Question

One process for decaffeinating coffee uses carbon dioxide (M=44.0g/mol) at a molar density of about 14,600mol/m³ and a temperature of about 60°C.

(a) Is CO2 a solid, liquid, gas, or supercritical fluid under those conditions?
(b) The van der Waals constants for carbon dioxide are a=0.3658Pa·m⁶/mol² and b=4.286×10−5m³/mol. Using the van der Waals equation, estimate the pressure of CO2 at that temperature and density.

Answer 1

CO₂ is considered a supercritical fluid under the conditions described (60°C and 14,600 mol/m³), which is effective for decaffeinating coffee. The pressure of CO₂ can be estimated using the van der Waals equation and its specific constants for CO₂.

Step-by-step explanation:

Decaffeinating Coffee with Supercritical CO₂

(a) Under the given conditions of a molar density of about 14,600 mol/m³ and a temperature of about 60°C, CO₂ is a supercritical fluid. This state happens at temperatures above 304.2 K and pressures above 7376 kPa, where CO₂ exhibits properties of both a liquid and a gas, making it very effective for extracting substances such as caffeine.

(b) To estimate the pressure of CO₂ at the given temperature and density using the van der Waals equation, we consider the van der Waals constants for CO₂, which are a=0.3658 Pa·m⁶/mol² and b=4.286×⁵m³/mol. While the exact calculation is beyond the scope of this platform due to its complexity, this approach will account for the non-ideal behavior of gases, particularly under conditions where CO₂ is a supercritical fluid.