Question

That is the \(\mathrm{pH}\) of a solution that has an \(\mathrm{H}^{+}\)concentration of a. \(1.75 \times 10^{-5} \mathrm{~mol} / \mathrm{L}\); b. \(6.50 \times 10^{-10} \mathrm{~mol} / \mathrm{L}\); c. \(1.0 \times 10^{-4} \mathrm{~mol} / \mathrm{L}\); d. \(1.50 \times 10^{-5} \mathrm{~mol} / \mathrm{L}\) ?

Short answer

a. pH ≈ 4.76; b. pH ≈ 9.19; c. pH = 4.00; d. pH ≈ 4.82.

Step-by-step solution

Understanding pH Calculation

The pH of a solution is calculated using the formula \( \mathrm{pH} = -\log_{10}[\mathrm{H}^{+}] \), where \([\mathrm{H}^{+}]\) is the concentration of hydrogen ions in moles per liter. This formula indicates that pH is the negative logarithm (base 10) of the \([\mathrm{H}^{+}]\) concentration.

Calculate pH for Case A

Using the given concentration for case (a): \(1.75 \times 10^{-5} \mathrm{~mol} / \mathrm{L}\), we apply the formula: \( \mathrm{pH} = -\log_{10}(1.75 \times 10^{-5}) \). Calculating, we find \( \mathrm{pH} \approx 4.76 \).

Calculate pH for Case B

For case (b) with \([\mathrm{H}^{+}] = 6.50 \times 10^{-10} \mathrm{~mol} / \mathrm{L}\), the calculation is \( \mathrm{pH} = -\log_{10}(6.50 \times 10^{-10}) \). This results in \( \mathrm{pH} \approx 9.19 \).

Calculate pH for Case C

For case (c), we use \([\mathrm{H}^{+}] = 1.0 \times 10^{-4} \mathrm{~mol} / \mathrm{L}\). The pH is calculated as \( \mathrm{pH} = -\log_{10}(1.0 \times 10^{-4}) \), which simplifies to \( \mathrm{pH} = 4.00 \).

Calculate pH for Case D

In case (d), with \([\mathrm{H}^{+}] = 1.50 \times 10^{-5} \mathrm{~mol} / \mathrm{L}\), apply the formula: \( \mathrm{pH} = -\log_{10}(1.50 \times 10^{-5}) \). The pH value is \( \mathrm{pH} \approx 4.82 \).

Key concepts

Understanding Hydrogen Ion Concentration

The concentration of hydrogen ions (B[ {H}^{+} ] ) in a solution is a fundamental aspect when it comes to calculating the pH. This concentration indicates how many moles of hydrogen ions are present in one liter of solution.

• A higher {H}^{+} concentration means a more acidic solution.
• Conversely, a lower {H}^{+} concentration indicates a more basic (alkaline) solution.

Measuring this is pivotal in acid-base chemistry because the nature and strength of the solution—whether acidic, neutral, or basic—can be understood through it. Remember, the concentration is usually given in scientific notation for precision and ease, such as {6.50 imes 10^{-10} ext{ mol/L} }.
It is important to handle these small numbers carefully during calculations as they greatly affect the pH value.

Logarithmic Scale and pH Calculation

The pH scale is a logarithmic scale used to measure the acidity or basicity of a solution. Unlike a linear scale, a logarithmic scale captures more detail by expanding small ranges at lower values. The formula for calculating pH, [ ext{pH} = - ext{log}_{10}[ ext{H}^{+}] ], demonstrates this principle.

• A change of one unit on the pH scale reflects a tenfold change in {H}^{+} concentration. Hence, even a small shift in pH can imply a significant change in acidity.
• The negative sign in the formula indicates that increasing {H}^{+} concentration lowers the pH, marking enhanced acidity.

Understanding the logarithmic nature of the pH scale helps us interpret solutions more accurately. A subtle change in pH might mean a substantial shift in the nature of the solution's acidity or basicity. Thus, when you see a pH of 4.76, like in case A, remember, this reflects much more than just a numerical change.

Insights into Acid-Base Chemistry

Acid-base chemistry explores the reactions and properties of acids and bases, providing critical insights into the pH behavior in solutions. When talking about acids and bases, we usually refer to their ability to donate or accept hydrogen ions, respectively.

• An acidic solution ( ext{pH} < 7 ) contains a higher concentration of {H}^{+} ions than a neutral solution.
• The neutral value of pH is 7, which typically indicates the presence of pure water.
• On the other hand, a basic solution ( ext{pH} > 7 ) is characterized by a lower concentration of {H}^{+} ions.

In practical scenarios, knowing the pH helps in numerous applications such as medicine, agriculture, and environmental science. Accurately calculating pH from {H}^{+} concentration allows chemists and scientists to make well-informed decisions regarding the suitability of a solution for a particular purpose.