The pKb of dimethylamine and pKa of acetic acid are 3.27 and 4.77 respectively at T (K). The correct option for the pH of dimethylammonium acetate solution is
6.25
8.5
5.5
7.75
The Correct Option is D
Solution and Explanation
Given:
- \( \text{p}K_b \) of dimethylamine = 3.27
- \( \text{p}K_a \) of acetic acid = 4.77
We will use the Henderson-Hasselbalch equation for the calculation. Since dimethylammonium acetate is a salt of a weak base (dimethylamine) and a weak acid (acetic acid), the pH can be determined by the following relationship:
\[ \text{pH} = \frac{1}{2} (\text{p}K_a + \text{p}K_b + 14) \]
Here is the detailed calculation:
1. Determine the \(\text{p}K_a\) of dimethylammonium ion:
\[ \text{p}K_a (\text{dimethylammonium ion}) = 14 - \text{p}K_b (\text{dimethylamine}) \]
\[ \text{p}K_a (\text{dimethylammonium ion}) = 14 - 3.27 = 10.73 \]
2. Calculate the pH using the above relationship:
\[ \text{pH} = \frac{1}{2} (\text{p}K_a (\text{acetic acid}) + \text{p}K_a (\text{dimethylammonium ion})) \]
\[ \text{pH} = \frac{1}{2} (4.77 + 10.73) \]
\[ \text{pH} = \frac{1}{2} \times 15.5 \]
\[ \text{pH} = 7.75 \]
Therefore, the correct pH of the dimethylammonium acetate solution is \( \textbf{7.75} \), which matches the given answer.
Conclusion:
The correct option for the pH of dimethylammonium acetate solution is option (D): 7.75.The correct answer is option (D): 7.75
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Concepts Used:
Solutions
A solution is a homogeneous mixture of two or more components in which the particle size is smaller than 1 nm.
For example, salt and sugar is a good illustration of a solution. A solution can be categorized into several components.
Types of Solutions:
The solutions can be classified into three types:
- Solid Solutions - In these solutions, the solvent is in a Solid-state.
- Liquid Solutions- In these solutions, the solvent is in a Liquid state.
- Gaseous Solutions - In these solutions, the solvent is in a Gaseous state.
On the basis of the amount of solute dissolved in a solvent, solutions are divided into the following types:
- Unsaturated Solution- A solution in which more solute can be dissolved without raising the temperature of the solution is known as an unsaturated solution.
- Saturated Solution- A solution in which no solute can be dissolved after reaching a certain amount of temperature is known as an unsaturated saturated solution.
- Supersaturated Solution- A solution that contains more solute than the maximum amount at a certain temperature is known as a supersaturated solution.