18]
Type=Const
Definition='Conversion factor 1000 mL = 1 L'
Unit='mL/L'
Description=0
Vnom=1000
PictureCount=0
DCount=0

[COMP 19]
Type=TypBNormal
Definition='Weight of KHP'
Unit='g'
Description=9
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 accounted for twice, once for the'
Description[8]='tare and once for the gross mass.'
Vnom=0,3888
Uexp==sqrt(2*sqr(0.00015/sqrt(3)))
Fcov=1
PictureCount=1
DCount=1

[COMP 20]
Type=TypBRectang
Definition='Purity of KHP'
Unit=''
Description=3
Description[0]='In the supplier''s catalogue, the purity of the KHP is given as 100%±0.05%. No'
Description[1]='further information concerning the uncertainty is given. Therefore this value'
Description[2]='is assumed to be of rectangular distribution.'
Vnom=1
Hlim=0,05%
PictureCount=1
DCount=1

[COMP 21]
Type=TypBNormal
Definition='Uncertainty contribution attributed to repeatability'
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 volumes delivered by the burette and the pipette. The'
Description[3]='magnitude of this uncertainty contribution is assessed during the method'
Description[4]='validation stage. The data shows that the overall repeatability of the'
Description[5]='titration experiment is 0.1%. 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 0.1%.'
Vnom=1
Uexp=0,1%
Fcov=1
PictureCount=1
DCount=1

[Correlations]
Description=0

[CalCorr]
CNT=25
R[0,17]=0.5261846
R[4,17]=-0.450024
R[8,17]=-0.4017443
R[12,17]=-0.0101601
R[0,2]=0.8614148
R[0,3]=0.5079021
R[4,6]=0.8045698
R[4,7]=0.5938581
R[8,10]=0.746643
R[8,11]=0.665225
R[12,13]=0.98134
R[12,15]=0.1840013
R[12,14]=0.053667
R[12,16]=0.0153334
R[17,21]=0.5510608
R[17,2]=0.4532632
R[17,6]=-0.3620758
R[17,10]=-0.2999596
R[17,7]=-0.2672504
R[17,11]=-0.2672504
R[17,3]=0.2672503
R[17,19]=0.1735877
R[17,20]=0.1590776
R[17,13]=-0.0099705
R[17,15]=-0.0018695