Eam ept., 8:00-9:30 PM EE 9 Mateal: Chapte -8 Lab -3
tandadzaton and Calbaton: Ttaton: ue of tandadzed oluton to detemne the concentaton of an unknown. Rele on a eacton of known tochomet, a oluton wth a eactant of well-known concentaton, and the dentfcaton of an equvalence pont. Etenal tandad calbaton: Often, gnal epone detemned fom a ee of tandad of known concentaton to detemne the gnal epone v. concentaton elatonhp. The concentaton of an unknown can be detemned dectl fom the known epone veu concentaton elatonhp. A plot of epone veu known concentaton call a calbaton cuve:
Cot of gaolne + ca wah H-tet lope $/Gal. egula U..$ m+b (Dependent vaable, ) ntecept Cot ($/Gal.)Gal + ca wah U.. Gallon (ndependent vaable, )
We all now know that we cannot epect all calbaton pont to fall eactl on the lne due to ndetemnate eo. Ou tak to fnd the lne that bet ft the data pont. Regeon anal a tem fo the poce of fndng the bet ft to the data (need not be lnea). We wll conde onl the method of leat quae fo two-dmenonal data.
The method of leat quae: Aumpton fo lnea elatonhp:. A lnea elatonhp (.e., m + b) et between,. An devaton fom a taght lne fom eo n the meauement of (.e., thee ae no eo n the value) Theefoe, we eek to mnmze the um of the quae of the edual ed ed ( ( b + m )) We defne the quantte,, and (quantte mla n appeaance to the numeato n the tandad devaton equaton): ( )
( ) ( ) ( ) ( ) ( )( ) numbe of paed (, ) data ued and
. The lope of the lne, m: m. The ntecept, b: b m 3. The tandad devaton about the egeon, : (a meaue of the ze of the devaton fom the egeon lne) m ( ( b + m )) note: degee of feedom ae lot n the detemnaton of b and m (alo tandad eo of the etmate o tandad eo)
4. The tandad devaton of the lope: m (note tpo n tet, b mtake) 5. The tandad devaton of the ntecept, b : b m ( ) ( ) 6. The tandad devaton fo eult obtaned fom the calbaton cuve, c : m ( ) + + M m c c whee c the aveage of M eplcate anale of the unknown value beng detemned fom the calbaton cuve, # calbaton pont (elaton onl appomate)
How well doe the egeon lne account fo the vaaton of wth? Th eflected n the coeffcent of detemnaton, R : ed R tot eg tot ed tot ( ( b + m )) ( ) ( ) + tot eg ed eg tot ed The cloe R to unt, the bette the egeon.
ote that uncetante n etablhment of the concentaton of an unknown ae geatet at the etemte of the calbaton cuve: m ( ) + + M m c c The cloe c to, the malle the uncetant:
Detemnaton of -octane hdocabon ample: A ee of -octane tandad wee njected onto a ga chomatogaph and the aea of the gnal wa obtaned a a functon of concentaton.
Reult (eample 8-4):.4537 5.07748.39669 m /.09 b m 0.6.09 + 0.6 m td. dev. of the lope b td. dev. of the ntecept td. dev. of egeon (tandad eo of the etmate) lope, m.09 ± 0.3 (± m ) ntecept, b 0.6 ± 0.6 (± b )
Epement 3 Enzmatc Quanttaton of Glucoe You ae aked on p. 4 to epot the leat-quae eult fom ou data: lope, m, and t tandad devaton, m m, ( ) ( ) Intecept, b, and t tandad devaton, b ( ) b
The tandad eo of the etmate, m ( ( ) ) b + m And coeffcent of detemnaton, R ed R tot eg tot R often cted ntead of R. R called the coelaton coeffcent.
tandad devaton fo the unknown detemned fom the calbaton cuve: m ( ) + + M m c c tue ± t (-),95 c ote: The numbe of degee of feedom fo the t-value, when the unknown detemned va a calbaton cuve, defned b the egeon lne and not elated to M (M affect c ). The numbe of degee of feedom -, whee the numbe of data pont ued to etablh the lne. φ f ( M )