Problem 46 - Chemistry An Atoms First Approach

Question

Calculate the \(\left[\mathrm{H}^{+}\right]\) of each of the following solutions at \(25^{\circ} \mathrm{C}\) Identify each solution as neutral, acidic, or basic. a. \(\left[\mathrm{OH}^{-}\right]=1.5 \mathrm{M}\) b. \(\left[\mathrm{OH}^{-}\right]=3.6 \times 10^{-15} \mathrm{M}\) c. \(\left[\mathrm{OH}^{-}\right]=1.0 \times 10^{-7} \mathrm{M}\) d. \(\left[\mathrm{OH}^{-}\right]=7.3 \times 10^{-4} \mathrm{M}\)

Step-by-Step Solution

Answer

The $\left[\mathrm{H}^{+}\right]$ concentrations for each solution are as follows: a. $\left[\mathrm{H}^{+}\right] = 6.67 \times 10^{-15}\ \mathrm{M}$, basic. b. $\left[\mathrm{H}^{+}\right] = 2.78 \times 10^{-9}\ \mathrm{M}$, acidic. c. $\left[\mathrm{H}^{+}\right] = 1.0 \times 10^{-7}\ \mathrm{M}$, neutral. d. $\left[\mathrm{H}^{+}\right] = 1.37 \times 10^{-12}\ \mathrm{M}$, basic.

Step 1: Calculate the concentration of H⁺ ions

Using the ion product of water, \(K_w = [\mathrm{H}^{+}][\mathrm{OH}^-]\) \([\mathrm{H}^{+}] = \frac{K_w}{[\mathrm{OH}^-]}\) Plug in the values: \([\mathrm{H}^{+}] = \frac{1.0 \times 10^{-14}}{1.5}\) \([\mathrm{H}^{+}] = 6.67 \times 10^{-15}\ \mathrm{M}\)

Step 2: Determine if the solution is neutral, acidic, or basic

Since the H⁺ ion concentration is less than the OH⁻ ion concentration, the solution is basic. b. \(\left[\mathrm{OH}^{-}\right]=3.6 \times 10^{-15} \mathrm{M}\)

Step 1: Calculate the concentration of H⁺ ions

Using the ion product of water, \([\mathrm{H}^{+}] = \frac{K_w}{[\mathrm{OH}^-]}\) Plug in the values: \([\mathrm{H}^{+}] = \frac{1.0 \times 10^{-14}}{3.6 \times 10^{-15}}\) \([\mathrm{H}^{+}] = 2.78 \times 10^{-9}\ \mathrm{M}\)

Step 2: Determine if the solution is neutral, acidic, or basic

Since the H⁺ ion concentration is greater than the OH⁻ ion concentration, the solution is acidic. c. \(\left[\mathrm{OH}^{-}\right]=1.0 \times 10^{-7} \mathrm{M}\)

Step 1: Calculate the concentration of H⁺ ions

Using the ion product of water, \([\mathrm{H}^{+}] = \frac{K_w}{[\mathrm{OH}^-]}\) Plug in the values: \([\mathrm{H}^{+}] = \frac{1.0 \times 10^{-14}}{1.0 \times 10^{-7}}\) \([\mathrm{H}^{+}] = 1.0 \times 10^{-7}\ \mathrm{M}\)

Step 2: Determine if the solution is neutral, acidic, or basic

Since the H⁺ ion concentration is equal to the OH⁻ ion concentration, the solution is neutral. d. \(\left[\mathrm{OH}^{-}\right]=7.3 \times 10^{-4} \mathrm{M}\)

Step 1: Calculate the concentration of H⁺ ions

Using the ion product of water, \([\mathrm{H}^{+}] = \frac{K_w}{[\mathrm{OH}^-]}\) Plug in the values: \([\mathrm{H}^{+}] = \frac{1.0 \times 10^{-14}}{7.3 \times 10^{-4}}\) \([\mathrm{H}^{+}] = 1.37 \times 10^{-12}\ \mathrm{M}\)

Step 2: Determine if the solution is neutral, acidic, or basic

Since the H⁺ ion concentration is less than the OH⁻ ion concentration, the solution is basic.

Key Concepts

Ion Product of Water

The ion product of water (\(K_w\)) is an essential concept in chemistry that helps us understand the balance between hydrogen ions (H⁺) and hydroxide ions (OH⁻) in water. At 25°C, the product of their concentrations is always \(1.0 \times 10^{-14}\). This relationship is expressed with the formula:

• \[K_w = [\mathrm{H}^{+}][\mathrm{OH}^-]\]

What this means is that if you know the concentration of one type of ion, you can easily calculate the concentration of the other ion.
For instance, when you know the \([\mathrm{OH}^-]\) concentration, you can rearrange the equation to \([\mathrm{H}^{+}] = \frac{K_w}{[\mathrm{OH}^-]}\) to find \([\mathrm{H}^{+}]\).This relationship is a powerful tool in determining the nature of a solution—whether it is acidic, neutral, or basic.

Acids and Bases

Acids and bases are two types of substances with distinct properties.
Acids are characterized by an increase in hydrogen ions \([\mathrm{H}^{+}]\) in a solution, while bases reduce them by providing hydroxide ions \([\mathrm{OH}^-]\).
In a neutral solution like pure water, both ion concentrations are equal, each being \(1.0 \times 10^{-7}\) M at 25°C.

• **Acidic Solution**: Occurs when \([\mathrm{H}^{+}] > [\mathrm{OH}^-]\).
• **Basic Solution**: Occurs when \([\mathrm{H}^{+}] < [\mathrm{OH}^-]\).
• **Neutral Solution**: Occurs when \([\mathrm{H}^{+}] = [\mathrm{OH}^-]\).

In an acidic solution, the excess \([\mathrm{H}^{+}]\) ions make the solution have a sour taste and a low pH.
In a basic solution, there's an abundance of \([\mathrm{OH}^-]\), which can make the solution taste bitter and feel slippery.Identifying whether a solution is acidic, basic, or neutral is crucial in chemical reactions and everyday applications, such as cooking and cleaning.

pH and pOH

The pH and pOH are scales used to specify how acidic or basic a solution is.
These scales provide a more convenient way to express ion concentrations, which can vary greatly from one solution to another.
The pH scale ranges from 0 to 14. A pH less than 7 indicates an acidic solution, while a pH greater than 7 indicates a basic solution. A pH of exactly 7 means the solution is neutral.

pH Calculation

To calculate the pH of a solution, you can use the following formula:

• \[\text{pH} = -\log_{10}[\mathrm{H}^{+}]\]

Using this formula helps find out how many hydrogen ions are in a solution. Similarly, pOH can be calculated via:

• \[\text{pOH} = -\log_{10}[\mathrm{OH}^-]\]

Importantly, there is a relationship between pH and pOH:\[\text{pH} + \text{pOH} = 14\]
Understanding these concepts is crucial for everyone studying chemistry since they give insight into the solution's characteristics based on the hydrogen and hydroxide ions present.