Calculate the Weight of Benzene Codistilled
| Parameter | Value | Molar Mass (g/mol) |
|---|---|---|
| Benzene (C₆H₆) | 533 mmHg | 78.11 |
| Water (H₂O) | 227 mmHg | 18.015 |
What is Calculate the Weight of Benzene Codistilled?
To calculate the weight of benzene codistilled is to determine the theoretical mass of benzene that will be carried over with a specific amount of water (steam) during a steam distillation process. This calculation is a fundamental application of physical chemistry used frequently in organic synthesis, purification of temperature-sensitive compounds, and industrial chemical engineering.
Steam distillation allows immiscible liquids like benzene and water to codistill at a temperature below the boiling point of either pure component. Pure benzene boils at 80.1°C and water at 100°C (at 1 atm), but a mixture of the two boils at approximately 69.3°C. This technique is invaluable for separating benzene from non-volatile impurities without subjecting it to higher, potentially degrading temperatures.
Engineers and chemists use this calculation to size equipment, estimate yield, and determine the efficiency of the separation process. A common misconception is that the liquids boil at an average of their boiling points; in reality, the mixture boils when the sum of their individual vapor pressures equals the external atmospheric pressure.
Calculate the Weight of Benzene Codistilled: Formula & Math
The calculation relies on Dalton's Law of Partial Pressures and the Ideal Gas Law. Because benzene and water are immiscible, they exert their own vapor pressures independently. The ratio of the number of moles of each component in the vapor phase is equal to the ratio of their vapor pressures.
The primary formula to calculate the weight of benzene codistilled is:
To solve for the weight of benzene (mbenzene):
mbenzene = mwater × [ (Pbenzene × 78.11) / (Pwater × 18.02) ]
Variable Definitions
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| mbenzene | Mass of Benzene | grams (g) | Variable |
| mwater | Mass of Water (Steam) | grams (g) | Variable |
| Pbenzene | Vapor Pressure of Benzene | mmHg or kPa | ~533 mmHg at 69°C |
| Pwater | Vapor Pressure of Water | mmHg or kPa | ~227 mmHg at 69°C |
| Mbenzene | Molar Mass of Benzene | g/mol | 78.11 (Constant) |
| Mwater | Molar Mass of Water | g/mol | 18.015 (Constant) |
Practical Examples
Example 1: Standard Laboratory Distillation
A chemist performs a steam distillation at standard atmospheric pressure (760 mmHg). The mixture boils at 69.3°C. At this temperature, the vapor pressure of water is 227 mmHg. Since the total pressure is 760 mmHg, the vapor pressure of benzene is 760 – 227 = 533 mmHg. The chemist collects 100g of water. How much benzene is codistilled?
- Inputs: Water Mass = 100g, Pbenzene = 533 mmHg, Pwater = 227 mmHg.
- Calculation: Mass Ratio = (533 × 78.11) / (227 × 18.015) ≈ 41632.63 / 4089.41 ≈ 10.18.
- Result: Mass Benzene = 100g × 10.18 = 1018g.
- Interpretation: This shows the high efficiency of steam distilling benzene; for every 1g of steam, you recover over 10g of benzene.
Example 2: Low-Efficiency Scenario
Suppose the distillation is run under a slight vacuum where the boiling temperature drops, and the vapor pressures change such that Pbenzene is 300 mmHg and Pwater is 150 mmHg. If 50g of water is collected:
- Inputs: Water Mass = 50g, Pbenzene = 300, Pwater = 150.
- Calculation: Ratio = (300 × 78.11) / (150 × 18.015). Note that 300/150 = 2.
- Simplification: Ratio = 2 × (78.11 / 18.015) ≈ 2 × 4.33 = 8.67.
- Result: Mass Benzene = 50g × 8.67 = 433.5g.
How to Use This Calculator
- Enter Water Weight: Input the mass of water collected in your receiver flask. This is usually determined by weighing the water layer after separation or measuring its volume (assuming density is roughly 1 g/mL).
- Enter Vapor Pressures: Input the vapor pressure of Benzene and Water at the distillation temperature. If you know the boiling temperature is 69.3°C at 1 atm, use the default values (533 mmHg and 227 mmHg).
- Review Results: The tool instantly calculates the weight of benzene codistilled.
- Analyze Ratio: Check the "Mass Ratio" to understand the efficiency. A higher ratio means less steam is required to distill the benzene.
Key Factors That Affect Results
When you calculate the weight of benzene codistilled, several physical and environmental factors influence the final numbers:
- Molar Mass Difference: Benzene (78.11 g/mol) is much heavier than water (18.02 g/mol). This naturally favors a higher mass of benzene for equivalent vapor pressures.
- Temperature: Vapor pressure is non-linear with temperature. A change in the boiling point (caused by altitude or vacuum) shifts the ratio of Pbenzene to Pwater.
- Atmospheric Pressure: At higher altitudes, total atmospheric pressure is lower. This lowers the boiling point of the mixture, altering the vapor pressure contributions of each component.
- Impurities: If the benzene or water contains dissolved solutes (like salts in water), the vapor pressure of that component will decrease (Raoult's Law), altering the distillation ratio.
- Miscibility: This calculator assumes complete immiscibility. In reality, benzene is slightly soluble in water (and vice versa) at higher temperatures, which causes minor deviations from the ideal theoretical yield.
- Efficiency of Condenser: If the cooling system is inefficient, highly volatile benzene vapor might escape while water condenses, leading to a measured mass lower than the theoretical calculation.
Frequently Asked Questions (FAQ)
This is due to two factors: Benzene has a much higher molar mass (78 vs 18), and at the codistillation temperature, its vapor pressure is significantly higher (533 vs 227 mmHg). These factors multiply to create a large mass ratio favors benzene.
Yes, provided the solvent is immiscible with water. You would need to replace the molar mass of benzene (78.11) and its vapor pressure with the values for your specific solvent (e.g., Toluene, Xylene).
At standard atmospheric pressure (760 mmHg), the mixture boils at approximately 69.3°C, which is lower than the boiling point of pure benzene (80.1°C).
Benzene is a known carcinogen. While this calculator provides theoretical data, any physical distillation must be performed in a fume hood with appropriate personal protective equipment (PPE). Check local safety regulations.
You would need to consult a Vapor Pressure Table or Antoine Equation data for both benzene and water at that specific temperature to find Pbenzene and Pwater.
Yes. In vacuum distillation, the total pressure is reduced. You must ensure the sum of Pbenzene and Pwater equals your vacuum system pressure.
No. The ratio of benzene to water codistilled is constant at a fixed temperature. However, the total amount of benzene collected depends directly on the amount of water (steam) used.
The formula relies on a ratio of pressures, so units cancel out. You can use mmHg, atm, Pa, or bar, as long as you use the same unit for both benzene and water.
Related Tools and Internal Resources
Explore our other engineering and chemistry calculation tools to assist with your laboratory or industrial processes:
- Steam Distillation Efficiency Calculator – Analyze thermal efficiency and energy costs.
- Molar Mass Calculator – Quickly determine molecular weights for various compounds.
- Vapor Pressure Estimator – Estimate vapor pressures using the Antoine Equation.
- Chemical Exposure Limits Guide – Safety data for handling benzene and other solvents.
- Pressure Unit Converter – Convert between mmHg, Pascals, and Atmospheres.
- Heat Exchanger Sizing Tool – Size condensers for your distillation setup.