Question

The density of liquid carbon disulfide, CS2, is 1293 kg m–3. Calculate the change in the molar Gibbs energy of carbon disulfide when it is compressed by a change in pressure from 1.00 bar to 4.00 bar.

Answer 1

Answer:

The change in the molar Gibbs energy of carbon disulfide is 1102.31 kJ/mol.

Explanation:

∆G = ∆H - T∆S

Using the steam table,

At 1 bar,

T1 = 99.6°C

H1 = 417 kJ/kg

S1 = 1.303 kJ/kg.K

At 4 bar,

T2 = 143.6°C

H2 = 605 kJ/kg

S2 = 1.776 kJ/kg.K

T = T2 - T1 = 143.6 - 99.6 = 44°C = 44+273 = 317 K

∆H = H2 - H1 = 605 - 417 = 188 kJ/kg

∆S = S2 - S1 = 1.776 - 1.303 = 0.473 kJ/kg.K

∆G = 188 - 317(0.473) = 188 - 149.941 = 38.059 kJ/kg

Density of CS2 = 1293 kg/m^3

Molar volume = 0.0224 m^3/mol

Change in molar Gibbs energy of CS2 = ∆G × density × molar volume = 38.059 kJ/kg × 1293 kg/m^3 × 0.0224 m^3/mol = 1102.31 kJ/mol

Answer 2

The Gibbs energy of the carbon disulfide is  5.89 J/mol.

• Considering calcium disulphide as an incompressible liquid.

• Molar mass of calcium disulphide = (1*12.01 + 2*32.065) g/mol = 76.14 g/mol = (76.14 g/mol)*(1 kg/1000 g) = 0.07614 kg/mol.
• Molar volume of calcium disulphide as
• Vm = (molar mass of CS2)/(density of CS2) = (0.07614 kg/mol)/1293 kg/m3) = 5.88863*10-5 m3/mol = (5.88863*10-5 m3/mol)*(1000 L/1 m3) = 0.0588863 L/mol.
• For an incompressible liquid, we define the change in Gibb’s free energy as
• ΔGm = Vm*Δp = (0.0588863 L/mol)(2.00 – 1.00) bar(1 atm/1.01325 bar) = 0.058116259 atm-L/mol = (0.058116259 L-atm/mol)*(101.33 J/1 L-atm) = 5.8889 J/mol ≈ 5.89 J/mol.

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