Respuesta :
Answer:
The pressure is [tex]P= - 6.39*10^8Pa[/tex]
The temperature is [tex]T =1218.63 K[/tex]
Explanation:
Generally Gibbs free energy is mathematically represented as
[tex]G = E + PV -TS[/tex]
Where E is the enthalpy
PV is the pressure volume energy (i.e PV energy)
S is the entropy
T is the temperature
For stability to occur the Gibbs free energy must be equal to zero
Considering Diamond
So at temperature of T = 300 K
[tex]E + PV - TS = 0[/tex]
making P the subject
[tex]P = \frac{TS-E}{V}[/tex]
Now substituting 300 K for T , 2900 J for E ,
[tex]3.42cm^3 = \frac{3.42}{1*10^6} = 3.42*10^{-6}m^3[/tex] for V and [tex]2.38 J/K[/tex] for S
[tex]P = \frac{(300 * 2.38)- 2900}{3.42*10^{-6}}[/tex]
[tex]P= - 6.39*10^8Pa[/tex]
The negative sign signifies the direction of the pressure
Given that [tex]P = 1*0^5Pa[/tex]
making T the subject
[tex]T = \frac{PV+E}{S}[/tex]
Substituting into the equation
[tex]T = \frac{1*10^5 * 3.42 *10^{-6}+2900}{2.38}[/tex]
[tex]T =1218.63 K[/tex]
Correct Data:
G S V
1 mol Graphite 0 J 5.74 J/K 5.30cm³
1 mol Diamond 2900 J 2.38 J/K 3.42cm³
Answer:
a) P = -639 MPa
b) T =1218.63 K
Explanation:
a) For stability of diamond, the gibb's free energy, G = 0 J
The Gibb's free energy is given by G = E + PV - TS
E + PV - TS = 0
where, E = enthalpy, P = pressure, S = entropy
E = 2900 J
T = 300 K
S = 2.38 J/K
V = 3.42 cm³ = 3.42 * 10⁻⁶ m³
2900 + P3.42 * 10⁻⁶ - 300(2.38) = 0
P3.42 * 10⁻⁶ = -2186
P = 2186/(3.42 * 10⁻⁶)
P = -639* 10⁶ Pa
P = -639 MPa
b) At P = 10⁵
E + PV - TS = 0
2900 + 10⁵(3.42 * 10⁻⁶) - T(2.38) = 0
T =1218.63 K
