Question

One of the two most common ingredients in medication designed for the relief of excess stomach acidity is aluminum hydroxide ( \(\mathrm{Al}(\mathrm{OH})_{3}\), formula weight \(=78 \mathrm{~g} / \mathrm{mole}\) ). If a patient suffering from a duodenal ulcer displays a hydrochloric acid (HCI, formula weight \(=36.5 \mathrm{~g} /\) mole \(),\) concentration of \(80 \times\) \(10^{-3} \mathrm{M}\) in his gastric juice and he produces 3 liters of gastric juice per day, how much medication containing \(2.6 \mathrm{~g} \mathrm{Al}(\mathrm{OH})_{3}\) per \(100 \mathrm{ml}\) of solution must he consume per day to neutralize the acid?

Short answer

The patient must consume approximately 240 ml of the medication containing 2.6 g Al(OH)3 per 100 ml solution per day to neutralize the excess stomach acid.

Step-by-step solution

Calculate moles of HCl produced per day

First, we need to find out the moles of HCl produced in the patient's gastric juice. We are given that the patient produces 3 liters of gastric juice per day and has a concentration of 80x10^-3 M. Using the formula, moles = concentration x volume, we can calculate the moles of HCl produced per day: Moles of HCl = (80 * 10^-3) M x 3 L = 0.24 moles So, the patient produces 0.24 moles of HCl per day.

Calculate moles of Al(OH)3 required

Now, we need to determine how many moles of Al(OH)3 are needed to neutralize the HCl. The balanced chemical equation for the reaction between HCl and Al(OH)3 is: Al(OH)3 + 3HCl -> AlCl3 + 3H2O From the balanced equation, we can see that 1 mole of Al(OH)3 reacts with 3 moles of HCl. Using stoichiometry, we can calculate the moles of Al(OH)3 needed: Moles of Al(OH)3 = (0.24 moles HCl) x (1 mole Al(OH)3 / 3 moles HCl) = 0.08 moles Al(OH)3 So, the patient needs 0.08 moles of Al(OH)3 to neutralize the HCl.

Determine the volume of medication required

Finally, we need to find out the volume of medication the patient must consume to get the required moles of Al(OH)3. We are given that the medication contains 2.6 g Al(OH)3 per 100 ml solution. First, we need to convert the grams of Al(OH)3 into moles. The formula weight of Al(OH)3 is 78 g/mol, so: 2.6 g ÷ 78 g/mol = 0.0333 moles Al(OH)3 per 100ml Next, we can calculate the volume of medication needed to provide 0.08 moles of Al(OH)3: Volume of medication = (0.08 moles Al(OH)3) x (100 ml / 0.0333 moles Al(OH)3) ≈ 240 ml So, the patient must consume approximately 240 ml of the medication per day to neutralize the stomach acid.

Key concepts

Stoichiometry

Stoichiometry is a fundamental concept in chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. When we perform stoichiometric calculations, we use balanced chemical equations to determine the proportions in which substances react to form products. This is crucial for calculating reactant needs, product yields, or in our case, the amount of a substance required to neutralize another.

In the exercise provided, the balanced equation for the reaction between aluminum hydroxide \( \text{Al(OH)}_3 \) and hydrochloric acid \( \text{HCl} \) is presented as one mole of \( \text{Al(OH)}_3 \) reacting with three moles of \( \text{HCl} \). This means that to neutralize every three moles of \( \text{HCl} \), one mole of \( \text{Al(OH)}_3 \) is needed. This stoichiometric relationship enables us to calculate the precise amount of aluminum hydroxide required based on the amount of hydrochloric acid present.

The key is to first determine the moles of \( \text{HCl} \), which serves as a starting point for further calculations. Then, using the stoichiometry of the reaction, the necessary quantity of the neutralizing agent \( \text{Al(OH)}_3 \) can be determined.

Moles and Molarity

Understanding moles and molarity is essential for dealing with concentration in solutions, especially in acid-base reactions.

• **Moles**: This is a unit for amount of substance, which allows chemists to count particles such as atoms and molecules in bulk. A mole is defined as exactly \(6.022 \times 10^{23}\) entities (Avogadro's number).
• **Molarity**: This is a measure of concentration of a solution. It's expressed as moles of solute per liter of solution (\(\text{M}\)).

In this specific calculation, the concentration of \( \text{HCl} \) in the gastric juice is given as \(80 \times 10^{-3} \text{ M}\). We calculate the total moles of \( \text{HCl} \) produced per day based on a daily production of 3 liters of gastric juice. Using the formula: \[\text{moles} = \text{concentration} \times \text{volume}\]it results in \(0.24\) moles of \( \text{HCl} \) per day. Understanding these foundational concepts helps in linking the volume of solution to be consumed with the moles of the reacting substance required for neutralization.

Chemical Reactions

Chemical reactions involve transforming reactants into products through bond formation and cleavage. The specific type of reaction discussed here is an acid-base neutralization, where an acid (\(\text{HCl}\)) reacts with a base (\(\text{Al(OH)}_3\)) to form a salt and water.

The balanced reaction equation is:\[\text{Al(OH)}_3 + 3 \text{HCl} \rightarrow \text{AlCl}_3 + 3 \text{H}_2\text{O}\]This tells us:

• One mole of aluminum hydroxide reacts with three moles of hydrochloric acid.
• The products are aluminum chloride \(\text{AlCl}_3\) and water \(\text{H}_2\text{O}\).

This equation emphasises the need for a balanced stoichiometry to determine how much base is required to effectively neutralize a given amount of acid. Each reactant must fully consume its corresponding quantity of the other to complete the reaction. Recognizing these patterns in different types of reactions is vital in predicting outcomes and reactions in chemistry.