Question

8 Acidity of Gastric HCl A technician in a hospital laboratory obtained a \(10.0 \mathrm{~mL}\) sample of gastric juice from a patient several hours after a meal and titrated the sample with \(0.1 \mathrm{~m} \mathrm{NaOH}\) to neutrality. The neutralization of gastric \(\mathrm{HCl}\) required \(7.2 \mathrm{~mL}\) of \(\mathrm{NaOH}\). The patient's stomach contained no ingested food or drink at the time of sample harvest. Therefore, assume that no buffers were present. What was the \(\mathrm{pH}\) of the gastric juice?

Short answer

The pH of the gastric juice is approximately 1.14.

Step-by-step solution

Understand the Reaction

The reaction is between hydrochloric acid (HCl) in the gastric juice and sodium hydroxide (NaOH). The equation for this neutralization is:\[ \text{HCl(aq)} + \text{NaOH(aq)} \rightarrow \text{NaCl(aq)} + \text{H}_2\text{O(l)} \] This means that one mole of HCl reacts with one mole of NaOH.

Calculate Moles of NaOH Used

The molarity of NaOH solution is given as \(0.1 \text{ M} \) and the volume used is \(7.2 \text{ mL} \), which needs to be converted to liters: \(7.2 \text{ mL} = 0.0072 \text{ L}\). Now, calculate the moles of NaOH used:\[\text{moles of NaOH} = 0.1 \text{ M} \times 0.0072 \text{ L} = 0.00072 \text{ moles}\]

Determine Moles of HCl in Gastric Juice

According to the balanced chemical equation, the moles of HCl will be equal to the moles of NaOH because they react in a 1:1 ratio. Therefore, the moles of HCl in the gastric juice are also \(0.00072 \text{ moles}\).

Calculate the Concentration of HCl in Gastric Juice

The volume of gastric juice is \(10.0 \text{ mL} = 0.010 \text{ L}\). Now compute the concentration of HCl:\[[\text{HCl}] = \frac{\text{moles of HCl}}{\text{volume of gastric juice in liters}} = \frac{0.00072}{0.010} = 0.072 \text{ M}\]

Calculate the pH of the Gastric Juice

The pH is calculated using the formula:\[\text{pH} = -\log_{10} [\text{H}^+]\]Since the concentration of HCl is equal to the concentration of \([\text{H}^+]\) due to complete dissociation, the pH is:\[\text{pH} = -\log_{10}(0.072) \approx 1.14\]

Key concepts

Neutralization Reaction

Neutralization reactions are a type of chemical reaction where an acid and a base react to form water and a salt. These reactions are essential in many biological and chemical processes, including the digestion process in our stomachs.
Gastric juice in the stomach contains hydrochloric acid (HCl), which helps break down food. Sometimes, when medical tests require, we need to neutralize this acid to understand its concentration. In the example provided, the technician used

• sodium hydroxide (NaOH)
• a known base

as a titrant to neutralize the stomach acid.

This reaction can be represented by the chemical equation:\[\text{HCl(aq)} + \text{NaOH(aq)} \rightarrow \text{NaCl(aq)} + \text{H}_2\text{O(l)}\]This equation means one mole of HCl reacts with one mole of NaOH. Understanding this one-to-one relationship is crucial in calculating how much base is needed to neutralize a given amount of acid in any solution.

This concept is valuable not only in labs but also in everyday applications, such as taking antacids to relieve heartburn or indigestion. Knowing how neutralization reactions work helps us understand and tackle such common issues.

Molarity Calculations

Molarity is a way to express the concentration of a solution. It is defined as the number of moles of solute per liter of solution. In the context of the stomach acid example, understanding molarity helps us know how concentrated the stomach acid is. Let's break this down a bit further.

To calculate the molarity, you need:

• The volume of the solution, typically in liters.
• The number of moles of the solute, such as HCl in the gastric juice.

For our exercise, we used sodium hydroxide (NaOH) to titrate gastric acid. We calculated the moles of NaOH from its given molarity (0.1 M) and the volume (7.2 mL or 0.0072 L). The calculation is:\[\text{Moles of } \text{NaOH} = 0.1 \text{ M} \times 0.0072 \text{ L} = 0.00072 \text{ moles}\]
This same amount of moles (0.00072) applies to the HCl since they react in a 1:1 molar ratio. When calculating molarity:\[\text{Molarity of HCl} = \frac{0.00072 \text{ moles}}{0.010 \text{ L}} = 0.072 \text{ M}\]
By understanding molarity, students can better comprehend chemical concentrations in various scenarios, such as those found in chemistry labs, medicines, and even culinary arts.

pH Calculation

The pH of a solution is a numerical value that expresses its acidity or basicity. It is calculated using the concentration of hydrogen ions \([ ext{H}^+]\) in the solution. The formula for calculating pH is:\[\text{pH} = -\log_{10} [\text{H}^+]\]
In the exercise with the gastric juice sample, this concept is applied to determine how acidic the gastric juice is after calculating its molarity to be 0.072 M HCl. Since HCl is a strong acid, it fully dissociates in water; hence, its concentration equals \([ ext{H}^+]\).

For the gastric juice,\[\text{pH} = -\log_{10}(0.072) \approx 1.14\]This low pH indicates that the gastric juice is highly acidic, which is typical for stomach conditions as the acidity aids in digestion.
Understanding pH is crucial across many scientific fields and day-to-day activities. It helps explain why different substances behave the way they do—whether causing different reactions in chemistry experiments or affecting our bodies, like the acid-base balance in our stomachs or blood.