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Chapter 6: Problem 99

The thallium (present as \(\mathrm{Tl}_{2} \mathrm{SO}_{4}\) ) in a \(9.486-\mathrm{g}\) pesticide sample was precipitated as thallium(I) iodide. Calculate the mass percent of \(\mathrm{Tl}_{2} \mathrm{SO}_{4}\) in the sample if \(0.1824 \mathrm{g}\) of TII was recovered.

Short Answer

Expert verified
Moles of \(\mathrm{TlI}\) = \(0.1824 \, \mathrm{g} / 331.28 \, \mathrm{g/mol}\) = \(5.5 \times 10^{-4} \, \mathrm{mol}\) Moles of \(\mathrm{Tl}_2\mathrm{SO}_{4}\) = \(5.5 \times 10^{-4} \, \mathrm{mol} / 2\) = \(2.75 \times 10^{-4} \, \mathrm{mol}\) Mass of \(\mathrm{Tl}_2\mathrm{SO}_{4}\) = \(2.75 \times 10^{-4} \, \mathrm{mol} \times 600.82 \, \mathrm{g/mol}\) = \(0.165 \, \mathrm{g}\) Mass percent of \(\mathrm{Tl}_2\mathrm{SO}_{4}\) = \((0.165 \, \mathrm{g} / 9.486 \, \mathrm{g}) \times 100\) = \(1.74 \%\)

Step by step solution

01

Calculate the moles of thallium(I) iodide, \(\mathrm{TlI}\), obtained

To calculate the moles of \(\mathrm{TlI}\) we use the formula: moles = mass / molar mass. The molar mass of \(\mathrm{TlI}\) = 204.38 g/mol (Tl) + 126.9 g/mol (I) = 331.28 g/mol (TlI). Given the mass of thallium(I) iodide recovered: Moles of \(\mathrm{TlI}\) = mass of \(\mathrm{TlI}\) / molar mass of \(\mathrm{TlI}\) Moles of \(\mathrm{TlI}\) = \(0.1824 \, \mathrm{g} / 331.28 \, \mathrm{g/mol}\)
02

Calculate the moles of \(\mathrm{Tl}_2\mathrm{SO}_{4}\) in the sample.

Since both thallium in thallium(I) iodide and thallium in thallium sulfate are in +1 oxidation state, the mole ratio between \(\mathrm{TlI}\) and \(\mathrm{Tl_2SO_4}\) is 2:1 (2 moles of \(\mathrm{TlI}\) for every 1 mole of \(\mathrm{Tl_2SO_4}\)). Moles of \(\mathrm{Tl}_2\mathrm{SO}_{4}\) = moles of \(\mathrm{TlI}\) / 2
03

Calculate the mass of \(\mathrm{Tl}_2\mathrm{SO}_{4}\) in the sample.

Now we will multiply the moles of \(\mathrm{Tl}_2\mathrm{SO}_{4}\) by its molar mass to get the mass of \(\mathrm{Tl}_2\mathrm{SO}_{4}\) in the sample. The molar mass of \(\mathrm{Tl}_2\mathrm{SO}_{4}\) = 2 × 204.38 g/mol (Tl) + 96.06 g/mol (S) + 64 g/mol × 4 (O) = 600.82 g/mol. Mass of \(\mathrm{Tl}_2\mathrm{SO}_{4}\) = moles of \(\mathrm{Tl}_2\mathrm{SO}_{4}\) × molar mass of \(\mathrm{Tl}_2\mathrm{SO}_{4}\)
04

Calculate the mass percent of \(\mathrm{Tl}_2\mathrm{SO}_{4}\) in the sample.

Now just divide the mass of \(\mathrm{Tl}_2\mathrm{SO}_{4}\) by the total sample mass and multiply by 100 to get the mass percent. Mass percent of \(\mathrm{Tl}_2\mathrm{SO}_{4}\) = (mass of \(\mathrm{Tl}_2\mathrm{SO}_{4}\) / mass of sample) × 100 Let's do the calculations:

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