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1 Calbraton Lecture Notes Calbraton Wth Standards Sgnal from Standards: N 11 1, 2.. N x y Calbraton Data Ponts Sgnal (Absorbance) y x Concentraton

2 Regresson Analyss: x avg x N x avg y avg y N y avg x. y s xy x. y N s xy y. y s yy y 2 N s yy x. x s xx x 2 N s xx Calculaton of lne: Slope: m s xy m s xx Intercept: b y avg m. x avg b y calc m. x b

3 Uncertanty Calculatons: In the regresson s yy m 2. s xx s r N 2 s r In the slope 2 s r s m s s m xx In the ntercept 2 x s b s. r s 2 2 b N. x x Analyss of an Unknown: j M 5 sgnal j sgnal avg j sgnal j M sgnal avg

4 Calculaton of unknown unknown sgnal avg m b unknown Calculaton of uncertanty n unknown s unknown s r m. 1 M 1 N sgnal avg y avg 2 m 2. s xx s unknown RSD s unknown unknown RSD % y unknown Data and Calbraton y calc 0.1 sgnal avg x trace 1 calbraton

5 Calbraton by Standard Addton (M&M's example): Mass of the M&M's n the bag: Mass ntal 50. gm Next you add 5 M&M's to the bag and fnd the new mass: MM added 5 Mass fnal 55. gm mass of the 5 M&M's that you added: Mass added Mass fnal Mass ntal Mass added gm From number of M&M's added, determne mass of each M&M Mass MM Mass added MM added Mass MM gm The number of M&M's ntally n the bag MM ntal Mass ntal Mass MM MM ntal And now t s tme to eat!!!

6 Calbraton by Standard Addton (M&M's example wth blank): Mass of the bag: Mass bag 10. gm Mass of the M&M's n the bag: Mass ntal 60. gm Next you add 5 M&M's to the bag and fnd the new mass: MM added 5 Mass fnal 65. gm mass of the 5 M&M's that you added: Mass added Mass fnal Mass ntal Mass added gm From number of M&M's added, determne mass of each M&M Mass MM Mass MM Mass added MM added gm The number of M&M's ntally n the bag MM ntal Mass ntal Mass bag Mass MM MM ntal And now t s tme to eat!!!

7 Standard Addton (Chemstry Problem) Analyss an sample of drt to determne the concentraton of lead Sgnal sample ppm 10 6 C standard 500. ppm V standard 0.1. ml Amount of lead added n the spke. mass spke 1 gm C. standard V.. standard 1. ml mass spke gm Calculate the ncrese n the concentraton of the sample. V total ml C spked mass spke V total. 1. gm 1. ml C spked C spked ppm Measure the sgnal of the spked sample Sgnal spked

8 The sgnal of the spke: Sgnal spke Sgnal spked Sgnal sample Sgnal spke Calculate nstrument response sgnal concentraton Response Sgnal spke C spked Response ppm 1 Now, recall the sgnal of the orgnal sample: Sgnal sample Ths corresponds to a sample concentraton of: C sample Sgnal sample Response C sample ppm

9 But we assumed that the sgnal from the "spked sample" s equal to the sgnal from the sample plus the sgnal from the spke. Or that: Sgnal spked Sgnal sample Sgnal spke However, the sample s slghtly dluted by the volume of the spkng soluton (0.1 ml n ths example). So "scale" the sgnal to account for dluton: V total V Sgnal sample_adjusted Sgnal. standard sample V total Sgnal sample_adjusted Repeat the above calculatons wth adjusted sgnal The sgnal of the spke: Sgnal spke_adjusted Sgnal spked Sgnal sample_adjusted Sgnal spke_adjusted The response Response_adjusted Sgnal spke_adjusted C spked Response_adjusted ppm 1 The adjusted response corresponds to a sample concentraton of: C sample_true C sample_true Sgnal sample Response_adjusted ppm

10 Calbraton wth an Internal Standard: Run #1, standard mxture wth known concentraton of Alar and decane. Alar Concentraton C alar_std ppm Peak Area A alar_std Decane Concentraton C decane_std ppm Peak Area A decane_std Calculate Response of Detector Alar Response alar A alar_std C alar_std Response alar ppm 1 Decane Response decane A decane_std C decane_std Response decane ppm 1 Relatve Response Response relatve Response alar Response decane Response relatve

11 Run #2, Unknown Alar concentraton spked wth a known concentraton of decane. Alar Concentraton C alar_unk Peak Area A alar_unk Decane Concentraton C decane_unk ppm Peak Area A decane_unk Response to standard (decane) Response decane A decane_unk C decane_unk Response decane ppm 1 Response to unknown (from relatve response) Response relatve Response alar Response decane Response alar Response. relatve Response decane Response alar ppm 1

12 Concentraton of unknown Response alar A alar_unk C alar_unk C alar_unk A alar_unk Response alar C alar_unk ppm

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