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

1. Understand the relationship between [H₃O⁺] and pH. The pH of a solution is calculated using the formula: $\mathrm{pH}=-\log \left({\mathrm{[H}}_{3}O\right])$. This formula tells us that pH is the negative logarithm (base 10) of the hydronium ion concentration.
2. Identify the given value for [H₃O⁺]. From the problem, the hydronium ion concentration is $4\times {10}^{-}$ M.
3. Substitute the given [H₃O⁺] value into the pH formula. This gives: $\mathrm{pH}=-\log (4\times {10}^{-})$.
4. Break the calculation into two parts for clarity. First, use the logarithmic property: $\log (4\times {10}^{-})=\log \left(4\right)+\log \left({10}^{-}\right)$. Then, recall that $\log \left({10}^{-}\right)=-2$.
5. Combine the results. The pH is calculated as: $\mathrm{pH}=-\left(\log \right(4)+-2)$. Simplify further to find the final pH value.

Key Concepts

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.