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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