When food enters the stomach, HCl is released and the [H3O+] of the stomach fluid rises to 4 × 10–2 M. What is the pH of the stomach fluid?

Understand the relationship between [H₃O⁺] and pH. The pH of a solution is calculated using the formula: pH=-log([H3O]). This formula tells us that pH is the negative logarithm (base 10) of the hydronium ion concentration. Identify the given value for [H₃O⁺]. From the problem, the hydronium ion concentration is 4×10-2 M. Substitute the given [H₃O⁺] value into the pH formula. This gives: pH=-log(4×10-2). Break the calculation into two parts for clarity. First, use the logarithmic property: log(4×10-2)=log(4)+log(10-2). Then, recall that log(10-2)=-2. Combine the results. The pH is calculated as: pH=-(log(4)+-2). Simplify further to find the final pH value.

Ch.10 Acids and Bases and Equilibrium

Timberlake - Chemistry: An Introduction to General, Organic, and Biological Chemistry 14th Edition

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Timberlake 14th Edition

Ch.10 Acids and Bases and Equilibrium

Problem 64

Chapter 10, Problem 64

When food enters the stomach, HCl is released and the [H₃O⁺] of the stomach fluid rises to 4 × 10^–2 M. What is the pH of the stomach fluid?

Verified step by step guidance

Understand the relationship between [H₃O⁺] and pH. The pH of a solution is calculated using the formula:

pH = - \log ({[H}_{3} O])

. This formula tells us that pH is the negative logarithm (base 10) of the hydronium ion concentration.

Identify the given value for [H₃O⁺]. From the problem, the hydronium ion concentration is

4 \times 10^{- 2}

Substitute the given [H₃O⁺] value into the pH formula. This gives:

pH = - \log (4 \times 10^{- 2})

Break the calculation into two parts for clarity. First, use the logarithmic property:

\log (4 \times 10^{- 2}) = \log (4) + \log (10^{- 2})

. Then, recall that

\log (10^{- 2}) = - 2

Combine the results. The pH is calculated as:

pH = - (\log (4) + - 2)

. Simplify further to find the final pH value.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

pH Scale

The pH scale measures the acidity or basicity of a solution, ranging from 0 to 14. A pH of 7 is neutral, while values below 7 indicate acidity and above 7 indicate alkalinity. The scale is logarithmic, meaning each whole number change represents a tenfold change in hydrogen ion concentration.

Hydronium Ion Concentration

Hydronium ion concentration, represented as [H₃O⁺], indicates the amount of hydronium ions present in a solution. It is directly related to the acidity of the solution; higher concentrations correspond to lower pH values. In this case, a concentration of 4 x 10⁻² M indicates a significant level of acidity.

Calculating pH

To calculate pH, the formula pH = -log[H₃O⁺] is used, where [H₃O⁺] is the concentration of hydronium ions in moles per liter. This calculation allows us to determine the acidity of the solution quantitatively. For example, if [H₃O⁺] is 4 x 10⁻² M, the pH can be calculated to find the exact acidity level.

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Related Practice

Textbook Question

Which of the following represents a buffer system? Explain.

a. H₃PO₃

b. NaNO₃

c. HC₂H₃O₂ and NaC₂H₃O₂

d. HCl and NaOH

Textbook Question

Identify each of the following as an acid or a base:

d. HI

Textbook Question

Someone with severe diabetes obtains energy by the breakdown of fats, which produce large amounts of acidic substances. How would this affect the pH of the blood plasma?

Textbook Question

Write the balanced chemical equation for the neutralization reaction of stomach acid HCl with Al(OH)₃, an ingredient in some antacids.

Textbook Question

If 32.8 mL of a 0.162 M NaOH solution is required to titrate 25.0 mL of a solution of H₂SO₄, what is the molarity of the H₂SO₄ solution?

H₂SO₄(aq) + 2 KOH(aq) → 2 H₂O(l) + K₂SO₄(aq)

Textbook Question

How many grams of Al(OH)₃ are required to neutralize 150. mL of stomach acid with a pH of 1.5?