Calculate the values of δg, δf and δsuniv for:
a) vaporization of 39 g of benzene at its boiling temperature (80.1 °c, 1 bar);
b) adiabatic expansion of 0.100 mol of an ideal gas, in vacuo (joule's experiment), with an initial temperature of 300 k, if the initial volume is 2.00 dm3 and the final volume is 6.00 dm3.
note: process a) is reversible, isothermal and isobaric.
data:
r = 8.314 j mol-1 k-1
1bar = 105 pa
m (c6h6) = 78.66 g mol-1

a.

ΔF = w  = 2.94 kJ

ΔSuniv = 0

ΔG  =  0

b.

ΔS = 0.1000×8.315×1.099 = 0.913 J/mol K

ΔQ =0

ΔH = 0

Explanation:

a. You have  to find the ΔG, ΔF, who are two forms of free energy

G: Gibbs free energy

F: Helmholtz free energy

-G: Gibbs free energy:

For solve these, you have the following equation:

ΔG = ΔH   – T ΔS           with T constant (Eq 1)

Where:

ΔG = change in Gibbs free energy

ΔH= change in enthalpy

T = temperature

ΔS = change in entropy

This process is irreversible and isothermic, it last means that temperature doesn’t change.

For that reason:

ΔS  = q/T      with p constant.   (Eq 2)

Where:

q = heat

And, with p constant, it just making P-V work, so:

ΔH = qp =q   (Eq 3)

where:

qp = heat at constant pressure.

-F: Helmholtz free energy

To find ΔF, you have to use the following equation:

ΔF = ΔU   – T ΔS   With T constant,  (Eq 4)

Where:

ΔF = change in Helmholtz free energy

ΔU= change in internal energy

T = temperature

ΔS = change in entropy

And also, you have to use the equation for internal energy:

ΔU = q + w (Eq 5)

b. For this problem we have to establish two states, A and B, based on the data given from the problem:

State A:

V1 = 2 dm³

T1 = 300K

State B:

V2 = 6 dm³

T2 = ?

Due to the adiabatic properties of the process, this expansion  makes that change on heat “q” equals to 0:

Δq= 0

SO we have to ask ourselves what is the value of the change in entropy. But we don’t know if the process is reversible or not. Also, we don’t know if the process is static or not, and the volume could be hard to define.

the molecules move in straight line until they collide with each other or with the walls of the container. collisions are perfectly elastic; when two molecules collide, they change their directions and kinetic energies, but the total kinetic energy is conserved.

explanation:

i believe the answer is a.