Question

Calculate the number of moles of \(\mathrm{KOH}\) in \(5.50 \mathrm{~mL}\) of a \(0.360 \mathrm{M} \mathrm{KOH}\) solution. What is the \(\mathrm{pOH}\) of the solution at \(25^{\circ} \mathrm{C} ?\)

Short answer

0.00198 moles of KOH; pOH is approximately 0.444.

Step-by-step solution

Identify Given Values

First, we need to identify all the given values from the problem. We have a potassium hydroxide (KOH) solution with a concentration of \(0.360 \text{ M}\) and a volume of \(5.50 \text{ mL}\). We also know that the temperature is \(25^{\circ} \text{C}\).

Convert mL to L

Since molarity is expressed in moles per liter, first convert the volume from milliliters to liters. The volume in liters is \(5.50 \text{ mL} \times \frac{1 \text{ L}}{1000 \text{ mL}} = 0.00550 \text{ L}\).

Calculate Moles of KOH

Use the molarity formula, \(M = \frac{n}{V}\), where \(n\) is the number of moles and \(V\) is the volume in liters. Rearrange to find \(n\): \[n = M \times V = 0.360 \text{ M} \times 0.00550 \text{ L} = 0.00198 \text{ moles of KOH}\]

Calculate pOH of the Solution

Potassium hydroxide is a strong base, so it dissociates completely in water. Therefore, the concentration of OH\(^-\) ions is equal to the concentration of KOH, which is \(0.360 \text{ M}\). Use the formula \(\text{pOH} = -\log[\text{OH}^-]\): \[\text{pOH} = -\log(0.360) \approx 0.444\]

Key concepts

Molarity

Molarity is a common way to express the concentration of a solution. It measures the number of moles of solute (the substance dissolved) per liter of solution. In formulaic terms, it is represented as:

• \( M = \frac{n}{V} \)

Where \( M \) is molarity, \( n \) is the number of moles, and \( V \) is the volume of the solution in liters.
To calculate the number of moles in a solution given molarity, you can rearrange this formula to solve for \( n \):

• \( n = M \times V \)

This relationship is crucial when you want to determine how much of a certain substance is present in a given volume of solution. It provides a straightforward way to quantify the amount of chemical substance in reactions, helping in stoichiometric calculations.

Concentration

The term concentration describes how much of a substance is contained within a certain volume of solution. There are several ways to express concentration, but molarity is one of the most important in chemistry. This is because it directly relates the quantity of solute to the volume of the solution.

• Higher concentration means more solute particles are packed into the same volume, making reactions faster due to increased particle interactions.
• In our context, we talk about potassium hydroxide (KOH) in water.

Understanding concentration is essential for predicting how substances will react in solution. For instance, the reaction rate, the extent of reaction, and other properties can change significantly with different concentrations.

pOH

pOH is a measure of the basicity, or alkalinity, of a solution. It is similar to pH, which measures acidity, but instead focuses on the concentration of hydroxide ions \( \text{OH}^- \) in the solution. The formula used is:

• \( \text{pOH} = -\log[\text{OH}^-] \)

This logarithmic scale means that as the concentration of hydroxide ions increases, the pOH value decreases. Conversely, a low concentration of \( \text{OH}^- \) ions results in a higher pOH value.
As a strong base, potassium hydroxide fully dissociates in solution, meaning the hydroxide ion concentration directly equals the molarity of the KOH solution. Calculating pOH from a known concentration helps chemists understand how alkaline a solution is, which is crucial for processes that depend on a specific pH or pOH environment.

Potassium Hydroxide

Potassium hydroxide, often abbreviated as KOH, is a common strong base used in various industrial and laboratory settings. Being a strong base means it dissociates completely in water to produce hydroxide ions:

• \( \text{KOH} \rightarrow \text{K}^+ + \text{OH}^- \)

This property makes KOH a popular choice for saponification of fats (making soap) and as a reagent in chemistry. In solutions, the concentration of KOH gives us the concentration of hydroxide ions directly, facilitating the calculation of pOH.
KOH's complete dissociation is particularly significant because it directly influences the solution's properties.

• Increased hydroxide ion concentration leads to a decrease in pOH, effectively making the solution more basic.

This detailed understanding of KOH helps in performing accurate chemical reactions and in the production of various products that require this alkaline environment.