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 ± 0.03 mol/cm3, L = 1.2 ± 0.1 cm, and A = 1.30 ± 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 mol/cm3, reducing the uncertainty in L to 0.05 cm, or reducing the uncertainty in A to 0.01?
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 =
Differentiate above equation with respect to “L” then
=
=
=
=(
)
=
=
=
= -0.7222
Hence, = -0.7222.
3).Consider,
M =
Differentiate above equation with respect to “C” then
=
=
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