Problem 11 - Chemistry and Chemical Reactivity

Question

What is the \(\mathrm{pH}\) of a \(0.0075 \mathrm{M}\) solution of HCl? What is the hydroxide ion concentration of the solution?

Step-by-Step Solution

Answer

The pH of the solution is 2.12, and the hydroxide ion concentration is \(1.33 \times 10^{-12} \text{ M}\).

Step 1: Understanding the Problem

We have a 0.0075 M solution of HCl. Since HCl is a strong acid, it completely dissociates in water. Therefore, the concentration of hydrogen ions, \([H^+]\), will be equal to the concentration of HCl.

Step 2: Calculate \\( ext{pH} \\\)

The \( ext{pH}\) of a solution is calculated using the equation: \[ ext{pH} = - ext{log}[H^+] \] where \([H^+] = 0.0075\). Thus, \( ext{pH} = - ext{log}(0.0075) \). Use a calculator to find \( ext{pH}\).

Step 3: Calculate the Hydroxide Ion Concentration

We use the formula \[ [OH^-] = rac{K_w}{[H^+]} \] where \( K_w \) is the ion-product constant of water, \( 1.0 imes 10^{-14} \). Substitute \( [H^+] = 0.0075 \) into the equation: \[ [OH^-] = rac{1.0 imes 10^{-14}}{0.0075} \] and calculate \( [OH^-] \).

Step 4: Interpretation of Results

Once calculated, the \( ext{pH} \) indicates the acidity of the solution, and the \( [OH^-] \) shows the concentration of hydroxide ions, which should be very low due to the acidic nature of the solution.

Key Concepts

Strong Acids

Strong acids are a fundamental concept in chemistry. Unlike weak acids, they completely dissociate in water. This means they break down entirely into their ions. For example, when hydrochloric acid (HCl) is dissolved in water, it separates completely into hydrogen ions \([H^+]\) and chloride ions \([Cl^-]\).
- **Complete dissociation** is the key aspect that defines strong acids. - This property leads to a simple relationship between the acid concentration and the concentration of hydrogen ions.
Since the dissociation is 100%, in a solution of HCl with a concentration of 0.0075 M, the concentration of hydrogen ions is also 0.0075 M.

Dissociation in Water

The concept of dissociation in water is vital to understanding acid and base chemistry. When substances like strong acids or bases dissolve, they dissociate into separate ions and allow for reactions to occur.

**Water molecules** play a crucial role. They help separate the ions due to their polar nature. This means each water molecule has a slight positive and negative side, aiding in dissociation.
For strong acids:

• This process occurs immediately and completely, creating a high concentration of ions, like in our example with HCl.

For other substances like weak acids or weak bases, dissociation is partial. The extent of dissociation affects properties like pH.

Ion-Product Constant

The ion-product constant of water \( K_w \) is a fundamental constant in aqueous chemistry. It represents the product of the concentrations of hydrogen ions \([H^+]\) and hydroxide ions \([OH^-]\), and is always equal to \(1.0 \times 10^{-14}\) at 25°C.This constant helps us understand the balance in neutral water where both ions have equal concentrations \([H^+] = [OH^-]\).

When you dissolve an acid like HCl in water:

• The concentration of hydrogen ions increases significantly, shifting the balance.
• The increase in \([H^+]\) is mirrored by a decrease in \([OH^-]\), due to this constant relationship.

Understanding \( K_w \) allows us to find the hydroxide ion concentration in an acidic solution, which is crucial for tasks like calculating pH or performing titrations.

Hydroxide Ion Concentration

The hydroxide ion concentration \([OH^-]\) is an essential measure in any solution involving acids and bases. In the context of an acidic solution, it tells us how few hydroxide ions are present due to the dominance of hydrogen ions.In our HCl solution, we use the equation \([OH^-] = \frac{K_w}{[H^+]}\) to calculate \([OH^-]\) given the high presence of \([H^+]\). Since our \([H^+]\) is 0.0075 M, which is significantly high in comparison:

• \([OH^-] = \frac{1.0 \times 10^{-14}}{0.0075 M} = 1.33 \times 10^{-12} M\)
• This low \([OH^-]\) reflects the acidic nature of the solution, leading to a low pH and confirming the acidic environment.

Understanding this concentration helps in comprehending the complete picture of how acids and bases interact in solutions.