Question

what pressure is generated when 5 mol of ethane is stored in a volume of 8 dm 3 at 25°C? Base calculations on each of the following: a) The Ideal Gas Equation. b) The truncated Virial equation with the second virial coefficient: B =-1 56.7x106 m3mor1 4)

Answer 1

Answer:

a) 40,75 atm

b) 30,11 atm

Explanation:

The Ideal Gas Equation is an equation that describes the behavior of the ideal gases:

                                     PV = nRT

where:

• P = pressure [atm]
• V = volume [L]
• n = number of mole of gas [n]
• R= gas constant = 0,08205 [atm.L/mol.°K]
• T=absolute temperature [°K]

Note: We can express this values with other units, but we must ensure that the units used are the same as those used in the gas constant.

The truncated virial equation of state, is an equation used to model the behavior of real gases. In this, unlike the ideal gas equation, other parameters of the gases are considered as the intermolecular forces and the space occupied by the gas

$\frac{Pv}{RT} = 1 + \frac{B}{v}$

where:

• v is the molar volume [L/mol]
• B is the second virial coefficient [L/mol]
• P the pressure [atm]
• R the gas constant = 0,08205 [atm.L/mol.°K]

a) Ideal gas equation:

We convert our data to the adecuate units:

n = 5 moles

V = 3 dm3 = 3 L

T = 25°C = 298°K

We clear pressure of the idea gas equation and replace the data:

PV = nRT ..... P = nRT/V = 5 * 0,08205 * 298/3 =40,75 atm

b) Truncated virial equation:

We convert our data to the adecuate units:

n = 5 moles

V = 3 dm3 = 3 L

T = 25°C = 298°K

B = -156,7*10^-6 m3/mol = -156,7*10^-3 L/mol

We clear pressure of the idea gas equation and replace the data:

$\frac{Pv}{RT} = 1 + \frac{B}{v} ...... P = (1 + \frac{B}{v}) \frac{RT}{v}$

and v = 3 L/5 moles = 0,6 L/mol

$P = (1 + \frac{-156,7*10^{-3} }{0,6} ) \frac{0,08205*298}{0,6} = 30,11 atm$