Question

Calculate the hydrogen ion concentration and the pH of each of the following solutions of strong acids. a. \(1.4 \times 10^{-3} M \mathrm{HClO}_{4}\) b. \(3.0 \times 10^{-5} M \mathrm{HCl}\) c. \(5.0 \times 10^{-2} M \mathrm{HNO}_{3}\) d. \(0.0010 M \mathrm{HCl}\)

Short answer

a) Hydrogen ion concentration: \(1.4 \times 10^{-3} M\), pH: ≈ 2.85 b) Hydrogen ion concentration: \(3.0 \times 10^{-5} M\), pH: ≈ 4.52 c) Hydrogen ion concentration: \(5.0 \times 10^{-2} M\), pH: ≈ 1.30 d) Hydrogen ion concentration: \(0.0010 M\), pH: ≈ 3.00

Step-by-step solution

Find the hydrogen ion concentration

Since this is a strong acid, the hydrogen ion concentration can be found directly from the molarity of the acid: [H+] = \(1.4 \times 10^{-3} M\)

Calculate the pH

Using the pH formula: pH = -log10(\(1.4 \times 10^{-3}\)) pH ≈ 2.85 #Solution#a: Hydrogen ion concentration: \(1.4 \times 10^{-3} M\) pH: ≈ 2.85 b. \(3.0 \times 10^{-5} M \mathrm{HCl}\)

Find the hydrogen ion concentration

Since this is a strong acid, the hydrogen ion concentration can be found directly from the molarity of the acid: [H+] = \(3.0 \times 10^{-5} M\)

Calculate the pH

Using the pH formula: pH = -log10(\(3.0 \times 10^{-5}\)) pH ≈ 4.52 #Solution#b: Hydrogen ion concentration: \(3.0 \times 10^{-5} M\) pH: ≈ 4.52 c. \(5.0 \times 10^{-2} M \mathrm{HNO}_{3}\)

Find the hydrogen ion concentration

Since this is a strong acid, the hydrogen ion concentration can be found directly from the molarity of the acid: [H+] = \(5.0 \times 10^{-2} M\)

Calculate the pH

Using the pH formula: pH = -log10(\(5.0 \times 10^{-2}\)) pH ≈ 1.30 #Solution#c: Hydrogen ion concentration: \(5.0 \times 10^{-2} M\) pH: ≈ 1.30 d. \(0.0010 M \mathrm{HCl}\)

Find the hydrogen ion concentration

Since this is a strong acid, the hydrogen ion concentration can be found directly from the molarity of the acid: [H+] = \(0.0010 M\)

Calculate the pH

Using the pH formula: pH = -log10(\(0.0010\)) pH ≈ 3.00 #Solution#d: Hydrogen ion concentration: \(0.0010 M\) pH: ≈ 3.00

Key concepts

Hydrogen Ion Concentration

When we're talking about hydrogen ion concentration, we're essentially looking at how many hydrogen ions are present within a solution. This is a critical piece to determining the acidity of the solution. In the context of strong acids, which completely dissociate in water, the hydrogen ion concentration is equivalent to the molarity of the acid. That means if you have a molarity of, say, 0.0010 M, the concentration of hydrogen ions, [H⁺], is exactly 0.0010 M.

To understand concepts like pH, it's essential to know that the higher the concentration of hydrogen ions, the more acidic, and thus the lower the pH of the solution.

**Key Points:**

• Hydrogen ion concentration is key in acidity determination.
• For strong acids, [H⁺] aligns directly with the molarity of the acid.
• Greater hydrogen ion concentration equates to lower pH.

Strong Acids

Strong acids are quite significant when learning about hydrogen ion concentration and pH because they dissociate fully in water. This means every molecule of the acid releases its hydrogen ion into the solution.

Some common examples of strong acids include hydrochloric acid (HCl), nitric acid (HNO₃), and perchloric acid (HClO₄). Because strong acids dissociate fully, calculating their [H⁺] is straightforward and simply based on their molarity, making them convenient for acid-base calculations.

**Key Points:**

• Strong acids completely dissociate in solution.
• [H⁺] in a strong acid solution equals the acid's molarity.
• Examples include HCl, HNO₃, HClO₄.

Molarity

Molarity is a way of expressing concentration, specifically the number of moles of a solute per liter of solution. When dealing with acids and bases, molarity is fundamental as it directly impacts calculations of hydrogen ion concentrations and pH.

For example, if you have a solution with a molarity of 0.0010 M of HCl, then every liter of that solution contains 0.0010 moles of hydrogen ions, since HCl is a strong acid and dissociates completely. This makes it easy to determine pH and other properties of the solution.

**Key Points:**

• Molarity defines concentration as moles per liter.
• It is crucial for calculating properties like hydrogen ion concentration.
• In a strong acid solution, [H⁺] is simply the molarity of the acid.

Logarithmic Calculations

Calculating pH involves logarithmic mathematics, which can initially seem complex, but it's generally quite straightforward. pH is defined as the negative logarithm (base 10) of the hydrogen ion concentration: \[pH = -\log_{10}{[H^+]}\]This means if you know the [H⁺], you can easily find the pH by plugging it into this formula. Using a calculator to find the logarithm is typically necessary unless you're dealing with powers of ten.

Example: For a solution with [H⁺] = 1.0 x 10⁻³ M, the pH would be \[pH = -\log_{10}(1.0 \times 10^{-3}) = 3.00\]**Key Points:**

• pH calculation relies on taking the negative log of [H⁺].
• Use a calculator for Logarithmic calculations unless the value is a power of ten.
• The formula simplifies the process of determining acidity levels.