Respuesta :
Answer:
(a). The Gibbs free energy change is 2.895 kJ and its positive.
(b). The Gibbs free energy change is 34.59 J/mole
(c). The pressure is 14924 atm.
(d). The Gibbs free energy of diamond relative to graphite is 4912 J.
Explanation:
Given that,
Temperature = 298 K
Suppose, density of graphite is 2.25 g/cm³ and density of diamond is 3.51 g/cm³.
[tex]\Delta H\ for\ diamond = 1.897 kJ/mol[/tex]
[tex]\Delta H\ for\ graphite = 0 kJ/mol[/tex]
[tex]\Delta S\ for\ diamond = 2.38 J/(K mol)[/tex]
[tex]\Delta S\ for\ graphite = 5.73 J/(K mol)[/tex]
(a) We need to calculate the value of [tex]\Delta G[/tex] for diamond
Using formula of Gibbs free energy change
[tex]\Delta G=\Delta H-T\Delta S[/tex]
Put the value into the formula
[tex]\Delta G= (1897-0)-298\times(2.38-5.73)[/tex]
[tex]\Delta G=2895.3[/tex]
[tex]\Delta G=2.895\ kJ[/tex]
The Gibbs free energy change is positive.
(b). When it is compressed isothermally from 1 atm to 1000 atm
We need to calculate the change of Gibbs free energy of diamond
Using formula of gibbs free energy
[tex]\Delta S=V\times\Delta P[/tex]
[tex]\Delta S=\dfrac{m}{\rho}\times\Delta P[/tex]
Put the value into the formula
[tex]\Delta S=\dfrac{12\times10^{-6}}{3.51}\times999\times10130[/tex]
[tex]\Delta S=34.59\ J/mole[/tex]
(c). Assuming that graphite and diamond are incompressible
We need to calculate the pressure
Using formula of Gibbs free energy
[tex]\beta= \Delta G_{g}+\Delta G+\Delta G_{d}[/tex]
[tex]\beta=V(-\Delta P_{g})+\Delta G+V\Delta P_{d}[/tex]
[tex]\beta=\Delta P(V_{d}-V_{g})+\Delta G[/tex]
Put the value into the formula
[tex]0=\Delta P(\dfrac{12\times10^{-6}}{3.51}-\dfrac{12\times10^{-6}}{2.25})\times10130+2895.3[/tex]
[tex]0=-0.0194\Delta P+2895.3[/tex]
[tex]\Delta P=\dfrac{2895.3}{0.0194}[/tex]
[tex]\Delta P=14924\ atm[/tex]
(d). Here, [tex]C_{p}=0[/tex]
So, The value of [tex]\Delta H[/tex] and [tex]\Delta S[/tex] at 900 k will be equal at 298 K
We need to calculate the Gibbs free energy of diamond relative to graphite
Using formula of Gibbs free energy
[tex]\Delta G=\Delta H-T\Delta S[/tex]
Put the value into the formula
[tex]\Delta G=(1897-0)-900\times(2.38-5.73)[/tex]
[tex]\Delta G=4912\ J[/tex]
Hence, (a). The Gibbs free energy change is 2.895 kJ and its positive.
(b). The Gibbs free energy change is 34.59 J/mole
(c). The pressure is 14924 atm.
(d). The Gibbs free energy of diamond relative to graphite is 4912 J.
