Question

Saccharin, an artificial sweetener, has the formula \(\mathrm{C}_{7} \mathrm{H}_{5} \mathrm{NO}_{3} \mathrm{S} .\) Suppose you have a sample of a saccharincontaining sweetener with a mass of \(0.2140 \mathrm{g} .\) After decomposition to free the sulfur and convert it to the \(\mathrm{SO}_{4}^{2-}\) ion, the sulfate ion is trapped as water-insoluble \(\mathrm{BaSO}_{4}\) (see Figure 4.8 ). The quantity of \(\mathrm{BaSO}_{4}\) obtained is \(0.2070 \mathrm{g}\). What is the mass percent of saccharin in the sample of sweetener?

Short answer

The mass percent of saccharin in the sample is approximately 75.87%.

Step-by-step solution

Calculate the Molar Mass of \( \text{BaSO}_4 \)

Start by calculating the molar mass of \( \text{BaSO}_4 \). This compound consists of barium (Ba), sulfur (S), and oxygen (O). The atomic masses are approximately: \( \text{Ba} = 137.33 \, \text{g/mol} \), \( \text{S} = 32.07 \, \text{g/mol} \), and \( \text{O} = 16.00 \, \text{g/mol} \). Therefore, the molar mass is calculated as follows:\[137.33 + 32.07 + 4 \times 16.00 = 233.39 \, \text{g/mol}\]

Calculate Moles of \( \text{BaSO}_4 \) Formed

Given the mass of \( \text{BaSO}_4 \) is \( 0.2070 \, \text{g} \), calculate the number of moles:\[\text{moles of } \text{BaSO}_4 = \frac{0.2070 \, \text{g}}{233.39 \, \text{g/mol}} = 0.000887 \, \text{moles}\]

Relate Moles of \( \text{SO}_4^{2-} \) to Moles of Saccharin

Each mole of \( \text{BaSO}_4 \) corresponds to one mole of \( \text{SO}_4^{2-} \) ions, which originates from one mole of saccharin containing sulfur. Thus, the moles of saccharin equals the moles of \( \text{BaSO}_4 \):\[0.000887 \, \text{moles of saccharin} = 0.000887 \, \text{moles of } \text{BaSO}_4\]

Calculate the Molar Mass of Saccharin

Calculate the molar mass of saccharin (\( \text{C}_7\text{H}_5\text{NO}_3\text{S} \)) by summing the atomic masses: carbon (C) is 12.01 g/mol, hydrogen (H) is 1.008 g/mol, nitrogen (N) is 14.01 g/mol, oxygen (O) is 16.00 g/mol, and sulfur (S) is 32.07 g/mol.\[7(12.01) + 5(1.008) + 14.01 + 3(16.00) + 32.07 = 183.18 \, \text{g/mol}\]

Calculate the Mass of Saccharin

Use the moles calculated for saccharin and its molar mass to find the saccharin's mass:\[\text{mass of saccharin} = 0.000887 \, \text{mol} \times 183.18 \, \text{g/mol} = 0.1624 \, \text{g}\]

Determine the Mass Percent of Saccharin

Finally, calculate the mass percent of saccharin in the sample:\[\text{Mass percent} = \left( \frac{\text{mass of saccharin}}{\text{mass of sample}} \right) \times 100 = \left( \frac{0.1624}{0.2140} \right) \times 100 \approx 75.87\%\]

Key concepts

Saccharin

Saccharin is a widely used artificial sweetener, known for its high sweetness potency relative to sugar. It has been employed in various food and beverage products, especially for those needing low-calorie sugar alternatives. The formula for saccharin is \( \text{C}_7\text{H}_5\text{NO}_3\text{S} \). This indicates that each molecule contains 7 carbon atoms, 5 hydrogen atoms, 1 nitrogen atom, 3 oxygen atoms, and 1 sulfur atom. Saccharin is a water-insoluble compound, which makes it useful in scenarios where a sweet taste without additional calories is desired.
Saccharin's role in this exercise is as a component of a sweetener, where its sulfur content is transformed into \( \text{SO}_4^{2-} \) and further precipitated as \( \text{BaSO}_4 \). This transformation allows chemists to calculate the amount of saccharin in the mixture by analyzing the resultant solid.

Molar Mass Calculation

The molar mass of a compound is the weight of one mole (Avogadro's number of particles) of the compound. This is crucial for converting between grams and moles. Molar mass is typically calculated by summing the atomic masses of all atoms present in the compound.
For instance, in calculating the molar mass of saccharin \( \text{C}_7\text{H}_5\text{NO}_3\text{S} \), the contribution from each type of atom is combined:

• Carbon: 7 atoms at 12.01 g/mol
• Hydrogen: 5 atoms at 1.008 g/mol
• Nitrogen: 1 atom at 14.01 g/mol
• Oxygen: 3 atoms at 16.00 g/mol
• Sulfur: 1 atom at 32.07 g/mol

The total molar mass equates to \( 183.18 \) g/mol.
For different compounds, each atomic mass is collected from periodic table values before multiplying by the number of atoms and summing the results.

Mass Percent Calculation

Mass percent is a way to express the concentration of a specific component in a mixture, showing how much of the mass of the mixture is due to that component. It is calculated by the formula:\[\text{Mass percent} = \left( \frac{\text{mass of component}}{\text{mass of mixture}} \right) \times 100\]
In the exercise, we wish to calculate the mass percent of saccharin in the sweetener sample. After finding the mass of saccharin (\(0.1624 \text{ g}\)) and knowing the total mass of the sweetener mixture (\(0.2140 \text{ g}\)), the calculation unfolds as:

• \( \frac{0.1624}{0.2140} \times 100 \approx 75.87\% \)

This indicates that approximately 75.87% of the sweetener's mass comes from saccharin.

Compound Decomposition

In analytical chemistry, compound decomposition refers to breaking down a compound into its components. This often allows chemists to focus on a particular element within a compound like sulfur in saccharin. By decomposing saccharin and capturing its sulfur component as the sulfate ion \( \text{SO}_4^{2-} \), we can further precipitate it to form \( \text{BaSO}_4 \).
This process leverages chemical reactions to transform elements into easily measurable forms. In this exercise, sulfur from saccharin becomes part of \( \text{BaSO}_4 \), a solid that can be weighed accurately.
The mass of \( \text{BaSO}_4 \) obtained is used in stoichiometric calculations to deduce the quantity of saccharin initially present, linking the mass of the desired analyte to a measurable physical quantity, the decomposed compound.