Problem 53 - Chemistry and Chemical Reactivity

Question

Calculating and Using pH A table wine has a pH of \(3.40 .\) What is the hydronium ion concentration of the wine? Is it acidic or basic?

Step-by-Step Solution

Answer

The hydronium ion concentration is approximately \(3.98 \times 10^{-4} \text{ M}\). The wine is acidic.

Step 1: Understanding pH Definition

The pH scale is used to measure the acidity or basicity of a solution. It is defined as the negative logarithm (base 10) of the hydronium ion concentration: \[ pH = -\log[H_3O^+] \] where \([H_3O^+]\) is the concentration of hydronium ions in moles per liter.

Step 2: Applying the pH Formula

Given that the pH of the wine is 3.40, we need to find the hydronium ion concentration, which is given by \[ [H_3O^+] = 10^{-pH} \] Substitute 3.40 into the equation: \[ [H_3O^+] = 10^{-3.40} \]

Step 3: Calculating Hydronium Ion Concentration

Calculate \([H_3O^+]\):\[ [H_3O^+] = 10^{-3.40} \approx 3.98 \times 10^{-4} \text{ moles per liter} \] Thus, the hydronium ion concentration is approximately \(3.98 \times 10^{-4} \text{ M}\).

Step 4: Determining Acidity or Basicity

A solution is considered acidic if its pH is less than 7 and basic if its pH is greater than 7. Since the pH of the wine is 3.40, which is less than 7, the wine is acidic.

Key Concepts

Hydronium Ion Concentration

Understanding hydronium ion concentration is a key part of studying solutions and their properties. - The hydronium ion, represented as \([H_3O^+]\), is a positively charged ion that forms when a proton (\(H^+\)) binds to a water molecule (\(H_2O\)).- In chemical equations, it acts as a measure of acidity. Whenever acids are dissolved in water, they release these protons that lead to the formation of hydronium ions.To find the concentration of hydronium ions from a given pH, we use the reverse of the logarithmic pH formula, which is:\[ [H_3O^+] = 10^{-pH} \]This equation helps us calculate the exact amount of hydronium ions in a solution. For example, if a solution has a pH of 3.4, then its hydronium ion concentration can be calculated using this formula, approximating to \(3.98 \times 10^{-4}\) moles per liter. This tells us how many hydronium ions are present in a specific volume, influencing the solution's acidity.

Acidic and Basic Solutions

Solutions can be classified as acidic or basic depending on their pH values.- **Acidic solutions** have a pH of less than 7. These solutions have a higher concentration of hydronium ions.- **Basic solutions** (also known as alkaline) have a pH greater than 7 and contain fewer hydronium ions, instead having more hydroxide ions (\(OH^-\)).Neutral solutions such as pure water have a pH exactly at 7, indicating a balance between hydronium and hydroxide ions.In the case of the table wine example, the pH is 3.40. Since this is below 7, the solution is clearly acidic. Understanding the distinction between acidic and basic solutions helps in determining the nature of the solution based on its hydronium ion content and its pH value.

pH Scale Definition

The pH scale is a logarithmic scale used to specify the acidity or basicity of an aqueous solution.- It ranges typically from 0 to 14. - A solution with a pH of 7 is neutral, having equal concentrations of hydronium and hydroxide ions.- Solutions with a pH less than 7 are acidic, while those with a pH greater than 7 are basic or alkaline.The pH scale is defined as:\[ pH = -\log[H_3O^+] \]This definition highlights that each unit change on the pH scale represents a tenfold change in hydronium ion concentration. For instance, a drop from pH 5 to 4 indicates the solution is ten times more acidic. In the wine example, the pH of 3.40 suggests a stronger presence of hydronium ions and hence a more acidic profile. The scale helps us easily compare acidity levels across different solutions using a simple numeric scale.