Problem 62 - Chemistry Matter and Change

Question

Antacid Fizz When an antacid tablet dissolves in water, the fizz is due to a reaction between sodium hydrogen carbonate \(\left(\mathrm{NaHCO}_{3}\right)\) also called sodium bicarbonate, and citric acid \(\left(\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}\right)\) $$\begin{array}{l}{3 \mathrm{NaHCO}_{3}(\mathrm{aq})+\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(\mathrm{aq}) \rightarrow} \\ {3 \mathrm{CO}_{2}(\mathrm{g})+3 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})+\mathrm{Na}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(\mathrm{aq})}\end{array}$$ How many moles of \(\mathrm{Na}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}\) can be produced if one tablet containing 0.0119 \(\mathrm{mol}\) of \(\mathrm{NaHCO}_{3}\) is dissolved?

Step-by-Step Solution

Answer

When 0.0119 moles of NaHCO3 are dissolved in the reaction, 0.00397 moles of Na3C6H5O7 can be produced, according to the given balanced chemical equation and stoichiometry.

Step 1: Identify the stoichiometry of the reaction

As per the given balanced chemical equation, we have: \[3 \, \mathrm{NaHCO}_{3}(\mathrm{aq})+\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(\mathrm{aq}) \rightarrow 3 \, \mathrm{CO}_{2}(\mathrm{g})+3 \, \mathrm{H}_{2} \mathrm{O}(\mathrm{l})+\mathrm{Na}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(\mathrm{aq})\] This means that 3 moles of NaHCO3 react with 1 mole of H3C6H5O7 to produce 1 mole of Na3C6H5O7.

Step 2: Setup the proportionality between reactants and products

Using the stoichiometry of the reaction, we can establish the proportionality between the moles of NaHCO3 consumed and the moles of Na3C6H5O7 produced. `moles of Na3C6H5O7` / `moles of NaHCO3` = 1 / 3

Step 3: Use moles of NaHCO3 to find moles of Na3C6H5O7

We can now substitute the given moles of NaHCO3, which is 0.0119 moles, and solve for the moles of Na3C6H5O7 produced: `moles of Na3C6H5O7` / 0.0119 = 1 / 3 To find the moles of Na3C6H5O7, we multiply both sides of the equation by 0.0119: `moles of Na3C6H5O7` = 0.0119 * (1 / 3)

Step 4: Calculate the moles of Na3C6H5O7 produced

Now we can calculate the moles of Na3C6H5O7: `moles of Na3C6H5O7` = 0.0119 * (1 / 3) = 0.00397 Thus, 0.00397 moles of Na3C6H5O7 can be produced when 0.0119 moles of NaHCO3 are dissolved in the reaction.

Key Concepts

Chemical Reaction Equations

Understanding chemical reactions begins with the balanced chemical equation. A chemical equation represents the substances involved in a reaction, the reactants, and products, and their amounts as well. For instance, in the antacid reaction, the fizz that results when an antacid tablet dissolves in water gives us a clear visual of a chemical reaction occurring. The balanced chemical equation provided shows the conversion of sodium hydrogen carbonate (NaHCO₃) and citric acid (H₃C₆H₅O₇) into products including sodium citrate (Na₃C₆H₅O₇), carbon dioxide (CO₂), and water (H₂O).

This equation is not just a narrative; it provides crucial stoichiometric information. It tells us that three mols of sodium hydrogen carbonate react with one mol of citric acid to yield three mols of carbon dioxide, three mols of water, and importantly, one mol of sodium citrate. Such equations enable chemists to predict the outcome of reactions and design experiments accurately.

Mole Concept

The mole concept is a central tenet in chemistry, bridging the gap between the microscopic world of atoms and molecules and the macroscopic world we can measure. One mol represents Avogadro's number, approximately 6.022 x 10²³, of particles - whether they are atoms, molecules, ions, or other entities. In the antacid reaction exercise, we are given that one tablet contains 0.0119 mol of NaHCO₃. With the mole concept, we appreciate that this quantifies a countable number of sodium hydrogen carbonate molecules.

When we perform stoichiometric calculations, as in steps 2 to 4 of the solution, we are actually comparing the number of reactant particles to the number of product particles based on their ratio in the balanced chemical equation. Knowing the moles of one reactant or product allows us to calculate the moles of another substance in the reaction, provided we have the balanced equation as a reference.

Acid-Base Reactions

Acid-base reactions are a subset of chemical reactions where an acid reacts with a base to produce water and a salt. The antacid fizz is the result of such an acid-base reaction, where sodium hydrogen carbonate acts as a base and citric acid as the acid. The resulting 'fizz' is the release of carbon dioxide gas, a common indicator of acid-base reactions.

These reactions are not just limited to a laboratory—they are part of everyday life. Antacids, for example, neutralize excess stomach acid, thereby relieving discomfort. The stoichiometry of the reaction is vital for practical applications like dosing medications, as well as theoretical understanding, such as predicting the pH of the solution. It's important for students to recognize the proportionality and relationships in these reactions, as it helps in comprehending the quantitative aspects of chemistry.