Problem 40 - Chemistry and Chemical Reactivity

Question

An Alka-Seltzer tablet contains 324 mg of aspirin \(\left(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\right), 1904 \mathrm{mg}\) of \(\mathrm{NaHCO}_{3},\) and \(1000 .\) mg of citric acid \(\left(\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}\right) .\) (The last two compounds react with each other to provide the "fizz," bubbles of \(\mathrm{CO}_{2},\) when the tablet is put into water.) (a) Calculate the amount (moles) of each substance in the tablet. (b) If you take one tablet, how many molecules of aspirin are you consuming?

Step-by-Step Solution

Answer

0.0018 moles of aspirin, 0.0227 moles of NaHCO3, 0.0052 moles of citric acid; 1.08 × 10^21 molecules of aspirin.

Step 1: Calculate Molar Masses

To find the amount in moles, calculate the molar masses of the compounds. - Aspirin \((\mathrm{C}_9\mathrm{H}_8\mathrm{O}_4)\): Carbon = 12.01 g/mol, Hydrogen = 1.008 g/mol, Oxygen = 16.00 g/mol. Molar mass = \((9 \times 12.01) + (8 \times 1.008) + (4 \times 16.00)\) = 180.16 g/mol.- Sodium bicarbonate \((\mathrm{NaHCO}_3)\): Sodium = 22.99 g/mol, Hydrogen = 1.008 g/mol, Carbon = 12.01 g/mol, Oxygen = 16.00 g/mol. Molar mass = \((22.99 + 1.008 + 12.01 + 3\times16.00)\) = 84.01 g/mol.- Citric acid \((\mathrm{H}_3\mathrm{C}_6\mathrm{H}_5\mathrm{O}_7)\): Hydrogen = 1.008 g/mol, Carbon = 12.01 g/mol, Oxygen = 16.00 g/mol. Molar mass = \((3 \times 1.008) + (6 \times 12.01) + (5 \times 1.008) + (7 \times 16.00)\) = 192.12 g/mol.

Step 2: Convert Mass to Moles

Use the formula: \( \text{moles} = \frac{\text{mass in grams}}{\text{molar mass in g/mol}} \) to find the moles.- Aspirin: \( \frac{0.324 \text{ g}}{180.16 \text{ g/mol}} = 0.0018 \text{ moles} \)- Sodium bicarbonate: \( \frac{1.904 \text{ g}}{84.01 \text{ g/mol}} = 0.0227 \text{ moles} \)- Citric acid: \( \frac{1.000 \text{ g}}{192.12 \text{ g/mol}} = 0.0052 \text{ moles} \)

Step 3: Calculate Molecules of Aspirin

Use Avogadro's number (\(6.022 \times 10^{23}\) molecules/mol) to calculate the number of molecules in the moles of aspirin.- Molecules of aspirin = \(0.0018 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mol} = 1.08 \times 10^{21} \text{ molecules}\)

Key Concepts

Molar Mass

Molar mass is a fundamental concept in chemistry, providing insights into the mass of a given substance's atoms or molecules. For any chemical substance, knowing its molar mass allows us to convert between grams and moles, which is crucial for balancing chemical reactions and conducting stoichiometric calculations.
Molar mass is calculated by summing the atomic masses of all the atoms in a molecule. Each element on the periodic table has a specific atomic mass, typically found below the element symbol.

• Aspirin (\(\mathrm{C}_9\mathrm{H}_8\mathrm{O}_4\)) consists of carbon, hydrogen, and oxygen. Thus, its molar mass is computed as follows: carbon is 12.01 g/mol, hydrogen is 1.008 g/mol, and oxygen is 16.00 g/mol. The calculations become: \((9 \times 12.01) + (8 \times 1.008) + (4 \times 16.00) = 180.16\) g/mol.
• Sodium bicarbonate (\(\mathrm{NaHCO}_3\)) has sodium (22.99 g/mol), hydrogen (1.008 g/mol), carbon (12.01 g/mol), and oxygen (16.00 g/mol) involved, resulting in a molar mass calculation of: \((22.99 + 1.008 + 12.01 + 3 \times 16.00) = 84.01\) g/mol.
• For citric acid (\(\mathrm{H}_3\mathrm{C}_6\mathrm{H}_5\mathrm{O}_7\)), the corresponding molar mass extends from adding the atomic masses: \((3 \times 1.008) + (6 \times 12.01) + (5 \times 1.008) + (7 \times 16.00) = 192.12\) g/mol.

Avogadro's Number

Avogadro's number is a constant that plays an essential role in connecting moles to molecules. It quantifies the number of units, such as atoms, ions, or molecules, in one mole of a substance. This number is incredibly large: \(6.022 \times 10^{23}\).
When you have 1 mole of a given substance, you possess exactly \(6.022 \times 10^{23}\) units of that substance, making it the bridge between the macroscopic and microscopic worlds. This connection is an invaluable tool in chemistry, allowing precise measurements and conversions in chemical reactions.
For example, if you ingest one Alka-Seltzer tablet, you're consuming approximately \(0.0018\) moles of aspirin. To determine how many aspirin molecules this equates to, you'll multiply the moles of aspirin by Avogadro's number: \[0.0018\text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mole} = 1.08 \times 10^{21} \text{ molecules.}\]This conversion highlights just how numerous molecules are in even a tiny mass of a substance.

Chemical Reactions

Chemical reactions involve the transformation of reactants into products through the breaking and forming of chemical bonds. In the case of the Alka-Seltzer tablet, the fizzing reaction when dissolved in water is due to a reaction between sodium bicarbonate (\(\mathrm{NaHCO}_3\)) and citric acid (\(\mathrm{H}_3\mathrm{C}_6\mathrm{H}_5\mathrm{O}_7\)). This reaction releases carbon dioxide (\(\mathrm{CO}_2\)), causing the familiar bubbles.
Chemical reactions can be influenced by several factors, including:

• The concentrations of reactants.
• The temperature of the system.
• The presence of catalysts.

For the reaction in Alka-Seltzer, the chemical equation typically looks like:\[\mathrm{NaHCO}_3 + \mathrm{H}_3\mathrm{C}_6\mathrm{H}_5\mathrm{O}_7 \rightarrow \mathrm{CO}_2 + \text{other products}\]Understanding the reactants and products in a chemical reaction is crucial for determining the quantities needed and predicting the outcomes.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the relationships between the quantities of reactants and products in a chemical reaction. It relies heavily on the concept of the mole and molar mass to solve problems related to the mass and moles of substances involved.
The primary goal of stoichiometry is to calculate how much product will result from a given amount of reactants, or conversely, how much reactant is necessary to produce a desired quantity of product.

• It connects the macroscopic world we observe with the microscopic world of atoms and molecules.
• In Alka-Seltzer, stoichiometry helps us calculate the precise amounts of sodium bicarbonate and citric acid involved, ensuring the correct fizzing reaction to release a quantified amount of carbon dioxide (\(\mathrm{CO}_2\)).

In solving stoichiometric problems, it's important to start with a balanced chemical equation. This equation enables the conversion of grams to moles using the molar mass and provides the mole-to-mole ratios needed to forecast the transformation of reactants into products. Stoichiometry thus serves as an essential tool for managing chemical reactions efficiently and effectively.