Question

Stomach acid is approximately \(0.020 \mathrm{M} \mathrm{HCl}\). What volume of this acid is neutralized by an antacid tablet that weighs \(330 \mathrm{mg}\) and contains \(41.0 \% \mathrm{Mg}(\mathrm{OH})_{2}, 36.2 \% \mathrm{NaHCO}_{3}\), and \(22.8 \% \mathrm{NaCl} ?\) The reactions in- volved are $$ \begin{gathered} \mathrm{Mg}(\mathrm{OH})_{2}(s)+2 \mathrm{H}^{+}(a q) \longrightarrow \mathrm{Mg}^{2+}(a q)+2 \mathrm{H}_{2} \mathrm{O} \\ \mathrm{HCO}_{3}^{-}(a q)+\mathrm{H}^{+}(a q) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O} \end{gathered} $$

Short answer

Answer: The volume of stomach acid neutralized by the antacid tablet is approximately 0.303 L.

Step-by-step solution

Calculate the moles of \(Mg(OH)_2\) and \(NaHCO_3\) in the tablet

First, we need to find out how much of each active ingredient is present in the antacid tablet. Given that the tablet weighs \(330\,\text{mg}\) and contains \(41.0 \%\) \(Mg(OH)_2\) and \(36.2 \%\) \(NaHCO_3\): $$\text{Mass of}\, Mg(OH)_2 = 0.410 \times 330\,\text{mg} = 135.3\,\text{mg}$$ $$\text{Mass of}\, NaHCO_3 = 0.362 \times 330\,\text{mg} = 119.46\,\text{mg}$$ Now we can convert these masses into moles by using their molar masses: \(Mg(OH)_2 = 58.32 \,g/mol\), \(NaHCO_3 = 84.01\, g/mol\) $$\text{Moles of}\, Mg(OH)_2 = \frac{135.3\,\text{mg}}{58.32\, g/mol} \times \frac{1\,g}{1000\,\text{mg}} = 0.00232\,\text{mol}$$ $$\text{Moles of}\, NaHCO_3 = \frac{119.46\,\text{mg}}{84.01\, g/mol} \times \frac{1\,g}{1000\,\text{mg}} = 0.00142\,\text{mol}$$

Calculate the moles of \(H^+\) ions neutralized by the tablet

We can use the given chemical reactions and stoichiometry to find out how many moles of \(H^+\) ions are neutralized by \(Mg(OH)_2\) and \(NaHCO_3\). From the reactions: $$Mg(OH)_2 + 2H^+ \rightarrow Mg^{2+} + 2H_2O$$ $$HCO_3^- + H^+ \rightarrow CO_2 + H_2O$$ There is a \(1:2\) ratio between moles of \(Mg(OH)_2\) and moles of \(H^+\) ions, and a \(1:1\) ratio between moles of \(HCO_3^-\) and moles of \(H^+\) ions. $$\text{Moles of}\, H^+\, \text{neutralized by}\, Mg(OH)_2 = 2 \times 0.00232\,\text{mol} = 0.00464\,\text{mol}$$ $$\text{Moles of}\, H^+\, \text{neutralized by}\, NaHCO_3 = 1 \times 0.00142\,\text{mol} = 0.00142\,\text{mol}$$ Total moles of \(H^+\) ions neutralized by the antacid tablet: $$\text{Total moles of}\, H^+= 0.00464\,\text{mol} + 0.00142\,\text{mol} = 0.00606\,\text{mol}$$

Calculate the volume of stomach acid neutralized by the tablet

Now, we can apply the formula \(C = \frac{n}{V}\), where \(C\) is the concentration of \(HCl\) in stomach acid and \(n\) is the moles of \(H^+\) ions neutralized. Rearranging the formula to find \(V\): $$V = \frac{n}{C}$$ Substituting the values, \(C = 0.020\,\text{M}\) and \(n = 0.00606\,\text{mol}\): $$V = \frac{0.00606\,\text{mol}}{0.020\,\text{M}} = 0.303\,\text{L}$$ This means that the volume of stomach acid neutralized by the antacid tablet is approximately \(0.303\,\text{L}\).

Key concepts

Stoichiometry

Stoichiometry is a fundamental concept in chemistry that involves calculating relative quantities of reactants and products in chemical reactions. It is like a recipe that tells us how much of each substance we need to get a desired chemical reaction outcome. In our problem, it helps us figure out how each ingredient in the antacid tablet reacts with stomach acid to neutralize it. When we know how many moles of active ingredients like \(Mg(OH)_2\) and \(NaHCO_3\) are involved, we can use stoichiometry to predict the amount of stomach acid that can be neutralized. This concept relies heavily on the balanced chemical equations we learn to understand the reaction ratios. Each reactant and product in these reactions has coefficients in the equation that denote the proportion needed or produced. By knowing these proportions, stoichiometry empowers us to predict the outcome of chemical interactions efficiently and accurately.

Neutralization Reaction

A neutralization reaction is a type of chemical reaction where an acid and a base interact to form water and a salt. This is a vital process in chemistry, especially when dealing with antacids and stomach acid. During a neutralization reaction, the acidic hydrogen ions (\(H^+\)) react with the basic hydroxide ions (\(OH^-\)) to form water (\(H_2O\)). This interaction reduces the acidity of the solution. In the context of our exercise, the antacid components, \(Mg(OH)_2\) and \(NaHCO_3\), act as bases.

They react with the stomach acid, \(HCl\), neutralizing the excessive hydrogen ions that cause acidity. The reaction not only decreases acid concentration but also produces harmless byproducts like water and carbon dioxide. Understanding neutralization is crucial for determining how effectively antacids work. The efficiency of an antacid is based on its ability to neutralize acid through reactions that alter the pH balance in the stomach.

Molarity

Molarity is a measure of the concentration of a solution, expressed in moles of solute per liter of solution (mol/L). It's a crucial measurement in chemistry for determining how strong or weak a solution is. In our problem, we're given the molarity of stomach acid as 0.020 M, which indicates there are 0.020 moles of \(HCl\) per liter of solution. This helps us understand how much stomach acid we are dealing with and enables us to calculate the volume of acid that can be neutralized.

Calculating molarity involves knowing the amount of solute (in moles) and the total volume of the solution. When a solution is added to a reaction, its molarity tells us how much of the solute is available to react. This measurement is fundamental in determining reaction outcomes, helping us figure out the correct amount needed for neutralization and reaction completion.

Chemical Equations

Chemical equations represent chemical reactions at a fundamental level. They use symbols and formulas to display reactants and products, showing what happens when substances interact. In our context, chemical equations illustrate the reactions between \(Mg(OH)_2\), \(NaHCO_3\), and \(H^+\) ions. They are crucial because they allow us to see the stoichiometric relationships.

Each chemical equation provides a balanced representation of the reaction process. For instance, \(Mg(OH)_2 + 2H^+ \rightarrow Mg^{2+} + 2H_2O\) shows us the 1:2 ratio needed between \(Mg(OH)_2\) and \(H^+\) ions for complete neutralization. Accurate chemical equations ensure precise stoichiometric calculations, allowing us to predict how much of each substance will react and what products will form. Understanding these equations and how to balance them is a cornerstone in chemistry, as they provide a map for solving reaction-related problems.