Problem 29 - Chemistry The Molecular Science

Question

The hydronium ion concentration of a cyanoacetic acid solution is \(0.032 \mathrm{M}\). Calculate its pOH.

Step-by-Step Solution

Answer

The pOH of the solution is 12.5.

Step 1: Determine pH from Hydronium Ion Concentration

First, use the formula for pH which is \[pH = -\log[H_3O^+]\]where \([H_3O^+]\) is the hydronium ion concentration. Given, \([H_3O^+] = 0.032\, M\), substitute the value to find pH:\[pH = -\log(0.032) = 1.5\]

Step 2: Calculate pOH from pH

Use the relationship between pH and pOH given by the equation:\[pH + pOH = 14\]Solve for pOH by substituting the pH value calculated in step 1:\[pOH = 14 - 1.5 = 12.5\]

Key Concepts

Hydronium Ion Concentration

The hydronium ion concentration \( [H_3O^+] \) is a measure of how acidic or basic a solution is. In the context of acids, hydronium ions result from the reaction of hydrogen ions \( H^+ \) with water \(H_2O\). Notice that the hydronium ion is represented as \( H_3O^+ \).
For cyanoacetic acid, you are given the hydronium ion concentration as \( 0.032 \, M \). This concentration plays a crucial role in determining the solution's pH, as the pH is calculated directly from the hydronium ion concentration using the formula:
\[ pH = -\log[H_3O^+] \]
This formula implies that a higher hydronium concentration will result in a lower pH, indicating a more acidic solution.

pH and pOH Relationship

The pH and pOH have a special relationship in aqueous solutions, where their sum always equals 14 at 25°C. You can express this relationship with the equation:
\[ pH + pOH = 14 \]
This means that if you know either the pH or the pOH of a solution, you can quickly find the other.
For the cyanoacetic acid solution with a hydronium ion concentration of 0.032 M, the calculated pH is 1.5. Using the relationship, the pOH is found by subtracting the pH from 14:
\[ pOH = 14 - 1.5 = 12.5 \]
Understanding this balance helps emphasize how hydrogen ion concentration (pH) and hydroxide ion concentration (pOH) interact to define a solution's acidity or basicity.

Cyanoacetic Acid

Cyanoacetic acid is an organic compound with the chemical formula \( C_3H_3NO_2 \). It's a derivative of acetic acid, including a cyano group which gives it distinctive properties.
As a weak acid, cyanoacetic acid only partially dissociates in water to form hydronium ions. This partial dissociation is why the hydronium ion concentration, \( 0.032 \, M \), needs to be calculated when assessing its acidity.
Here's why understanding compounds like cyanoacetic acid is significant:

• The presence of the cyano group influences acidity.
• It serves many roles in chemical synthesis.
• Being aware of hydronium ion concentration aids in predicting reactions and solutions' behaviors.

Cyanoacetic acid's study emphasizes the importance of knowing both structural and concentration factors when evaluating a substance's acidic characteristics.