25.0 mL quinine 50.0 mL 0.656 at 348 nm 25.7 ppm 0.976

25.0 mL quinine 50.0 mL 0.656 at 348 nm 25.7 ppm 0.976

A 25.0 mL aliquot of an aqueous quinine solution was diluted to 50.0 mL and found to have an absorbance of 0.656 at 348 nm when measured in a 2.50-cm cell. A second 25.0 mL aliquot was mixed with 10.00 mL of a solution containing 25.7 ppm of quinine; after dilution to 50.0 mL, this solution had an absorbance of 0.976 (2.50-cm cell). Calculate the concentration of quinine in parts per million in the sample.

Beer-Lambert 법칙

A = ε • C • L

> A: 흡광도

> ε: 몰흡광계수(용질과 관련된 상수)

> C: 용질의 몰농도(M)

> L: 시료 용기의 길이(cm)

( 참고 https://ywpop.tistory.com/12905 )

---> 용질과 시료 용기가 동일하므로,

흡광도(A)는 농도(C)에 비례한다.

A ∝ C

희석 전 quinine 농도(M1)를 x (ppm)라 두면,

희석 후 quinine 농도(M2)를 계산하면,

M1V1 = M2V2

( 참고 https://ywpop.tistory.com/2859 )

M2 = M1V1 / V2

= (x ppm × 25.0 mL) / (50.0 mL)

= x × 25.0 / 50.0

= 0.5x (ppm)

A ∝ C 비례식의

비례 상수, k를 계산하면,

A = k × C

k = A / C

= 0.656 / 0.5x

= 1.312/x

[두 번째 실험]

희석 후 25.0 mL 시료 속 quinine 농도

= x × 25.0 / 50.0

= 0.5x (ppm)

25.7 ppm quinine 10.00 mL의

희석 후 농도

= (25.7 ppm × 10.00 mL) / (50.0 mL)

= (25.7 × 10.00) / (50.0)

= 5.14 ppm

희석 후 전체 농도

= 0.5x + 5.14 (ppm)

A = k × C 로부터,

x를 계산하면,

0.976 = (1.312/x) (0.5x + 5.14)

0.976 = 0.656 + 6.74368/x

6.74368/x = 0.32

x = 6.74368 / 0.32

= 21.074

답: 약 21.1 ppm

[ 관련 글 https://ywpop.tistory.com/471400 ]

25.0 mL quinine 50.0 mL 0.636 at 348 nm 25.7 ppm 0.903

[키워드] quinine 용액의 흡광도 기준, quinine 용액의 농도 측정 기준