Caryophyllene: A Nonelectrolyte Compound

Caryophyllene A Nonelectrolyte Is One Of The Compounds

1. (7 points) Caryophyllene, a nonelectrolyte, is one of the compounds responsible for the flavor of cloves. A 207 mg sample of caryophyllene was dissolved in 1.00 g of chloroform (K_b = 3.63 °C/m), increasing the boiling point of chloroform by 3.68 °C. What is the molar mass of caryophyllene?

2. (3 points) Which alkane compound has the highest vapor pressure? a. C₄H₁₀ b. C₇H₁₆ c. C₅H₁₂ d. C₈H₁₈ e. C₆H₁₄

3. (5 points) A solution is prepared by adding 0.250 mol naphthalene, which is not volatile, to 2.25 mol diethyl ether. What is the vapor pressure of this solution at 25 °C given that the vapor pressure of pure diethyl ether is 532 torr?

4. (6 points) A solution of 5.00 g of lithium chloride in 1.00 kg of water has a freezing point of -0.410 °C. What is the actual van ’t Hoff factor for this salt at this concentration? K_f (water) = 1.86 °C/m

5. (6 points) A solution is prepared by mixing 75 g of benzene (C₆H₆) with 25 g of toluene (C₇H₈). Both toluene and benzene are volatile. Use the following data to determine the vapor pressure of this solution at 20 °C.

Substance Vapor Pressure at 20 °C (torr): Benzene 75, Toluene ?.

6. (6 points) For each of the following pairs of compounds, identify the one that is more likely to be soluble in water. Explain the rationale for your choice.

• (A) Br₂ or NaBr
• (B) CH₃CH₂OH or CH₃OCH₃
• (C) CO₂ or KOH

7. (6 points) Identify the dominant intermolecular forces present in each of the following molecules: CH₃CH₂-O-CH₂CH₃, H₂O, and N₂.

8. (6 points) If water contains about 42 mg of oxygen per liter at 20 °C and 1.0 atm, what would be the value of Henry’s law constant for oxygen dissolving in water? The mole fraction of oxygen in air is 0.21.

9. (3 points) When aluminum metal reacts with iron (III) oxide to form aluminum oxide and iron metal, 30 kJ of heat are given off for each mole of aluminum metal consumed, under constant pressure and standard conditions. What is the correct value for the standard enthalpy of reaction in the thermochemical equation below?

2 Al (s) + Fe₂O₃(s) → 2 Fe(s) + Al₂O₃(s)

10. (3 points) Of all the noble gases, ________ has the weakest intermolecular force and hence the lowest boiling point. a. He b. Kr c. Ne d. Xe e. Ar

11. (10 points) For each of the following, state the steric number, electron domain geometry, molecular geometry, hybridization, and whether it is polar or non-polar: NH₃, BCl₃, CHCl₃, CO₂, H₂O.

12. (10 points) Gasoline is primarily a mixture of hydrocarbons and is sold with an octane rating based on properties of isooctane (C₈H₁₈), which has an enthalpy of vaporization of 35.8 kJ/mol and a boiling point of 98.2 °C. Determine the vapor pressure of isooctane on a very hot summer day when the temperature is 38 °C in torr.

Paper For Above instruction

The investigation of physical and chemical properties of organic compounds and solutions is fundamental in the field of chemistry, offering insights into molecular behavior, intermolecular forces, and thermodynamic principles. This paper addresses several key aspects, including molar mass determination via colligative properties, vapor pressure analysis, solution colligative effects, intermolecular forces, Henry’s law, thermochemical reactions, and physical properties of noble gases. Each topic is explored with detailed scientific reasoning and relevant calculations, providing a comprehensive understanding of these concepts.

Determining the Molar Mass of Caryophyllene

Caryophyllene is a sesquiterpene responsible for the distinct aroma of cloves, classified as a nonelectrolyte in solution. To determine its molar mass, we use the boiling point elevation method, which relies on colligative properties. The formula for boiling point elevation is ΔT_b = i · K_b · m, where i is the van ’t Hoff factor (which is 1 for nonelectrolytes), K_b is the ebullioscopic constant, and m is the molality.

Given data include sample mass (207 mg), solvent mass (1.00 g of chloroform), boiling point elevation (3.68 °C), and K_b (3.63 °C/m). First, convert the mass of caryophyllene to grams (0.207 g). The molality (m) is obtained from:

m = ΔT_b / (i · K_b) = 3.68 / (1 · 3.63) ≈ 1.014 mol/kg.

The number of moles of caryophyllene is:

Number of moles = mass / molar mass = 0.207 g / M.

Since molality is moles per kilogram of solvent, and the solvent is 1.00 g (0.001 kg), then:

1.014 mol / 0.001 kg = 1014 mol / kg, which suggests a mismatch. More correctly, the molality can be calculated directly as:

m = moles of solute / kg solvent = (0.207 / M) / 0.001, so:

0.207 / M / 0.001 = 1.014, leading to M = (0.207 / 0.001) / 1.014 ≈ 203.8 g/mol.

This approximate molar mass aligns closely with known values, confirming the methodology validity. This calculation demonstrates how colligative properties help estimate molecular weights of non-electrolyte organic compounds.

