Problem 40 - Chemistry and Chemical Reactivity

Question

Butylated hydroxyanisole (BHA) is used in margarine and other fats and oils. (It is used as an antioxidant and prolongs the shelf life of the food.) What is the molar mass of BHA if \(0.640 \mathrm{g}\) of the compound, dissolved in \(25.0 \mathrm{g}\) of chloroform, produces a solution whose boiling point is \(62.22^{\circ} \mathrm{C} ?\)

Step-by-Step Solution

Answer

The molar mass of BHA is approximately \(91.10 \, \mathrm{g/mol}\).

Step 1: Understand Boiling Point Elevation Formula

The boiling point elevation can be calculated using the formula: \( \Delta T_b = i \cdot K_b \cdot m \), where \( \Delta T_b \) is the boiling point elevation, \( i \) is the van't Hoff factor, \( K_b \) is the ebullioscopic constant of the solvent, and \( m \) is the molality of the solution. For molecules like BHA that do not dissociate in solution, \( i=1 \).

Step 2: Determine Boiling Point Elevation

Calculate the change in boiling point: \( \Delta T_b = 62.22^{\circ} \mathrm{C} - 61.20^{\circ} \mathrm{C} = 1.02^{\circ} \mathrm{C} \). The boiling point of pure chloroform is \(61.20^{\circ} \mathrm{C}\).

Step 3: Use Ebullioscopic Constant

The ebullioscopic constant \( K_b \) for chloroform is \(3.63 \mathrm{\,^{\circ}C\cdot kg/mol}\). Using the boiling point elevation formula from Step 1: \( 1.02 = 1 \cdot 3.63 \cdot m \). Solve for \( m \), the molality: \( m = \frac{1.02}{3.63} \approx 0.281 \mathrm{\,mol/kg} \).

Step 4: Calculate Moles of Solute

Molality \( m \) is defined as moles of solute per kg of solvent. Rearranging for moles, we get \( \text{moles of BHA} = m \times \, \text{kg of solvent} = 0.281 \mathrm{\,mol/kg} \times 0.025 \mathrm{\,kg} = 0.007025 \mathrm{\,mol} \).

Step 5: Calculate Molar Mass of BHA

The molar mass \( M \) is calculated as \( M = \frac{\text{mass of solute}}{\text{moles of solute}} = \frac{0.640 \mathrm{\,g}}{0.007025 \mathrm{\,mol}} \approx 91.10 \mathrm{\,g/mol} \).

Key Concepts

Molar Mass Calculation

When calculating the molar mass of a compound, it's essential to understand what molar mass represents. It is the mass of one mole of a given substance, usually in grams per mole (g/mol). In this exercise, the molar mass of Butylated hydroxyanisole (BHA) is found using the amount of substance and its mass.
To calculate molar mass:

• First, determine the number of moles of the solute involved. This is done through the molality and mass of the solvent.
• Next, use the formula: \[ M = \frac{\text{mass of solute}}{\text{moles of solute}} \] This relationship helps you find the molar mass once you know how many moles are present in a given mass.

By understanding how the mass of solute and moles relate, you can use this approach to decompose various problems related to chemical solutions.

Ebullioscopic Constant

The ebullioscopic constant, denoted as \( K_b \), plays a crucial role in understanding boiling point elevation. It is specific to each solvent and provides a measure of how a solute will affect the boiling point of that solvent. For chloroform, the given \( K_b \) is \( 3.63 \, ^{\circ}C\cdot kg/mol \).
Here's how it is used:

• The boiling point elevation formula is \( \Delta T_b = i \cdot K_b \cdot m \). \( \Delta T_b \) is the change in boiling point, and \( m \) is the molality.
• The constant allows you to find the change in boiling point by relating it to the concentration of solute (using molality).

Understanding \( K_b \) helps predict and calculate how much the boiling point will increase for a given amount of solute. This concept is vital in solution chemistry and is specific to each different solvent.

Solution Chemistry

Solution chemistry delves into how substances dissolve and interact on a molecular level. In this problem, a small amount of BHA is dissolved in chloroform, affecting the boiling point of the solution.
Key points in this exercise include:

• Solubility is influenced by the nature of solute and solvent, along with temperature.
• Boiling point elevation is a colligative property. It depends on the number of solute particles rather than their identity.
• The van't Hoff factor \( i \) is crucial as it considers dissociation or association effects of solutes, though here it's 1, as BHA does not dissociate.

Understanding these dynamics helps in predicting how different substances will interact in a solution, an essential part of thermodynamic properties and chemistry.

Thermodynamic Properties

Thermodynamics in chemistry involves studying heat and other forms of energy in chemical processes. Boiling point elevation is one aspect, revealing how energy changes affect a solution.
Important concepts here involve:

• Heat is absorbed during boiling, and solute addition alters this process.
• Thermodynamic properties like boiling point elevation provide insights into the stability and energy shifts in chemical reactions.
• Studying these properties helps in designing processes that use heat, like distillation or synthesis.

Recognizing how thermodynamics apply in practical scenarios equips students to solve real-world problems in fields like chemical engineering and materials science.