Question

For each pair of concentrations, tell which represents the more basic solution. a. \(\left[\mathrm{H}^{+}\right]=2.02 \times 10^{-7} M\) or \(\left[\mathrm{OH}^{-}\right]=5.05 \times 10^{-5} M\) b. \(\left[\mathrm{H}^{+}\right]=1.79 \times 10^{-5} M\) or \(\left[\mathrm{OH}^{-}\right]=4.21 \times 10^{-6} M\) c. \(\left[\mathrm{H}^{+}\right]=1.25 \times 10^{-12} M\) or \(\left[\mathrm{OH}^{-}\right]=6.51 \times 10^{-3} M\)

Short answer

For each pair, the more basic solution is: a. \(\left[\mathrm{OH}^{-}\right]=5.05 \times 10^{-5} M\) b. \(\left[\mathrm{OH}^{-}\right]=4.21 \times 10^{-6} M\) c. \(\left[\mathrm{OH}^{-}\right]=6.51 \times 10^{-3} M\)

Step-by-step solution

a. Compare concentrations of [H+] and [OH-] in the first pair

We have: \(\left[\mathrm{H}^{+}\right]=2.02 \times 10^{-7} M\) and \(\left[\mathrm{OH}^{-}\right]=5.05 \times 10^{-5} M\)

a. Determine the more basic solution for the first pair

Because the [OH-] concentration is significantly higher than the [H+] concentration in this pair, the solution with \(\left[\mathrm{OH}^{-}\right]=5.05 \times 10^{-5} M\) is more basic.

b. Compare concentrations of [H+] and [OH-] in the second pair

We have: \(\left[\mathrm{H}^{+}\right]=1.79 \times 10^{-5} M\) and \(\left[\mathrm{OH}^{-}\right]=4.21 \times 10^{-6} M\)

b. Determine the more basic solution for the second pair

Because the [OH-] concentration is lower than the [H+] concentration in this pair, the solution with \(\left[\mathrm{OH}^{-}\right]=4.21 \times 10^{-6} M\) is more basic (despite being less concentrated, the solution is still more basic than its counterpart with the higher [H+] concentration).

c. Compare concentrations of [H+] and [OH-] in the third pair

We have: \(\left[\mathrm{H}^{+}\right]=1.25 \times 10^{-12} M\) and \(\left[\mathrm{OH}^{-}\right]=6.51 \times 10^{-3} M\)

c. Determine the more basic solution for the third pair

Because the [OH-] concentration is significantly higher than the [H+] concentration in this pair, the solution with \(\left[\mathrm{OH}^{-}\right]=6.51 \times 10^{-3} M\) is more basic.

Key concepts

pH and pOH

Understanding the concepts of pH and pOH is crucial in acid-base chemistry. These values help us determine how acidic or basic a solution is. The pH scale, which ranges from 0 to 14, measures the hydrogen ion concentration \([H^+]\) in a solution. A pH less than 7 is acidic, 7 is neutral, and more than 7 is basic. The formula to calculate pH is: \[ \text{pH} = -\log_{10} [H^+] \] Conversely, pOH measures the hydroxide ion concentration \([OH^-]\) and follows a similar scale. The formula to calculate pOH is: \[ \text{pOH} = -\log_{10} [OH^-] \] Both pH and pOH are related through the equation: \[ \text{pH} + \text{pOH} = 14 \] This relationship allows us to find either pH or pOH if the concentration of either ion is known. It reflects the inverse nature of hydrogen and hydroxide ions in solutions: as one increases, the other decreases. This dynamic balance is fundamental to understanding the behavior of acids and bases.

Hydrogen Ion Concentration

Hydrogen ion concentration is a key player in determining the acidity of a solution. The symbol \([H^+]\) represents the concentration of hydrogen ions in molarity (M), which is moles per liter. A high \([H^+]\) means more acidic, while a lower concentration indicates a more basic environment. To figure out if a solution is acidic or basic, compare its hydrogen ion concentration to the neutral concentration at 25°C, which is \(1 \times 10^{-7}\) M. Some practical hints to work with hydrogen ions include:

• The smaller the exponent in \([H^+]\), the higher the acidity.
• Common acids, when dissolved, release \([H^+]\) into solutions, causing the pH to drop below 7.

Thus, in comparing hydrogen ion concentrations in different conditions, being able to interpret these values is crucial for assessing whether a solution is more acidic or basic.

Hydroxide Ion Concentration

The concentration of hydroxide ions \([OH^-]\) is the main determinant of the basicity of a solution. A higher \([OH^-]\) concentration signifies a more basic solution. Hydroxide ions are produced when bases dissolve in water. To compare solutions based on their basicity, it's essential to understand:

• Hydroxide ion concentrations exceeding \(1 \times 10^{-7}\) M suggest basicity, as this means a pH higher than 7.
• A larger negative exponent in \([OH^-]\) indicates a lower hydroxide concentration, often linked with acidic solutions.

For practical chemistry problems, comparing the hydroxide ion concentrations can directly point out which solution is more basic, especially when paired with hydrogen ion concentrations to reinforce the results within the pH and pOH context.