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Calculate the \(\left[\mathrm{H}^{+}\right]\) in each of the following solutions, and indicate whether the solution is acidic or basic. a. \(\left[\mathrm{OH}^{-}\right]=5.99 \times 10^{-8} \mathrm{M}\) b. \(\left[\mathrm{OH}^{-}\right]=8.99 \times 10^{-6} \mathrm{M}\) c. \(\left[\mathrm{OH}^{-}\right]=7.00 \times 10^{-7} \mathrm{M}\) d. \(\left[\mathrm{OH}^{-}\right]=1.43 \times 10^{-12} \mathrm{M}\)

Short Answer

Expert verified
a. [H+] = \(1.67 \times 10^{-7} \mathrm{M}\), basic b. [H+] = \(1.11 \times 10^{-9} \mathrm{M}\), basic c. [H+] = \(1.43 \times 10^{-8} \mathrm{M}\), basic d. [H+] = \(6.99 \times 10^{-3} \mathrm{M}\), acidic

Step by step solution

01

Calculate [H+] for the first solution

Since we know the [OH-] is 5.99 × 10^(-8) M, we can find [H+] using the equation \[ [H^{+}] = \frac{K_w}{[OH^{-}]} = \frac{1.0 \times 10^{-14}}{5.99 \times 10^{-8} M} \]
02

Evaluate [H+]

The [H+] in the solution is calculated as: \[ [H^{+}] = 1.67 \times 10^{-7} \mathrm{M} \]
03

Determine the nature of the solution

Since [H+] < [OH-], the solution is basic. b:
04

Calculate [H+] for the second solution

Since we know the [OH-] is 8.99 × 10^(-6) M, we can find [H+] using the equation \[ [H^{+}] = \frac{K_w}{[OH^{-}]} = \frac{1.0 \times 10^{-14}}{8.99 \times 10^{-6} M} \]
05

Evaluate [H+]

The [H+] in the solution is calculated as: \[ [H^{+}] = 1.11 \times 10^{-9} \mathrm{M} \]
06

Determine the nature of the solution

Since [H+] < [OH-], the solution is basic. c:
07

Calculate [H+] for the third solution

Since we know the [OH-] is 7.00 × 10^(-7) M, we can find [H+] using the equation \[ [H^{+}] = \frac{K_w}{[OH^{-}]} = \frac{1.0 \times 10^{-14}}{7.00 \times 10^{-7} M} \]
08

Evaluate [H+]

The [H+] in the solution is calculated as: \[ [H^{+}] = 1.43 \times 10^{-8} \mathrm{M} \]
09

Determine the nature of the solution

Since [H+] < [OH-], the solution is basic. d:
10

Calculate [H+] for the fourth solution

Since we know the [OH-] is 1.43 × 10^(-12) M, we can find [H+] using the equation \[ [H^{+}] = \frac{K_w}{[OH^{-}]} = \frac{1.0 \times 10^{-14}}{1.43 \times 10^{-12} M} \]
11

Evaluate [H+]

The [H+] in the solution is calculated as: \[ [H^{+}] = 6.99 \times 10^{-3} \mathrm{M} \]
12

Determine the nature of the solution

Since [H+] > [OH-], the solution is acidic.

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Key Concepts

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

Understanding Hydronium Ion Concentration
The hydronium ion concentration, often written as \([H^+]\), plays a critical role in describing the acidity of a solution. When an acid dissolves in water, it increases the concentration of these hydrogen ions, often leading to the formation of hydronium ions \((H_3O^+)\). High concentrations of \([H^+]\) mean the solution is acidic, whereas low concentrations indicate a basic or alkaline solution. To calculate \([H^+]\), we often use the ion-product of water \( (K_w) \), which relates the concentrations of hydrogen ions and hydroxide ions \([OH^-]\) in water. We can find \([H^+]\) using the equation: \[ [H^+] = \frac{K_w}{[OH^-]} \] where \((K_w)\) is a constant \((1.0 \times 10^{-14})\) at 25°C. This relationship allows us to determine the acidity of the solution if the hydroxide concentration is known.
Determining Solution Acidity
Solution acidity refers to whether a solution is acidic, neutral, or basic, depending on the concentration of hydrogen ions \([H^+]\). A solution becomes more acidic as the concentration of \([H^+]\) rises and more basic as the concentration of \([OH^-]\) rises. For instance, a neutral solution at 25°C has equal \([H^+]\) and \([OH^-]\) of \(1.0 \times 10^{-7} M\). If \([H^+]\) exceeds \([OH^-]\), the solution is acidic, while if \([H^+]\) is less, it is basic.
  • If \([H^+] > [OH^-]\), the solution is acidic.
  • If \([H^+] = [OH^-]\), the solution is neutral.
  • If \([H^+] < [OH^-]\), the solution is basic.
In practical applications, this information helps identify products' uses in various industrial processes, laboratory settings, and even natural environments.
The Ion Product of Water (K_w)
The ion product of water \(K_w\) is a fundamental concept in understanding acid-base equilibrium. It represents the product of the molar concentrations of hydrogen ions \([H^+]\) and hydroxide ions \([OH^-]\) in water. At a given temperature (25°C), \(K_w\) equals \(1.0 \times 10^{-14}\). So, \[K_w = [H^+][OH^-]\]. This relationship means that if you know either the \([H^+]\) or \([OH^-]\), you can determine the other. For example, if \([OH^-]\) is given, \([H^+]\) can be calculated by rearranging the equation to: \[ [H^+] = \frac{K_w}{[OH^-]} \]. This balance is crucial for maintaining the proper pH in various scientific applications and is an essential part of water's self-ionization process. Understanding \(K_w\) enables scientists and students alike to predict how changes in ion concentrations affect the overall pH of the solution.

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