Problem 35 - Chemistry and Chemical Reactivity

Question

A pesticide contains thallium( \(I\) ) sulfate, \(T I_{2} S O_{4} .\) Dissolving a 10.20 -g sample of impure pesticide in water and adding sodium iodide precipitates \(6.1964 \mathrm{g}\) of thallium (I) iodide, TII. $$ \mathrm{Tl}_{2} \mathrm{SO}_{4}(\mathrm{aq})+\mathrm{NaI}(\mathrm{aq}) \longrightarrow \mathrm{TII}(\mathrm{s})+\mathrm{Na}_{2} \mathrm{SO}_{4}(\mathrm{aq}) $$ What is the mass percent of \(\mathrm{TI}_{2} \mathrm{SO}_{4}\) in the original \(10.20-\mathrm{g}\) sample?

Step-by-Step Solution

Answer

The mass percent of \( \mathrm{Tl}_{2} \mathrm{SO}_{4} \) is approximately 46.27\%.

Step 1: Write the Reaction Equation

The chemical reaction provided is \( \mathrm{Tl}_{2} \mathrm{SO}_{4}(\mathrm{aq}) + 2\mathrm{NaI}(\mathrm{aq}) \rightarrow 2\mathrm{TII}(\mathrm{s}) + \mathrm{Na}_{2} \mathrm{SO}_{4}(\mathrm{aq}) \). This equation is used for determining the moles of reactants and products.

Step 2: Determine Molar Masses

Find the molar masses of the substances involved. \( \mathrm{Tl}_{2} \mathrm{SO}_{4} \) has a molar mass of approximately 504.8 g/mol, and \( \mathrm{TII} \) has a molar mass of approximately 331.8 g/mol.

Step 3: Convert Mass of \( \mathrm{TII} \) to Moles

Use the mass of produced \( \mathrm{TII} \) = 6.1964 g to find moles: \( moles\ of\ \mathrm{TII} = \frac{6.1964\ \mathrm{g}}{331.8\ \mathrm{g/mol}} \approx 0.0187\ \mathrm{mol} \).

Step 4: Relate Moles of \( \mathrm{Tl}_{2} \mathrm{SO}_{4} \)

From the equation, 1 mole of \( \mathrm{Tl}_{2} \mathrm{SO}_{4} \) produces 2 moles of \( \mathrm{TII} \). Therefore, calculate moles of \( \mathrm{Tl}_{2} \mathrm{SO}_{4} \) = \( \frac{0.0187}{2} = 0.00935\ \mathrm{mol} \).

Step 5: Convert Moles of \( \mathrm{Tl}_{2} \mathrm{SO}_{4} \) to Mass

Calculate the mass of \( \mathrm{Tl}_{2} \mathrm{SO}_{4} \) using its moles: \( mass\ =\ 0.00935\ \mathrm{mol}\ \times\ 504.8\ \mathrm{g/mol} \approx 4.72\ \mathrm{g} \).

Step 6: Calculate Mass Percent

The mass percent of \( \mathrm{Tl}_{2} \mathrm{SO}_{4} \) in the impure sample is \( \frac{4.72\ \mathrm{g}}{10.20\ \mathrm{g}} \times 100\% \approx 46.27\% \).

Key Concepts

Molar masses

In chemistry, understanding molar masses is essential for solving problems related to chemical reactions and calculations. The molar mass of a compound is the weight of a mole of its molecules and is expressed in grams per mole (g/mol). To calculate molar masses, sum the atomic masses of all atoms in a molecule based on the periodic table.
For example, the molar mass of thallium (I) sulfate (\(Tl_2SO_4\)) is obtained by adding:

• The molar mass of thallium (\(Tl\)) which is approximately 204.38 g/mol. With two thallium atoms, you multiply 204.38 by 2.
• The sulfur (S) with a molar mass of 32.07 g/mol.
• Four oxygen atoms each at approximately 16.00 g/mol.

This gives you \(Tl_2SO_4\)'s molar mass as approximately 504.8 g/mol. Knowing these numbers allows you to convert between the mass of substances and their corresponding moles, which is crucial for stoichiometric calculations.

Chemical reactions

Chemical reactions involve the transformation of reactants into products. In a balanced equation, the number of atoms for each element is the same on both sides, ensuring the conservation of mass.
Consider the reaction between thallium (I) sulfate and sodium iodide:

• The balanced equation is \(\mathrm{Tl}_2\mathrm{SO}_4(\mathrm{aq}) + 2\mathrm{NaI}(\mathrm{aq}) \rightarrow 2\mathrm{TII}(\mathrm{s}) + \mathrm{Na}_2\mathrm{SO}_4(\mathrm{aq})\).
• Here, 1 mole of \(\mathrm{Tl}_2\mathrm{SO}_4\) reacts with 2 moles of sodium iodide to produce 2 moles of thallium (I) iodide (\(\mathrm{TII}\)) and 1 mole of sodium sulfate.

This stoichiometry allows chemists to predict the amounts of products formed from given quantities of reactants. Understanding chemical reactions and their equations is fundamental in calculating the reactants needed or the products formed for any given process.

Mass percent calculation

Mass percent is a way of expressing the concentration of a component in a mixture or chemical compound. It indicates how much of the mixture's total weight comes from the given component. The formula for mass percent is:\[\text{Mass percent} = \left(\frac{\text{mass of component}}{\text{total mass of sample}}\right) \times 100\%\]Let's apply this to find the mass percent of \(\mathrm{Tl}_2\mathrm{SO}_4\) in the pesticide sample. After determining that 4.72 g of \(\mathrm{Tl}_2\mathrm{SO}_4\) is present in the original 10.20 g sample, you use the formula above:\[\text{Mass percent of } \mathrm{Tl}_2\mathrm{SO}_4 = \left(\frac{4.72 \text{ g}}{10.20 \text{ g}}\right) \times 100\%\]This calculation results in approximately 46.27%, meaning that nearly half of the sample's weight is composed of \(\mathrm{Tl}_2\mathrm{SO}_4\). Understanding how to calculate mass percent helps in determining the purity and composition of mixtures.