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Chapter 16: Problem 36

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

Expert verified
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

01

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

We have: \(\left[\mathrm{H}^{+}\right]=2.02 \times 10^{-7} M\) and \(\left[\mathrm{OH}^{-}\right]=5.05 \times 10^{-5} M\)
02

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.
03

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

We have: \(\left[\mathrm{H}^{+}\right]=1.79 \times 10^{-5} M\) and \(\left[\mathrm{OH}^{-}\right]=4.21 \times 10^{-6} M\)
04

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).
05

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

We have: \(\left[\mathrm{H}^{+}\right]=1.25 \times 10^{-12} M\) and \(\left[\mathrm{OH}^{-}\right]=6.51 \times 10^{-3} M\)
06

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.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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掳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.

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Most popular questions from this chapter

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. \(\left[\mathrm{H}^{+}\right]=8.44 \times 10^{-6} M\)

Which of the following do \(n o t\) represent a conjugate acid-base pair? For those pairs that are not conjugate acid-base pairs, write the correct conjugate acid-base pair for each species in the pair. a. \(\mathrm{H}_{2} \mathrm{SO}_{4}, \mathrm{SO}_{4}^{2-}\) b. \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}, \mathrm{HPO}_{4}^{2-}\) c. \(\mathrm{HClO}_{4}, \mathrm{Cl}^{-}\) d. \(\mathrm{NH}_{4}^{+}, \mathrm{NH}_{2}^{-}\)

Anions containing hydrogen (for example, \(\mathrm{HCO}_{3}^{-}\) and \(\mathrm{H}_{2} \mathrm{PO}_{4}^{2-}\) ) show amphoteric behavior when reacting with other acids or bases. Write equations illustrating the amphoterism of these anions.

Which of the following do not represent a conjugate acid-base pair? For those pairs that are not conjugate acid-base pairs, write the correct conjugate acid-base pair for each species in the pair. a. HI \(, \mathrm{I}^{-}\) b. \(\mathrm{HClO}, \mathrm{HClO}_{2}\) c. \(\mathrm{H}_{3} \mathrm{PO}_{4}, \mathrm{PO}_{4}^{3-}\) d. \(\mathrm{H}_{2} \mathrm{CO}_{3}, \mathrm{CO}_{3}^{2-}\)

Calculate the hydrogen ion concentration, in moles per liter, for solutions with each of the following \(\mathrm{pH}\) or pOH values. a. \(\mathrm{pOH}=0.90\) b. \(\mathrm{pH}=0.90\) c. \(\mathrm{pOH}=10.3\) d. \(\mathrm{pH}=5.33\)
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