Question

A sample of 0.300 mg pure chromium was added to excess hydrochloric acid to form a 10.0 mL aqueous solution of a chromium (III) salt, which has a violet hue. Exactly 1.00 mL of the resulting solution was analyzed using a spectrophotometer in a 1.00-cm cell at 575 nm, and the percent transmittance for the solution was 62.5%. What is the extinction coefficient?

Answer 1

extinction coefficient (ε) = 347 L·mol⁻¹·cm⁻¹

Explanation:

The chemical reaction between chromium (Cr) and hydrochloric acid (HCl):

2 Cr + 6 HCl → 2 CrCl₃ + 3 H₂

number of moles = mass / molar weight

number of moles of Cr = 0.3 × 10⁻³ (g) / 52 (g/mole)

number of moles of Cr = 5.77 × 10⁻⁶ moles

From the chemical reaction we see that 2 moles of Cr will produce 2 moles of CrCl₃ so 5.77 × 10⁻⁶ moles of Cr will produce 5.77 × 10⁻⁶ moles of CrCl₃.

molar concentration = number of moles / volume (L)

molar concentration of CrCl₃ = 5.77 × 10⁻⁶ / 10 × 10⁻³

molar concentration of CrCl₃ = 5.77 × 10⁻⁴ moles / L

Now we need to transform percent transmittance (%T) in absorbance (A) using the following formula:

A = 2 - log (%T)

A = 2 - log (62.5)

A = 2 - 1.8

A = 0.2

We know that absorbance (A) is defined in respect with extinction coefficient (ε), cell length (l) and concentration (c):

A = εlc

ε = A / lc

ε = 0.2 / (1 × 5.77 × 10⁻⁴)

ε = 0.0347 × 10⁴

ε = 347 L·mol⁻¹·cm⁻¹

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