1. 中村 進 (NMIJ/AIST, Japan) e-mail: susumu-nakamura@aist.go.jp
ガラス電極pH計での不確かさについて
中村　進 (NMIJ/AIST, Japan)
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2. Traceability system for pH measurement
(Notion definition)
Primary (Harned cell) method
Primary pH buffer solution
(NMIJ, ….)
Secondary (Glass electrode) method
Secondary pH buffer solution

3. ガラス電極法での不確かさの要因 液間電位差 スターラの回転渦電流による電位変化 温度効果 ガラス電極表面の汚れ メモリ効果
測定電位のバイアス
アルカリ誤差
電気的なノイズ　　　　など
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4. (bracketing procedure)
2点測定法
(bracketing procedure)
2種類のpH標準液(pH1 と pH2）を用いて、試料のpH値を挟むように測定する。
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5. Two point calibration
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6. Mathematical model
where k1 and k2 are slope factors of pH vs. temperature near T  25 C for buffers S1 and S2 respectively;
Ej = Ej1 - EjX is residual liquid junction potential
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7. Uncertainty budget for general case
Factor
Unit
Standard uncertainty
Sensitivity coefficient
Sensitivity coefficient unit
Uncertainty contribution
pH1 1
0.01
0.50
0.0050
pH2 E1 V
0.0002
8.4
1/V
0.0017 E2 Ex
-17
0.0034 T K
0.1
1/K
Ej
0.0006 17
0.010
0.013
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Combined standard uncertainty
Data from the IUPAC Recommendations 2002

8. Contribution of different parameters to uncertainty of pHX
 60 %
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9. 不確かさの小さいpH測定 I. ほぼ同一組成の水溶液でのpH値では、液間電位差は無視できるので、 Ej  0  u(Ej)  0
II. Harnedセルで求めた一次標準液を使用すると、
u(pH1)  u(pH2)   0.005;
III. Differential - potentiometric cellを使用した場合
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10. Using of calibration solution of the same nominal composition
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11. Using of calibration solution of the same nominal composition
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12. Uncertainty budget for case I
Factor
Unit
Standard uncertainty
Sensitivity coefficient
Sensitivity coefficient unit
Uncertainty contribution
pH1 1
0.01
0.02
pH2
0.98
0.0098 E1 V
0.0002
0.36
1/V E2 17
0.0033 Ex
-17
0.0034 T K
0.1
1/K
0.0019
0.011
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Combined standard uncertainty

13. Uncertainty budget for case I + II
Factor
Unit
Standard uncertainty
Sensitivity coefficient
Sensitivity coefficient unit
Uncertainty contribution
pH1 1
0.0015
0.02
pH2
0.98 E1 V
0.0002
0.36
1/V E2 17
0.0033 Ex
-17
0.0034 T K
0.1
1/K
0.0019
0.0053
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Combined standard uncertainty

14. Contribution of different parameters to uncertainty of pHX
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15. Uncertainty of electromotive force
測定起電力の不確かさは以下のように計算する。
平均値が期待値にどれだけ近いのか
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u2 ：ガラス電極を含むpHメータの不確かさ

16. Uncertainty of electromotive force
u5 ：pHメータの最小メモリの統計的誤差
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17. Differential – potentiometric cell
①         compartment of standard buffer solution S;
②         compartment of certified buffer solution X;
③         hydrogen gas electrodes;
④         sintered glass disk D4;
⑤         sintered glass disks D0;
⑥         water traps ⑥ ① ② ⑤ ③ ④
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18. Pt  H2  Buffer S ¦ Buffer X  H2  Pt
Mathematical model
Pt  H2  Buffer S ¦ Buffer X  H2  Pt
where E is electromotive force of differential - potentiometric cell
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19. Uncertainty budget for differential cell
Factor
Unit
Standard uncertainty
Sensitivity coefficient
Sensitivity coefficient unit
Uncertainty contribution
pH1 1
0.0015
1.00 E V 17
1/V
0.001 T K
0.01
0.0191
1/K
0.0002
0.0018
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Combined standard uncertainty

20. Contribution of different parameters to uncertainty of pHX
 85 %
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21. 結論 ガラス電極法によるpH測定での拡張不確かさ U (k = 2) は、0.025  0.030
Differential – potentiometric cell を用いた場合の拡張不確かさは  0.004
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