Problem 78 - 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 \(\operatorname{acid}\left(\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}\right) .\) (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

Aspirin: 0.00180 mol, NaHCO₃: 0.0227 mol, Citric Acid: 0.00521 mol; 1.08 × 10²¹ aspirin molecules.

Step 1: Identify Molar Masses

First, we need to find the molar masses of each substance.- Aspirin \( (\mathrm{C}_{9}\mathrm{H}_{8}\mathrm{O}_{4}) \): \( 12.01\times9 + 1.01\times8 + 16.00\times4 = 180.17 \text{ g/mol} \)- Sodium bicarbonate \( (\mathrm{NaHCO}_{3}) \): \( 22.99 + 1.01 + 12.01 + 16.00\times3 = 84.01 \text{ g/mol} \)- Citric acid \( (\mathrm{H}_{3}\mathrm{C}_{6}\mathrm{H}_{5}\mathrm{O}_{7}) \): \( 1.01\times3 + 12.01\times6 + 1.01\times5 + 16.00\times7 = 192.13 \text{ g/mol} \).

Step 2: Calculate Moles of Aspirin

Convert the mass of aspirin to moles using its molar mass:\[\frac{324 \text{ mg}}{1000} \times \frac{1}{180.17 \text{ g/mol}} = 0.00180 \text{ mol}\]

Step 3: Calculate Moles of Sodium Bicarbonate

Convert the mass of sodium bicarbonate to moles:\[\frac{1904 \text{ mg}}{1000} \times \frac{1}{84.01 \text{ g/mol}} = 0.0227 \text{ mol}\]

Step 4: Calculate Moles of Citric Acid

Convert the mass of citric acid to moles:\[\frac{1000 \text{ mg}}{1000} \times \frac{1}{192.13 \text{ g/mol}} = 0.00521 \text{ mol}\]

Step 5: Calculate Molecules of Aspirin

To find the number of molecules of aspirin, multiply the moles by Avogadro's number \( (6.022 \times 10^{23} \text{ molecules/mol}) \):\[0.00180 \text{ mol} \times 6.022 \times 10^{23} = 1.08 \times 10^{21} \text{ molecules}\]

Key Concepts

Molar Mass

Molar mass is an essential concept in chemistry that connects the mass of a substance to the amount of substance (in moles). The molar mass of a compound is the sum of the atomic masses of all its atoms. It is expressed in grams per mole (g/mol). In the case of aspirin

• Identify each element present in the compound and note its atomic mass from the periodic table.
• Multiply the atomic mass of each element by the number of times the element appears in the compound's formula.
• Add the total masses together to determine the molar mass of the compound.

For aspirin \[12.01 \times 9 + 1.01 \times 8 + 16.00 \times 4 = 180.17 \, \text{g/mol}\].
Doing this calculation accurately allows us to convert mass into moles, which is crucial for further calculations in chemical reactions and processes. Similarly, calculate the molar mass for substances like sodium bicarbonate and citric acid.

Avogadro's Number

Avogadro's number is a fundamental constant in chemistry, representing the number of atoms, ions, or molecules in one mole of a substance. Its value is approximately \(6.022 \times 10^{23} \, \text{entities/mol}\).
This number provides a bridge between the macroscopic scale that we can measure and the microscopic world of atoms and molecules.

• To find the number of particles in a given amount of substance, we multiply the number of moles by Avogadro’s number.
• It is essential when converting from macroscopic measurements like grams to the microscopic world of molecules.

For example, to determine how many molecules of aspirin you consume from one Alka-Seltzer tablet, use Avogadro's number \(0.00180 \, \text{mol} \times 6.022 \times 10^{23} = 1.08 \times 10^{21} \, \text{molecules}\)}.

Chemical Reactions

Chemical reactions involve rearranging atoms to form new substances. In reactions, bonds between atoms in the reactants break, and new bonds form to create products. Chemical reactions typically have reactants, products, and often, catalysts or environmental conditions that influence the rate or outcome.

• Reactants are the starting substances in any chemical reaction, and products are the substances formed as a result of the reaction.
• Reactions can be categorized into various types such as synthesis, decomposition, single-replacement, double-replacement, and combustion.

For the Alka-Seltzer fizz reaction, citric acid and sodium bicarbonate are the reactants. When they interact in water, they transform into new products, creating bubbles of carbon dioxide \(\text{CO}_2\). It demonstrates a type of chemical change where a gas is released.

Fizz Reaction

The term 'fizz reaction' refers to the bubbling or effervescence observed when certain chemicals react in water. This fun and visually engaging reaction occur due to the release of gas, usually carbon dioxide \(\text{CO}_2\). In the context of Alka-Seltzer, the reaction is caused by the interaction between citric acid \(\text{H}_3\text{C}_6\text{H}_5\text{O}_7\) and sodium bicarbonate \(\text{NaHCO}_3\).

• The citric acid donates protons \((\text{H}^+)\), neutralizing the alkaline sodium bicarbonate.
• During this reaction, carbon dioxide gas bubbles release, which are responsible for the fizzing effect that is common in effervescent tablets.

This process not only neutralizes acidity but also accelerates the delivery of the active ingredients, making it an effective mechanism in medicinal tablets and fun science experiments alike.