Problem 11 - Chemistry and Chemical Reactivity

Question

What is the pH of a 0.0075 M solution of HCl? What is the hydroxide ion concentration of the solution?

Step-by-Step Solution

Answer

The pH is approximately 2.12 and the hydroxide ion concentration is approximately \(1.32 \times 10^{-12}\) M.

Step 1: Identify the Type of Acid

Hydrochloric acid (HCl) is a strong acid, meaning it dissociates completely in water to release hydrogen ions ( H⁺) and chloride ions (Cl⁻).

Step 2: Calculate the Hydronium Ion Concentration

Since HCl dissociates completely, the concentration of hydronium ions ( H₃O⁺) is equal to the concentration of the HCl solution. Thus, the hydronium ion concentration is 0.0075 M.

Step 3: Use the pH Formula

The pH of a solution is calculated using the formula:\[pH = -\log[H₃O⁺]\]Substitute the hydronium ion concentration:\[pH = -\log(0.0075)\]

Step 4: Calculate the pH

Using a calculator, calculate the pH:\[pH = -(-2.124)\approx 2.12\]

Step 5: Use the pOH and pH Relationship

The relationship between pH and pOH at 25°C is given by:\[pH + pOH = 14\]We already know the pH, which is 2.12. Use this to find the pOH:\[pOH = 14 - 2.12 = 11.88\]

Step 6: Calculate the Hydroxide Ion Concentration

To find the hydroxide ion concentration, use the formula:\[[OH⁻] = 10^{-pOH}\]Thus, substituting the pOH value:\[[OH⁻] = 10^{-11.88}\]

Step 7: Calculate [OH⁻] Concentration

Using a calculator, find:\[[OH⁻] \approx 1.32 \times 10^{-12} \text{ M}\]

Key Concepts

Strong Acid

When we talk about an acid being "strong," we refer to its ability to fully dissociate in water. This means that when hydrochloric acid (HCl), a common strong acid, is added to water, it breaks up entirely into hydrogen ions (H⁺) and chloride ions (Cl⁻).
This is an important characteristic because the concentration of hydrogen ions resulting from the dissociation directly impacts the acidity of the solution.

• Strong acids completely ionize in water.
• This complete ionization results in a high concentration of hydrogen ions (H⁺).
• Common examples include HCl, HNO₃, and H₂SO₄.

Knowing an acid's strength helps in understanding its behavior in solutions and during chemical reactions.

Hydronium Ion Concentration

Hydronium ions (H₃O⁺) are formed in solution when hydrogen ions (H⁺) associate with water molecules. Strong acids like HCl dissociate entirely, which means the concentration of HCl in solution is equal to the hydronium ion concentration.

• For example, a 0.0075 M solution of HCl will also have a 0.0075 M concentration of H₃O⁺ ions.
• This straightforward relationship is key in calculating pH, as the hydronium concentration is directly used in the formula \( pH = -\log[H₃O⁺] \).

Once you identify the hydronium ion concentration, determining other properties like pH becomes much easier.

Hydroxide Ion Concentration

Understanding hydroxide ion concentration (OH⁻) is another vital part of analyzing a solution's properties. Although we start with acids, by using the properties of water's ionization, we can determine how much OH⁻ is present.
Using the relationship \( pH + pOH = 14 \) at room temperature, once you find the pH, you can later find the pOH and subsequently calculate [OH⁻].

• For a solution with a pH of 2.12, the pOH would be \( 14 - 2.12 = 11.88 \).
• Then, use \( [OH⁻] = 10^{-pOH} \).

These calculations show that even though a solution might be acidic, there is still some presence of OH⁻, albeit small.

pOH

pOH is a measure similar to pH, but it considers the concentration of hydroxide ions instead of hydronium ions. This concept provides a complete picture of a solution's character by considering its basic nature.
The core equation linking pH and pOH boils down to \( pH + pOH = 14 \). This is particularly helpful when you know one and want to find the other. It works effectively in solutions at 25°C.

• For a given pH, finding pOH is straightforward: just subtract the pH value from 14.
• This interplay shows that a lower pH corresponds to a higher pOH and vice versa.

Understanding the pH and pOH helps effectively describe a solution's acidity or basicity.