Question

Boric acid and glycerin form a complex \(\mathrm{B}(\mathrm{OH})_{3}(\mathrm{aq})+\) glycerin \((\mathrm{aq}) \rightleftharpoons \mathrm{B}(\mathrm{OH})_{3} \cdot\) glycerin(aq) with an equilibrium constant of 0.90. If the concentration of boric acid is 0.10 M, how much glycerin should be added, per liter, so that \(60 . \%\) of the boric acid is in the form of the complex?

Short answer

Add 1.67 M of glycerin per liter.

Step-by-step solution

Understanding the Equilibrium

The given system reaches equilibrium with the reaction \( \text{B(OH)}_3 + \text{glycerin} \rightleftharpoons \text{B(OH)}_3 \cdot \text{glycerin} \). The equilibrium constant \( K \) is 0.90. We need to ensure that 60% of boric acid forms the complex.

Setting Up the Expression

Let the initial concentration of boric acid be \( 0.10 \ \text{M} \). If 60% forms the complex, the concentration of the complex at equilibrium is \( 0.06 \ \text{M} \). The concentration of unreacted boric acid at equilibrium is \( 0.10 - 0.06 = 0.04 \ \text{M} \).

Applying the Equilibrium Constant

The equilibrium constant \( K = 0.90 \) is expressed as \[ K = \frac{[\text{B(OH)}_3 \cdot \text{glycerin}]}{[\text{B(OH)}_3][\text{glycerin}]} = \frac{0.06}{0.04 \times [\text{glycerin}]} \]

Solving for Glycerin Concentration

Rearrange the equation and solve for the glycerin concentration: \[ 0.90 \times 0.04 \times [\text{glycerin}] = 0.06 \]\[ [\text{glycerin}] = \frac{0.06}{0.90 \times 0.04} = 1.67 \ \text{M} \]

Conclusion

To achieve the desired complex formation, add approximately \( 1.67 \ \text{M} \) of glycerin per liter to the solution.

Key concepts

Boric Acid

Boric acid, with the chemical formula \(\text{B(OH)}_3\), is a weak monobasic acid often used in antiseptics, insecticides, and various chemical reactions. It is known for its gentle properties and ability to form complexes with other molecules.
When added to water, boric acid does not fully dissociate, which means it remains largely in its original state. This characteristic makes it useful in forming complexes, as it can interact with other chemical species without fully breaking down.

• Features weak acidity
• Forms complexes with agents like glycerin
• Used in various applications, from medical to industrial

Glycerin

Glycerin, also known as glycerol, is a simple polyol compound that is colorless, odorless, and sweet-tasting. It has three hydroxyl (\(-OH\)) groups, making it highly soluble in water and enabling it to form hydrogen bonds with other molecules.
In the context of chemical reactions, glycerin can serve as a stabilizing or complexing agent. Its ability to participate in hydrogen bonding allows it to readily interact with other compounds like boric acid.

• Highly soluble in water due to multiple hydroxyl groups
• Sweet-tasting and non-toxic
• Used in cosmetics, food, and pharmaceuticals

Equilibrium Constant

The equilibrium constant \( K \) is a crucial concept in understanding chemical equilibria. It quantifies the ratio of concentrations of products to reactants at equilibrium at a given temperature. In this reaction, it is given as \( K = 0.90 \).
The equilibrium constant helps to understand how far a reaction will proceed. For a reaction:
\(\text{B(OH)}_3 + \text{glycerin} \rightleftharpoons \text{B(OH)}_3 \cdot \text{glycerin}\)
The expression for \( K \) is:
\[ K = \frac{[\text{B(OH)}_3 \cdot \text{glycerin}]}{[\text{B(OH)}_3][\text{glycerin}]} \]
A \( K \) value of 0.90 indicates that the reaction slightly favors the formation of the complex, but not overwhelmingly so.

• Reflects the balance between reactants and products
• Aids in calculating concentrations needed for desired outcomes

Complex Formation

Complex formation involves the combination of two or more molecules to form a more complex structure. In this case, boric acid and glycerin combine to form a complex \(\text{B(OH)}_3 \cdot \text{glycerin}\).
Complexes are often stabilized by interactions like hydrogen bonds or coordination bonds. The stability and formation of such complexes depend on factors like the concentrations of the components and their chemical compatibility.

• Essential for processes like catalysis and enzyme-substrate interactions
• Impacts properties like solubility and reactivity
• Can be influenced by temperature, pressure, and concentration

Understanding how and why complexes form can help in controlling chemical reactions and designing chemical processes that rely on specific interactions.