Answer: The mass percentage of [tex]Tl_2SO_4[/tex] is 5.86%
Explanation:
To calculate the mass percentage of [tex]Tl_2SO_4[/tex] in the sample it is necessary to know the mass of the solute ([tex]Tl_2SO_4[/tex] in this case), and the mass of the solution (pesticide sample, whose mass is explicit in the letter of the problem).
To calculate the mass of the solute, we must take the mass of the [tex]TlI[/tex] precipitate. We can establish a relation between the mass of [tex]TlI[/tex] and [tex]Tl_2SO_4[/tex] using the stoichiometry of the compounds:
[tex]moles\ of\ TlI = \frac{0.1824 g}{331.27\frac{g}{mol} } = 5.51*10^{-4}\ mol.[/tex]
Since for every mole of Tl in [tex]TlI[/tex] there are two moles of Tl in [tex]Tl_2SO_4[/tex], we have:
[tex]moles\ of\ Tl_2SO_4 = 2 * moles\ of\ TlI = 1,102*10^{-3}\ mol[/tex]
Using the molar mass of [tex]Tl_2SO_4[/tex] we have:
[tex]mass\ of\ Tl_2SO_4 = 1,102*10^{-3}\ mol * 504.83\ \frac{g}{mol}= 0.56\ g[/tex]
Finally, we can use the mass percentage formula:
[tex]mass\ percentage = (\frac{solute\ mass}{solution\ mass} )*100 = (\frac{mass\ of\ Tl_2SO_4}{pesticide\ sample\ mass})*100 = (\frac{0.56g}{9.486g})*100 = 5.86\%[/tex]
