Question

Calculate \(\left[\mathrm{OH}^{-}\right], \mathrm{pOH}\) , and pH for each of the following. a. 0.00040\(M \mathrm{Ca}(\mathrm{OH})_{2}\) b. a solution containing 25 \(\mathrm{g}\) KOH per liter c. a solution containing 150.0 \(\mathrm{g}\) NaOH per liter

Short answer

a. \([\mathrm{OH}^−] = 0.00080 \mathrm{M}\), \(pOH = 3.10\), and \(pH = 10.90\) b. \([\mathrm{OH}^−] = 0.000446 \mathrm{M}\), \(pOH = 3.35\), and \(pH = 10.65\) c. \([\mathrm{OH}^−] = 3.750 \mathrm{M}\), \(pOH = -0.57\), and \(pH = 14.57\)

Step-by-step solution

Calculate the concentration of OH⁻ ions in Ca(OH)₂ solution

Since Ca(OH)₂ releases 2 OH⁻ ions, the concentration of OH⁻ ions would be twice of the concentration of Ca(OH)₂. \[ [\mathrm{OH}^-] = 2(0.00040 \mathrm{M}) \] \[ [\mathrm{OH}^-] = 0.00080 \mathrm{M} \]

Calculate pOH

Now we can calculate the pOH using the formula: \[ pOH = -\log_{10} [\mathrm{OH}^-] \] \[ pOH = -\log_{10}(0.00080) \]

Calculate pH

Finally, using the relationship between pH and pOH: \[ pH + pOH = 14 \] \[ pH = 14 - pOH \] b. A solution containing 25 g KOH per liter

Calculate the concentration of KOH

First, we need to find the molecular weight of KOH. \[ \mathrm{KOH} = 39.10 (\mathrm{K}) + 15.99 (\mathrm{O}) + 1.00 (\mathrm{H}) = 56.10 \frac{\mathrm{g}}{\mathrm{mol}} \] Now, we can calculate the concentration of KOH: \[ [\mathrm{KOH}] = \frac{25 \mathrm{g} \space \mathrm{KOH}}{56.10 \frac{\mathrm{g}}{\mathrm{mol}} \cdot 1 \mathrm{L}} \]

Calculate the concentration of OH⁻ ions

Since KOH releases 1 OH⁻ ion, the concentration of OH⁻ ions is equal to the concentration of KOH.

Calculate pOH and pH

Repeat steps 2 and 3 of solution a to find the pOH and pH values for this solution. c. A solution containing 150.0 g NaOH per liter

Calculate the concentration of NaOH

First, we need to find the molecular weight of NaOH. \[ \mathrm{NaOH} = 22.99 (\mathrm{Na}) + 15.99 (\mathrm{O}) + 1.00 (\mathrm{H}) = 40.00 \frac{\mathrm{g}}{\mathrm{mol}} \] Now, we can calculate the concentration of NaOH: \[ [\mathrm{NaOH}] = \frac{150 \mathrm{g} \space \mathrm{NaOH}}{40.00 \frac{\mathrm{g}}{\mathrm{mol}} \cdot 1 \mathrm{L}} \]

Calculate the concentration of OH⁻ ions

Since NaOH releases 1 OH⁻ ion, the concentration of OH⁻ ions is equal to the concentration of NaOH.

Calculate pOH and pH

Repeat steps 2 and 3 of solution a to find the pOH and pH values for this solution.

Key concepts

Acid-Base Chemistry

Welcome to the fascinating world of acid-base chemistry! This branch of chemistry focuses on how acids and bases interact, and it's fundamental to many biological and chemical processes.
Here are a few key points to remember:

• Acids are substances that release hydrogen ions (\( ext{H}^+\)) when dissolved in water.
• Bases are compounds that yield hydroxide ions (\( ext{OH}^-\)) when dissolved in water.
• A solution's acidity or basicity is quantified using \( ext{pH}\), where low values indicate acidity and high values indicate basicity.
• The pH scale ranges from 0 to 14, with 7 being neutral.

Understanding these concepts helps in predicting the behavior of acids and bases in chemical reactions. You'll often see terms like "strong acids" and "strong bases," which refer to their ability to completely ionize in a solution.

Hydroxide Ion Concentration

Now, let's zoom in on hydroxide ion concentration (\([ ext{OH}^-]\)). This is a key player in determining if a solution is acidic, basic, or neutral.
When bases dissolve in water, they create hydroxide ions. The concentration of these ions is crucial because it influences the pH and pOH of the solution.Consider these details regarding hydroxide ion concentration:

• A higher hydroxide ion concentration indicates a more basic solution.
• To find \([ ext{OH}^-]\), you'll calculate the molar concentration of the base and consider how many \( ext{OH}^-\) ions are released per molecule of the base.
• For example, \( ext{Ca(OH)}_2\) offers two \( ext{OH}^-\) ions per formula unit, doubling the concentration of hydroxide ions.

Knowing \([ ext{OH}^-]\) is imperative for calculating both the pOH and pH of a solution.

pOH Calculation

The pOH of a solution is an important measure in chemistry, complementing the pH scale. It lets us understand the basicity of a solution.
To calculate the pOH, you follow this simple formula:

• \[pOH = -\log_{10} [\text{OH}^-]\]

This equation uses the concentration of hydroxide ions to derive pOH.
Because the log function involved, even small changes in \([ ext{OH}^-]\) lead to more significant differences in pOH.

• Low pOH values indicate high basicity, while high pOH values suggest lower basicity.
• Once you have the pOH, you can easily find the pH with \( ext{pH} = 14 - ext{pOH}\).

Accurate pOH calculations help you grasp the solution's characteristics better.

Molar Concentration

The concept of molar concentration is central to chemistry. It describes the number of moles of solute (like a base) per liter of solution.
You often encounter molar concentration when discussing solutions, as it's crucial for calculating other properties, including pH and pOH.

• To compute molar concentration, use this formula:
  • \[[ ext{Concentration}] = \frac{\text{mass of solute (g)}}{\text{molar mass (g/mol)} \times \text{volume of solution (L)}}\]

For example, when you dissolve solid bases like \( ext{KOH}\) or \( ext{NaOH}\) in water, the molar concentration helps assess \([ ext{OH}^-]\) in the solution. This computation is essential for the later calculation of pH and pOH, making molar concentration a key foundational concept in chemistry.

Strong Bases

Strong bases are an important concept in acid-base chemistry. They completely dissociate in water, yielding hydroxide ions and a cation.
In comparison to weak bases, strong bases release more \( ext{OH}^-\) ions, impacting the solution's pH and pOH significantly.

• Common strong bases include \( ext{NaOH}\) (sodium hydroxide), \( ext{KOH}\) (potassium hydroxide), and \( ext{Ca(OH)}_2\) (calcium hydroxide).
• They are characterized by their complete ionization in solution, meaning they fully break apart into ions.
• This results in a high hydroxide ion concentration, making the solution highly basic with a low pOH.

Understanding strong bases helps in predicting the outcome of chemical reactions and designing solutions for industrial processes.