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Chapter 4: Problem 121

Douglasite is a mineral with the formula 2 $\mathrm{KCl} \cdot \mathrm{FeCl}_{2}\( . 2 \)\mathrm{H}_{2} \mathrm{O}$ . Calculate the mass percent of douglasite in a 455.0 \(\mathrm{-mg}\) sample if it took 37.20 \(\mathrm{mL}\) of a \(0.1000-M \mathrm{AgNO}_{3}\) solution to precipitate all the \(\mathrm{Cl}^{-}\) as AgCl. Assume the douglasite is the only source of chloride ion.

Short Answer

Expert verified
The mass percent of douglasite in the 455.0 mg sample is approximately 112.64%.

Step by step solution

01

Calculate the moles of AgNO3

To calculate the moles of AgNO3, we will use the given volume and molarity of the solution: \(Moles\, of\, AgNO_3 = Volume\, of\, solution × Molarity\) Moles of AgNO3 = \(37.20 \, mL × 0.1000 \, M\) Note: Convert the volume from mL to L Moles of AgNO3 = \(0.03720 \, L × 0.1000 \, M = 3.72 × 10^{-3} \, moles\)
02

Calculate the moles of Cl- ions in the sample

Since AgCl is formed from the reaction of AgNO3 with Cl- ions, the number of moles of Cl- ions will be equal to the number of moles of AgNO3. Moles of Cl- ions = Moles of AgNO3 = \(3.72 × 10^{-3} \, moles\)
03

Calculate the moles of douglasite

Looking at the formula for douglasite (2 KCl·FeCl2), there are three moles of Cl- ions in one mole of douglasite. We will use this molar ratio to calculate the moles of douglasite. Moles of douglasite = \(\frac{moles\, of\, Cl-}{moles\, of\, Cl- per\, mole\, of\, douglasite}\) Moles of douglasite = \(\frac{3.72 × 10^{-3} \, moles}{3}\) Moles of douglasite = \(1.24 × 10^{-3} \, moles \)
04

Calculate the mass of douglasite present in the sample

To calculate the mass of douglasite, we need to multiply the moles of douglasite by its molar mass: Molar mass of douglasite ≈ (2 × M(KCl) + M(FeCl2) + 2 × M(H2O)) Molar mass of douglasite ≈ 2 × (39.10 + 35.45) + (55.85 + 2 × 35.45) + 2 × (2 × 1.01 + 16.00) g/mol ≈ 413.7 g/mol Now, calculating the mass of douglasite in the sample: Mass of douglasite = Moles of douglasite × Molar mass of douglasite Mass of douglasite = \(1.24 × 10^{-3} \, moles × 413.7 \, \frac{g}{mol} ≈ 0.5125 \, g\)
05

Calculate the mass percent of douglasite in the sample

Finally, we will calculate the mass percent of douglasite in the sample: Mass percent of douglasite = \(\frac{Mass\, of\, douglasite}{Mass\, of\, sample} × 100\) Mass percent of douglasite = \(\frac{0.5125 \, g}{0.4550 \, g} × 100 ≈ 112.64\%\) In conclusion, the mass percent of douglasite in the 455.0 mg sample is approximately 112.64%.

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