When I was a boy, Uncle Wilbur let me watch as he analyzed the iron content of runoff from his banana ranch. A 25.0-mL sample was acidified with nitric acid and treated with excess KSCN to form a red complex. (KSCN itself is colorless.) The solution was then diluted to 100.0 mL and put in a variable-path length cell. For comparison, a 10.0-mL reference sample of 6.74 times 10^-4 M Fe^3+ was treated with HNO_3 and KSCN and diluted to 50.0 mL, The reference was placed in a cell with a 1.00-cm light path. The runoff sample exhibited the same absorbance as the reference when the path length of the runoff cell was 2.41 cm. What was the concentration of iron in Uncle Wilbur's runoff?

C = 2.24x10⁻⁴ M

Explanation:

The concentration of iron in Uncle Wilbur's runoff can be calculated using Beer-Lambert law:

  (1)

Where:

A: is the absorbance of the compound

ε: is the molar absorptivity of the compound

C: is the concentration of the compound

l: is the optical path length

Since the runoff sample exhibited the same absorbance as the reference sample, we can find the concentration using equation (1):      

   (2)

Where:

Subscripst 1 and 2 refer to Uncle Wilbur's runoff and to reference sample, respectively.

l₁ = 2.41 cm

l₂ = 1.00 cm

We can find C₂ as follows:

   (3)

Where:

: is the initial concentration of the reference sample = 6.74x10⁻⁴ M

: is the initial volume = 10.0 mL

: is the final volume = 50.0 mL

Now, we can find C₁ using equation (2):

Finally, since the runoff solution was diluted to 100.0 mL, the initial concentration can be calculated using equation (3) for :

Therefore, the concentration of iron in Uncle Wilbur's runoff is 2.24x10⁻⁴ M.

I hope it helps you!