Problem 30 - Chemistry The Molecular Science

Question

A solution of benzyl amine, \(\mathrm{C}_{7} \mathrm{H}_{7} \mathrm{NH}_{2}\), has a hydroxide ion concentration of \(2.4 \times 10^{-3} \mathrm{M}\). Calculate the \(\mathrm{pH}\) of the solution. Calculate its \(\mathrm{pOH}\).

Step-by-Step Solution

Answer

pH is approximately 11.38, and pOH is about 2.62.

Step 1: Calculate the pOH

First, we need to find the \(\text{pOH}\) of the solution. We use the equation \(\text{pOH} = -\log [\text{OH}^-]\). Given the hydroxide ion concentration \( [\text{OH}^-] = 2.4 \times 10^{-3} \, \text{M}\), we plug it into the equation: \[ \text{pOH} = -\log (2.4 \times 10^{-3}) \approx 2.62 \]

Step 2: Convert pOH to pH

To find the \(\text{pH}\), we use the relationship between pH and pOH: \[ \text{pH} + \text{pOH} = 14 \] We already found the \(\text{pOH}\) to be approximately 2.62. Substitute this into the equation: \[ \text{pH} = 14 - \text{pOH} = 14 - 2.62 = 11.38 \]

Key Concepts

Benzyl Amine and Its Role in pH

Benzyl amine, with the chemical formula \(\mathrm{C}_{7} \mathrm{H}_{7} \mathrm{NH}_{2}\), is an organic compound that acts as a weak base in solution.
This means that it partially accepts protons (or donates hydroxide ions) when mixed with water.
Because benzyl amine is a weak base, when it dissolves, it increases the concentration of hydroxide ions \([\text{OH}^-] \) in the solution, rather than hydrogen ions \([\text{H}^+] \).

Understanding benzyl amine's behavior in water helps to predict how it will influence the pH of the solution.

• As a base, it will tend to raise the pH above 7, making the solution more basic.
• The more benzyl amine present, the more hydroxide ions will be produced, which will further increase the pH.

The presence of benzyl amine makes the calculation of pH crucial, especially in laboratory settings where precise chemical reactions are necessary.

Understanding Hydroxide Ion Concentration

The hydroxide ion concentration \([\text{OH}^-]\) is a key factor in determining the basicity of a solution.
In the case of the benzyl amine solution, it has been given as \(2.4 \times 10^{-3} \, \text{M}\).
This concentration provides an insight into how many hydroxide ions are present, which helps us understand the solution's strength as a base.

Why is \([\text{OH}^-]\) important?

• It measures the number of hydroxide ions available to neutralize any added acids, affecting not only pH but also the chemical behavior of the solution.
• A higher \([\text{OH}^-]\) directly implies a higher basic character and hence a higher pH.

Knowing the \([\text{OH}^-]\) is crucial because it directly feeds into calculating the pOH and consequently, the pH, which could influence reactions, solubility, and other properties of the solution.

Calculating pOH and Its Relationship with pH

The pOH is a measure of the alkalinity of a solution, calculated using the hydroxide ion concentration.
To find pOH, the formula \(\text{pOH} = -\log [\text{OH}^-] \) is used.
For our benzyl amine solution, substituting \(2.4 \times 10^{-3} \, \text{M}\) into the equation gives a pOH of approximately 2.62.

How does pOH relate to pH?

• The relationship is straightforward: \(\text{pH} + \text{pOH} = 14\). This means once you know the pOH, you can easily determine the pH, and vice versa.
• In our example, with a pOH of 2.62, the pH can be calculated as \(14 - 2.62 = 11.38\).
• This result tells us that the solution is basic, as expected from a benzyl amine solution.

Understanding the interplay between pOH and pH is vital in chemistry, helping in everything from predicting reaction outcomes to ensuring the safe handling and application of chemicals.