Vapor Pressure and Boiling Point in Alkanes

The vapor pressure trend among alkanes corresponds inversely to molecular weight, where lighter alkanes have higher vapor pressures. Among the options, C₄H₁₀ (butane) exhibits the highest vapor pressure because it has the lowest molecular weight, and thus weaker intermolecular forces leading to easier evaporation.

Calculating Vapor Pressure of a Solution

The vapor pressure of a solution containing a non-volatile solute (naphthalene) is calculated using Raoult’s Law: ΔP = X_solvent · P_°. The mole fraction of diethyl ether (solvent) is:

X_ether = n_ether / (n_ether + n_naphthalene) = 2.25 / (2.25 + 0.250) ≈ 0.9.

Therefore, vapor pressure of the solution at 25 °C is:

P_solution = X_ether · P_° = 0.9 · 532 ≈ 478.8 torr.

Freezing Point Depression and Van ’t Hoff Factor

The freezing point depression ΔT_f relates to molality, van ’t Hoff factor (i), and K_f: ΔT_f = i · K_f · m. From the problem, ΔT_f = 0.410 °C, molality m = 5 g / 18 g/mol / 1 kg ≈ 0.278 mol/kg, thus:

i = ΔT_f / (K_f · m) = 0.410 / (1.86 · 0.278) ≈ 0.79.

This indicates partial dissociation or ion pairing, as the van ’t Hoff factor is less than 1, which is expected at this concentration and ionic interactions.

Vapor Pressure of Benzene-Toluene Mixture

Using Dalton’s Law and Raoult’s Law, the vapor pressure of the mixture is calculated by the weighted sum of vapor pressures of each component. Vapor pressures at 20 °C are: Benzene = 75 Torr; Toluene = ? (assumed known for calculation). The mole fractions are calculated based on respective masses and molar masses:

mole fraction benzene, X_benzene = (mass / molar mass) / total moles, similarly for toluene, then the vapor pressure is:

P_total = X_benzene · P_benzene + X_toluene · P_toluene.

Solubility and Intermolecular Forces

Solubility in water depends on polarity and intermolecular interactions. NaBr, an ionic compound, is highly soluble due to strong ion-dipole forces, whereas Br₂, a nonpolar molecule, has limited solubility. CH₃CH₂OH (ethanol) is more polar than CH₃OCH₃ (dimethyl ether), making ethanol more soluble. KOH, being ionic, exhibits high water solubility compared to CO₂, which dissolves via weak van der Waals forces.

Intermolecular Forces in Specific Molecules

In CH₃CH₂-O-CH₂CH₃, dominant forces include dipole-dipole and London dispersion forces. In H₂O, hydrogen bonding prevails as the primary force. N₂ exhibits London dispersion forces due to nonpolar diatomic nature.

Henry’s Law and Gas Solubility

Given oxygen's concentration in water and the ideal gas law, Henry’s law constant (k_H) can be calculated using: C = k_H · P. Rearranged as k_H = C / P. Substituting the values (42 mg/L = 0.042 g/L, M_O2 ≈ 32 g/mol, P = 1 atm), we find:

k_H ≈ (0.042 / 32) mol/L / 1 atm ≈ 0.0013125 mol/(L·atm).

Thermochemistry of Aluminum and Iron (III) Oxide Reaction

The reaction releases 30 kJ per mole of aluminum, indicating the enthalpy change (ΔH_rxn) is negative:

ΔH_rxn = –30 kJ/mol × number of moles reacted = –30 kJ/mol × 1 mol = –30 kJ.

Noble Gas Intermolecular Forces

Among noble gases, helium (He) has the weakest London dispersion forces and the lowest boiling point due to its small size and minimal polarizability.

Geometry and Polarity of Selected Molecules

NH₃: Steric number = 4, electron domain geometry = tetrahedral, molecular geometry = trigonal pyramidal, hybridization = sp³, polar due to lone pair.

BCl₃: Steric number = 3, electron domain shape = trigonal planar, molecular geometry = trigonal planar, hybridization = sp², non-polar.

CHCl₃: Steric number = 4, tetrahedral, trichloromethane, hybridization = sp³, polar.

CO₂: Steric number = 2, linear, hybridization = sp, non-polar.

H₂O: Steric number = 4, bent, hybridization = sp³, polar.

Vapor Pressure of Isooctane at Elevated Temperature

Using the Clausius-Clapeyron equation and known enthalpy of vaporization (35.8 kJ/mol), vapor pressure P₁ at T₁=98.2 °C and T₂=38 °C can be calculated. Assuming vapor pressure at boiling is 760 torr at 98.2 °C, solving for P₂ yields an approximate vapor pressure of about 19.3 atm (or 146.4 torr) at 38 °C.

Conclusion

The detailed analysis indicates how fundamental thermodynamic principles, intermolecular forces, and solution chemistry concepts interrelate to determine physical properties such as molar masses, vapor pressures, freezing point depression, and solubility. A comprehensive understanding of these principles is critical for advancing knowledge in organic and physical chemistry, with broad applications in industrial, environmental, and biological contexts.

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