A student prepared an unknown sample by making a dilute solution of the unknown sample. The dilute sample was prepared by adding 5.0 mL of the unknown sample to a 25.0 mL flask. What is the concentration (mM) of the diluted unknown sample that has an absorbance of 0.270

0.27 mM

Explanation:

According to the law of Lambert Beer:

A = C * E * L

Where:

A = Absorbance

C = Concentration

E = molar absorptivity

L = Step Length

If me make C the subject of the formula, we have = A / E * L

We know Absorbance and we can assume L = 1 cm, but being an unknown substance, we must know the molar Absorptivity of it, therefore, only having that value we could calculate the concentration of the mixture using the previous equation.

Then we could use the dilution ratio:

Cc * Vc = Cd * Vd

from the above formula, to fin the concentrated Concentration, we have:

Cc = Cd * Vd / Vc

we then replace the known values.

Vd = Diluted volume 25 mL

Vc = Volume concentrated 5 mL

and we would not know the diluted concentration (Cd), which is what we had to calculate in the first section. Substituting it in the previous equation, we can obtain the initial concentration.

Assuming a molar absorptivity of 5000 M-1 * cm - 1 we would have:

Cd = 0.270 / 5000 * 1

= 5.4 x 10 ^ - 5 M * (1000 mM / 1 M)

= 0.054 mM

and initial concentration:

Cc = 0.054 mM * (25 mL / 5 mL)

= 0.27 mM.