Question

Calculate the pH corresponding to each of the following hydrogen ion concentrations, and indicate whether each solution is acidic, basic, or neutral. a. \(\left[\mathrm{H}^{+}\right]=0.00512 M\) b. \(\left[\mathrm{H}^{+}\right]=3.76 \times 10^{-5} M\) c. \(\left[\mathrm{H}^{+}\right]=5.61 \times 10^{-10} M\) d. \(\left[\mathrm{H}^{+}\right]=8.44 \times 10^{-6} M\)

Short answer

a. The pH for \(\left[\mathrm{H}^{+}\right]=0.00512\, M\) is approximately 2.29, which means the solution is acidic. b. The pH for \(\left[\mathrm{H}^{+}\right]=3.76 \times 10^{-5}\, M\) is approximately 4.42, which means the solution is acidic. c. The pH for \(\left[\mathrm{H}^{+}\right]=5.61 \times 10^{-10}\, M\) is approximately 9.25, which means the solution is basic. d. The pH for \(\left[\mathrm{H}^{+}\right]=8.44 \times 10^{-6}\, M\) is approximately 5.07, which means the solution is acidic.

Step-by-step solution

Use the formula: \(pH = -\log[\mathrm{H}^+]\) \(pH = -\log(0.00512)\) Now, calculate the pH: \(pH \approx 2.29\) #b. Determine if the solution is acidic, basic, or neutral#

Since the pH is less than 7, the solution is acidic. #c. Calculate pH for \(\left[\mathrm{H}^{+}\right]=3.76 \times 10^{-5}\, M\)#

Use the formula: \(pH = -\log[\mathrm{H}^+]\) \(pH = -\log(3.76 \times 10^{-5})\) Now, calculate the pH: \(pH \approx 4.42\) #d. Determine if the solution is acidic, basic, or neutral#

Since the pH is less than 7, the solution is acidic. #e. Calculate pH for \(\left[\mathrm{H}^{+}\right]=5.61 \times 10^{-10}\, M\)#

Use the formula: \(pH = -\log[\mathrm{H}^+]\) \(pH = -\log(5.61 \times 10^{-10})\) Now, calculate the pH: \(pH \approx 9.25\) #f. Determine if the solution is acidic, basic, or neutral#

Since the pH is greater than 7, the solution is basic. #g. Calculate pH for \(\left[\mathrm{H}^{+}\right]=8.44 \times 10^{-6}\, M\)#

Use the formula: \(pH = -\log[\mathrm{H}^+]\) \(pH = -\log(8.44 \times 10^{-6})\) Now, calculate the pH: \(pH \approx 5.07\) #h. Determine if the solution is acidic, basic, or neutral#

Since the pH is less than 7, the solution is acidic.

Key concepts

Understanding Hydrogen Ion Concentration

Hydrogen ion concentration, represented by \([\mathrm{H}^+]\), is the number of hydrogen ions present in a solution. This concentration determines how acidic or basic a solution is. The greater the number of hydrogen ions, the more acidic the solution.

When you see concentrations written as \(M\) (molarity), it tells you how many moles of hydrogen ions are in one liter of solution. For example, a concentration of \[0.00512 \, M\] means there are 0.00512 moles of hydrogen ions per liter.

Hydrogen ion concentration is a key factor in calculating pH. It provides the numerical value needed to find the pH. It's the starting point for determining if a solution is acidic, neutral, or basic.

Classifying Solutions as Acidic, Basic, or Neutral

A solution's pH determines if it is acidic, neutral, or basic. The pH scale ranges from 0 to 14.

Here's a simple breakdown:

• pH less than 7 - The solution is acidic. It has more hydrogen ions than hydroxide ions.
• pH equal to 7 - The solution is neutral. This means an equal amount of hydrogen ions and hydroxide ions, like pure water.
• pH greater than 7 - The solution is basic. There are more hydroxide ions than hydrogen ions.

To determine the nature of a solution, just look at its pH value. If it’s less than 7, it’s acidic; if it’s more than 7, it’s basic. Neutral solutions hover right at 7.

Role of Logarithmic Functions in Chemistry

Logarithmic functions play a vital role in chemistry, especially in pH calculations. The pH of a solution is determined using a logarithmic function: \(pH = -\log[\mathrm{H}^+]\).

The function uses the negative logarithm because it allows for a more manageable range of numbers. Hydrogen ion concentrations vary widely, but their corresponding pH values are compressed into a convenient scale from 0 to 14.

Logarithms help translate exponential growth or decay into a linear scale, making it easier to understand changes in hydrogen ion concentration. A small change in \[pH\] can indicate a large change in ion concentration. This highlights the importance of accurately using logarithms in determining how acidic or basic a solution is.