Question

Find the weight percent of iron (55.85 g/mol) in a rock. Suppose that a 0.1773 g rock is crushed and dissolved in nitric acid. The solution is diluted to 100.00 mL. Then 15.00 mL of this solution is mixed with 10 mL 0.200 M chromophore. The resulting Fe complex has an absorption of 0.431 at 508 nm. A second solution is prepared exactly the same as above but spiked with 1 mL of 750 ppm Fe solution, which then gives an absorption of 0.808.

Answer 1

The instrumental analysis of the rock is carried out following the standard addition method. In this technique, the sample without standard solution has an absorbance given by the equation:

In this form of the Beer's Law, we have:

ε : molar absorptivity of the substance

b: optical path

V_x: volume of the sample

C_x: concentration of the substance in the sample

V_t: volume of the sample after dilution.

With the first addition of standard solution, the absorbance of the sample will be given by the equation:

In this equation

V_s: volume of standard added

C_s: concentration of the standard.

If we divide equation (2) by equation (1), we have:

Solving for the concentration of the substance in the sample (Cx):

We have the data:

Absorbance without standard: A₁ = 0.431

Absorbance with standard: A₂ = 0.808

Volume of the sample: V_x = 25.00mL

Volume of the standard: V_s = 1.0mL

Concentration of standard: C_s = 750 ppm Fe⁺³

Substituting all of these values in equation (3), the concentration of Fe⁺³ in the measured sample is:

But this sample was prepared by mixing 15.00 mL of the diluted solution of rock with 10 mL of the chromophore. To calculate the concentration of Fe⁺³ in the 15.00mL we will use:

Where C is the concentration and V is the volume, the subindex -c is referred to the concentrated solution (15.00 mL) and the subindex -D is referred to the diluted solution (25.0 mL). Solving for the concentration in concentrated solution (C_c):

This is the same concentration for the 100 mL stock solution prepared at dissolving the rock in nitric acid. Remember that ppm units can be written as:

Converting 100 mL to liters:

The mass of Fe+3 in that volume is given by:

Converting the mass into gram units:

The weight percent of iron in the rock is given by:

Subtituting known data: