Elixirs such as Alka-Seltzer use the reaction of sodium bicarbonate with citric acid in aqueous solution to produce a fizz: \(3 \mathrm{NaHCO}_{3}(a q)+\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{7}(a q) \longrightarrow\) $$ 3 \mathrm{CO}_{2}(g)+3 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{Na}_{3} \mathrm{C}_{6} \mathrm{H}_{3} \mathrm{O}_{7}(a q) $$ a. What mass of \(\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{7}\) should be used for every \(1.0 \times 10^{2}\) \(\mathrm{mg} \mathrm{NaHCO}_{3} ?\) b. What mass of \(\mathrm{CO}_{2}(\mathrm{~g})\) could be produced from such a mixture?

Sodium bicarbonate, commonly known as baking soda, is a versatile chemical compound with the formula \( NaHCO_3 \). It is a key ingredient in baking because it acts as a leavening agent, causing dough to rise by producing carbon dioxide gas when it reacts with an acid. Moreover, it is used in many over-the-counter antacids to relieve heartburn and indigestion. Its effectiveness as an antacid is due to its ability to react with stomach acids, leading to the production of neutral salts and the release of carbon dioxide gas.

When dealing with chemical reactions involving sodium bicarbonate, it's crucial to understand its molar mass—approximately 84 grams per mole—which allows us to convert between mass and moles of the substance. This conversion is a fundamental aspect of stoichiometry, aiding in quantifying how much sodium bicarbonate is needed or produced in a chemical reaction.

Citric acid is an organic compound with the chemical formula \( C_6H_8O_7 \), recognized widely for its presence in citrus fruits. Beyond its role as a natural preservative and a flavor enhancer in food and beverages, citric acid also participates in key biochemistry pathways, notably the citric acid cycle or Krebs cycle, which is vital for energy production in living cells.

In chemistry experiments and product formulations like effervescent tablets, citric acid's ability to donate protons in an aqueous solution initiates reactions, such as its reaction with sodium bicarbonate to produce carbon dioxide gas—a well-known effervescence. Its molar mass of approximately 192 grams per mole is used in stoichiometry to determine the amount of citric acid required to react completely with a given quantity of another reactant, like sodium bicarbonate.

The mole concept is a fundamental principle in chemistry that provides a bridge between the atomic, microscopic world and the practical, macroscopic world we experience. It defines a mole as Avogadro's number—approximately \( 6.022 \times 10^{23} \) entities—of anything, whether it be atoms, molecules, ions, or electrons. This concept allows chemists to count particles in a substance by weighing it.

Understanding the mole concept is essential when performing stoichiometric calculations in chemical reactions. In the context of effervescent reactions, it helps us equate the moles of reactants, like sodium bicarbonate and citric acid, to the moles of products formed. From these relationships, we can predict the quantities of products that result from a certain amount of reactants.

Molar mass is a physical property defined as the mass of a given substance (chemical element or chemical compound) divided by the amount of substance (mole). It is expressed in units of grams per mole (\(g/mol\)) and it reflects the mass of one mole of molecules or atoms of the substance. The molar mass provides an essential link between the mass of a material and the number of particles present.

In the context of stoichiometry, knowing the molar mass of the reactants and products involved allows for the translation of mass in grams to the number of moles, which is critical for the balanced chemical equation. For instance, with the proper molar masses, one can thus calculate the grams of citric acid needed to react with a specific mass of sodium bicarbonate, as well as the expected grams of carbon dioxide gas that will be produced.