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The Beer-Lambert law relates the absorbance A of a
Chapter 3, Problem 9E(choose chapter or problem)
The Beer-Lambert law relates the absorbance \(A\) of a solution to the concentration \(C\) of a species in solution by A = MLC, where \(L\) is the path length and \(M\) is the molar absorption coefficient. Assume that \(C=1.25\pm0.03\mathrm{\ mol}/\mathrm{cm}^3\), \(L=1.2\pm0.1\mathrm{\ cm}\), and \(A=1.30 \pm 0.05\).
a. Estimate \(M\) and find the uncertainty in the estimate.
b. Which would provide a greater reduction in the uncertainty in \(M\): reducing the uncertainty in \(C\) to \(0.01\mathrm{\ mol}/\mathrm{cm}^3\), reducing the uncertainty in \(L\) to 0.05 cm, or reducing the uncertainty in \(A\) to 0.01?
Equation Transcription:
Text Transcription:
A
C
L
M
C = 1.52 pm 0.03 mol/cm^3
L = 1.2 pm 0.1 cm
A = 1.30 pm 0.05
0.01 mol/cm^3
Questions & Answers
QUESTION:
The Beer-Lambert law relates the absorbance \(A\) of a solution to the concentration \(C\) of a species in solution by A = MLC, where \(L\) is the path length and \(M\) is the molar absorption coefficient. Assume that \(C=1.25\pm0.03\mathrm{\ mol}/\mathrm{cm}^3\), \(L=1.2\pm0.1\mathrm{\ cm}\), and \(A=1.30 \pm 0.05\).
a. Estimate \(M\) and find the uncertainty in the estimate.
b. Which would provide a greater reduction in the uncertainty in \(M\): reducing the uncertainty in \(C\) to \(0.01\mathrm{\ mol}/\mathrm{cm}^3\), reducing the uncertainty in \(L\) to 0.05 cm, or reducing the uncertainty in \(A\) to 0.01?
Equation Transcription:
Text Transcription:
A
C
L
M
C = 1.52 pm 0.03 mol/cm^3
L = 1.2 pm 0.1 cm
A = 1.30 pm 0.05
0.01 mol/cm^3
ANSWER:Solution 9E
Step1 of 3:
We have Beer-Lambert law in that A be the absorbance of a solution to the concentration C of a species and Let A = MLC.
Where,
L = Path length.
= 1.2 ± 0.1 cm.
M = the molar absorption coefficient.
C = 1.25 ± 0.03 mol/cm3.
A = 1.30 ± 0.05.
Here our goal is:
a).We need to estimate M and find the uncertainty in the estimate.
b).We need to check Which would provide a greater reduction in the uncertainty in M: reducing the uncertainty in C to 0.01 mol/cm3, reducing the uncertainty in L to 0.05 cm, or reducing the uncertainty in A to 0.01?
Step2 of 3:
a).
We have C = 1.25, L = 1.2,
A = 1.30 and
Let
A = MLC
M =
=
=
= 0.8667
Hence, M = 0.8667.
1).Consider,
M =
Differentiate above equation with respect to “A” then
=
=(1)
=
=
= 0.6667
Hence, = 0.6667.
2).Consider,
M =