Problem 59 - Chemistry and Chemical Reactivity

Question

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

Step-by-Step Solution

Answer

Add 1.67 M of glycerin per liter.

Step 1: Write the equilibrium expression

The reaction is \( \mathrm{B}(\mathrm{OH})_{3}(\mathrm{aq}) + \text{glycerin (aq)} \rightleftharpoons \mathrm{B}(\mathrm{OH})_{3} \cdot \text{glycerin (aq)} \). The equilibrium constant expression is: \[ K = \frac{[\mathrm{B}(\mathrm{OH})_{3} \cdot \text{glycerin}]}{[\mathrm{B}(\mathrm{OH})_{3}][\text{glycerin}]} \] with \( K = 0.90 \).

Step 2: Define the change in concentration

Define the initial concentration of boric acid as \( [\mathrm{B}(\mathrm{OH})_{3}] = 0.10 \text{ M} \). If 60% of this converts to the complex, then 0.060 M of \( \mathrm{B}(\mathrm{OH})_{3} \) forms the complex and 0.040 M remains uncomplexed.

Step 3: Write the equilibrium concentrations

Let \( x \text{ M} \) be the concentration of glycerin added. At equilibrium:- \( [\mathrm{B}(\mathrm{OH})_{3}] = 0.040 \text{ M} \)- \( [\text{glycerin}] = x \text{ M} \)- \( [\mathrm{B}(\mathrm{OH})_{3} \cdot \text{glycerin}] = 0.060 \text{ M} \)

Step 4: Use the equilibrium constant to solve for x

Substitute the equilibrium concentrations into the equilibrium expression:\[ 0.90 = \frac{0.060}{0.040 \cdot x} \]Solve for \( x \):\[ x = \frac{0.060}{0.040 \times 0.90} \]\[ x = \frac{0.060}{0.036} = 1.67 \text{ M} \]

Step 5: Conclusion

To ensure that 60% of the boric acid is in the form of the complex, you need to add 1.67 M of glycerin per liter.

Key Concepts

Boric Acid

Boric acid, with the chemical formula \( \text{B(OH)}_3 \), is a weak monobasic acid. It is often found in powder or crystalline form and is known for its antiseptic, antifungal, and insecticidal properties. In solution, boric acid acts as a Lewis acid, meaning it can accept electron pairs, making it useful in various chemical applications.
One unique property of boric acid is its ability to form complexes. When boric acid is dissolved in water, it partially dissociates, but not in the traditional manner of donating hydrogen ions. Instead, it forms a complex with water molecules, making it very effective in the formation of other complexes in chemical reactions, like the formation with glycerin.

• Boric acid has a mild action, making it less aggressive than other acids.
• It is utilized in medical and laboratory settings, and is safe when used properly.

Understanding the behavior of boric acid in chemical equilibria is crucial, particularly when it interacts with other compounds like glycerin, as it highlights its capability to stabilize them into new complex forms.

Glycerin

Glycerin, also known as glycerol, is a simple polyol compound with a structure of \( \text{C}_3\text{H}_8\text{O}_3 \). It appears as a colorless, odorless, viscous liquid that is sweet-tasting and non-toxic. It is commonly used in food, pharmaceuticals, and cosmetics due to its moisturizing properties.
In chemical reactions, glycerin can act as a ligand, donating electron pairs to form complexes with metal ions or other compounds such as boric acid. This quality is what facilitates its role in the formation of the boric acid-glycerin complex discussed in this problem.

• Glycerin's structure allows it to participate in hydrogen bonding and other intermolecular interactions.
• It is often used to improve texture and moisture content in products.

When combined with boric acid, glycerin enhances the stability of the resultant complex, thereby influencing the chemical equilibrium. This property is leveraged to achieve specific concentrations of substances in solutions.

Equilibrium Constant

The equilibrium constant, denoted as \( K \), is a dimensionless number that gives insight into the extent of a chemical reaction at equilibrium. Specifically, it indicates the ratio of the concentrations of products to reactants when a reaction is at equilibrium. In our exercise, the equilibrium constant is 0.90, reflecting the balance between boric acid, glycerin, and their complex.
For the provided reaction, the equilibrium expression is:
\[ K = \frac{[\text{B(OH)}_3 \cdot \text{glycerin}]}{[\text{B(OH)}_3][\text{glycerin}]} \]
Understanding and calculating this constant is crucial, as it helps predict how much of each reactant and product will be present once equilibrium is established.

• If \( K > 1 \), the reaction favors products at equilibrium.
• If \( K < 1 \), the reaction favors reactants.

In our exercise, \( K = 0.90 \), indicating a near-balance between reactant and product, suggesting that significant amounts of both are present at equilibrium.

Complex Formation

Complex formation refers to the process where molecules or ions bind together to form a larger aggregate, called a complex. This process often involves a central atom or ion and surrounding molecules known as ligands. In this exercise, boric acid and glycerin form such a complex.
Complexes are significant in chemistry because they exhibit different properties than their individual components. These properties can include changes in solubility, stability, and reactivity.

• The formation of complexes can affect equilibrium in a reaction.
• They are used to stabilize reactive species and in catalysis.

In the given problem, the formation of the boric acid-glycerin complex is integral to shifting the chemical equilibrium toward the desired products. It highlights the essential role of complex formation in manipulating chemical reactions to achieve specific outcomes in a controlled environment.