Final answer:
The increase in Gibbs energy of ethanol when the pressure is increased isothermally from 1 bar to 3001 bar is calculated using the equation ΔG = V * ΔP, taking into account ethanol's molar volume derived from its density and molar mass, resulting in an increase of 49.765 kJ for 13 g of ethanol.
Step-by-step explanation:
The question deals with calculating the increase in Gibbs energy of ethanol when the pressure is increased isothermally. In thermodynamics, the change in Gibbs free energy with pressure at constant temperature for a pure substance can be determined from the equation ΔG = V * ΔP, where V is the molar volume of the substance, ΔP is the change in pressure, and ΔG is the change in Gibbs energy.
To find the molar volume of ethanol, we use its density (0.78 g/cm³) and its molar mass (approximately 46.07 g/mol). The molar volume (V) is calculated by dividing the molar mass by the density:
V = Molar mass / Density = 46.07 g/mol / 0.78 g/cm³ = 59.064 cm³/mol
Next, convert the molar volume to liters by dividing by 1000:
V = 59.064 cm³/mol / 1000 = 0.059064 L/mol
Since the pressure is given in bars, we need to calculate the change in pressure in bar:
ΔP = Final pressure - Initial pressure = 3001 bar - 1 bar = 3000 bar
To find the increase in Gibbs energy for 13 g of ethanol, first convert it to moles:
n = Mass / Molar mass = 13 g / 46.07 g/mol = 0.282 mol
Next, calculate the change in Gibbs energy:
ΔG = n * V * ΔP
ΔG = 0.282 mol * 0.059064 L/mol * 3000 bar
ΔG = 49.765 kJ (since 1 L*bar = 0.1 kJ)