A 20.0-mL sample of lake water 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 50.0-mL and put in a 1.00 cm pathlength cell, where it yielded an absorbance of 0.345. For comparison, a 5.0-mL reference sample of 4.80 x 10-4 M Fe3 was treated with HNO3 and KSCN and diluted to 50.0 mL. The reference solution was also placed in a 1.00-cm cell and gave an absorbance of 0.512. What is the concentration of Fe3 in Jordan Lake

8.09x10⁻⁵M of Fe³⁺

Explanation:

Using Lambert-Beer law, the absorbance of a sample is proportional to its concentration.

In the problem, the Fe³⁺ is reacting with KSCN to produce Fe(SCN)₃ -The red complex-

The concentration of Fe³⁺ in the reference sample is:

4.80x10⁻⁴M Fe³⁺ × (5.0mL / 50.0mL) = 4.80x10⁻⁵M Fe³⁺

Because reference sample was diluted from 5.0mL to 50.0mL.

That means a solution of  4.80x10⁻⁵M Fe³⁺ gives an absorbance of 0.512

Now, as the sample of the lake gives an absorbance of 0.345, its concentration is:

0.345 × (4.80x10⁻⁵M Fe³⁺ / 0.512) = 3.23x10⁻⁵M.  

As the solution was diluted from 20.0mL to 50.0mL, the concentration of Fe³⁺ in Jordan lake is:

3.23x10⁻⁵M Fe³⁺ × (50.0mL / 20.0mL) = 8.09x10⁻⁵M of Fe³⁺

The tenement was the size of an triangular yard space with dim light as an average cellar.

Explanation:

(passage below)

"I counted the other day the little ones, up to ten years or so, in a Bayard Street tenement that for a yard has a triangular space in the center with sides fourteen or fifteen feet long, just room enough for a row of ill-smelling closets [toilets] at the base of the triangle and a hydrant at the apex [highest point]. There was about as much light in this “yard” as in the average cellar. I gave up my self-imposed task in despair when I had counted one hundred and twenty-eight in forty families. . . . "