Problem 108 - Chemistry An Atoms First Approach

Question

Saccharin \(\left(\mathrm{C}_{7} \mathrm{H}_{5} \mathrm{NO}_{3} \mathrm{S}\right)\) is sometimes dispensed in tablet form. Ten tablets with a total mass of 0.5894 g were dissolved in water. The saccharin was oxidized to convert all the sulfur to sulfate ion, which was precipitated by adding an excess of barium chloride solution. The mass of BaSO_ obtained was \(0.5032 \mathrm{g} .\) What is the average mass of saccharin per tablet? What is the average mass percent of saccharin in the tablets?

Step-by-Step Solution

Answer

The average mass of saccharin per tablet is 0.03949 g (or 39.49 mg), and the average mass percent of saccharin in the tablets is 66.98%.

Step 1: Write balanced chemical equation for the reaction

First, we need to write the balanced chemical equation for the reaction of saccharin with barium chloride to produce barium sulfate and other products: \( C_7H_5NO_3S + Ba^{2+} \rightarrow BaSO_4 + \text{other products} \)

Step 2: Calculate moles of BaSO4

To determine the mass of saccharin, we'll first find the moles of BaSO4 produced from the given mass of BaSO4 (0.5032 g). To do this, we need the molar mass of BaSO4: Molar mass of BaSO4 = Ba + S + 4 * O = 137.33 + 32.07 + 4 * 16.00 = 233.39 g/mol Now, we'll find the moles of BaSO4: moles of BaSO4 = mass of BaSO4 / molar mass of BaSO4 = 0.5032 g / 233.39 g/mol = 0.002156 mol

Step 3: Calculate moles of saccharin

From the balanced chemical equation, we can see that the mole ratio of saccharin to BaSO4 is 1:1. So, the moles of saccharin in the ten tablets are equal to the moles of BaSO4 produced. moles of saccharin = moles of BaSO4 = 0.002156 mol

Step 4: Calculate mass of saccharin

Now, we'll find the mass of saccharin from its moles and molar mass. First, let's find the molar mass of saccharin: Molar mass of saccharin = C * 7 + H * 5 + N * 1 + O * 3 + S * 1 = 12.01 * 7 + 1.01 * 5 + 14.01 * 1 + 16.00 * 3 + 32.07 * 1 = 183.18 g/mol Then, we'll calculate the mass of saccharin: mass of saccharin = moles of saccharin * molar mass of saccharin = 0.002156 mol * 183.18 g/mol = 0.3949 g

Step 5: Calculate average mass of saccharin per tablet

Now that we know the mass of saccharin in the ten tablets, we can find the average mass of saccharin per tablet: average mass of saccharin per tablet = mass of saccharin / number of tablets = 0.3949 g / 10 = 0.03949 g (or 39.49 mg)

Step 6: Calculate average mass percent of saccharin in the tablets

Finally, we'll calculate the average mass percent of saccharin in the tablets: average mass percent of saccharin = (mass of saccharin / total mass of tablets) * 100 = (0.3949 g / 0.5894 g) * 100 = 66.98 % So, the average mass of saccharin per tablet is 39.49 mg, and the average mass percent of saccharin in the tablets is 66.98%.

Key Concepts

Molar Mass Calculations

In chemistry, calculating the molar mass of compounds is essential for various quantitative analyses. The molar mass is the mass of one mole of a substance and it is usually expressed in grams per mole (g/mol). Determining the molar mass involves adding together the atomic masses of all the atoms present in a molecule. These atomic masses can be found on the periodic table.

For example, in the original exercise, we calculated the molar mass of saccharin, \(C_7H_5NO_3S\). We added:

• Seven carbon atoms (\(12.01 \text{ g/mol} \times 7\)
• Five hydrogen atoms (\(1.01 \text{ g/mol} \times 5\)
• One nitrogen atom (\(14.01 \text{ g/mol} \times 1\)
• Three oxygen atoms (\(16.00 \text{ g/mol} \times 3\)
• One sulfur atom (\(32.07 \text{ g/mol} \times 1\)

This calculation yielded a molar mass of 183.18 g/mol for saccharin. Accurately calculating molar masses is crucial for further stoichiometric calculations in chemical reactions.

Stoichiometry

Stoichiometry is like a recipe for chemical reactions. It tells us the quantitative relationship between reactants and products in a chemical equation. Understanding stoichiometry allows chemists to predict the amounts of substances consumed and produced in a given chemical reaction. This involves using ratios derived from the balanced chemical equation.

In our case, we evaluated the stoichiometry from the balanced equation:\[C_7H_5NO_3S + Ba^{2+} \rightarrow BaSO_4 + \text{other products}\]The equation suggests a 1:1 ratio between saccharin and barium sulfate. This indicates that 1 mole of saccharin yields 1 mole of barium sulfate. From this ratio, we determined that the moles of barium sulfate formed (0.002156 mol) equaled the moles of saccharin present in the tablets.

Chemical Reactions

Chemical reactions are processes where substances (reactants) are transformed into new substances (products). Understanding these reactions is critical to predicting the outcomes in chemical processes and determining the necessary conditions for reactions.

In our scenario, saccharin was transformed into barium sulfate (BaSO_4) through a series of reactions. Saccharin and barium chloride reacted to precipitate barium sulfate, a common chemical process in qualitative analysis where ions are combined to form an insoluble solid. Recognizing the reactants and products, as well as balancing the chemical equation, helps in predicting reaction outcomes and facilitating further calculations like stoichiometry and mass percent.

Mass Percent Calculation

Mass percent, often referred to as percent composition, represents the concentration of a component in a mixture or compound. It is calculated by dividing the mass of the component by the total mass of the mixture and then multiplying by 100 to express it as a percentage.

To determine mass percent in the tablets, we used the formula:\[\text{mass percent} = \left(\frac{\text{mass of saccharin}}{\text{total mass of tablets}}\right) \times 100\]By inserting the values:

• Mass of saccharin: 0.3949 g
• Total mass of tablets: 0.5894 g

We calculated the mass percent as \(66.98\%\). This indicates how much of the tablet's mass is composed of saccharin, which is especially useful for verifying the content claim of such medicinal products.