Confusion in relation of Gibbs free energy and equilibrium constant

[tbn032]

Homework Statement

for the reaction
SO2(g)+(1/2)O2(g)⇌SO3(g);ΔH=-98.32KJ/mole,ΔS=-95J/(mole-K).
find Kp at 298 Kelvin?

Relevant Equations

SO2(g)+(1/2)O2(g)⇌SO3(g);ΔH=-98.32KJ/mole,ΔS=-95J/(mole-K).

SO₂(g)+1/2O₂(g)⇌SO₃(g);ΔH^o=-98.32KJ/mole,ΔS^o=-95J/(mole-K).
find K_p at 298 Kelvin?
In given question at first Δ G will be calculated using formula ΔG = Δ H – T x ΔS, by putting the given values in formula we get ΔG = -70.01 kJ/mol.
Then K_eq will be calculated using equation = Δ G = -RT ln K_eq ,ln K_eq = -70010J/-8.314 x 298 = 28.25 .or K_eq = e^28.25 = 1.86x10¹².
Now my confusion is K_eq=K_por K_eq=K_c(depending on if we measure the equilibrium constant in terms of pressure or molarity, gases can be measured in both).and
K_p = K_c(RT)^Δn and Δn=-1/2(for this reaction).
No information about the pressure or concentration is given so how do I conclude that K_eq=K_p or K_eq=K_c and thus calculate the correct value of K_p

 

[Astronuc]

Given the temperature 298 Kelvin, is this reaction at the 'standard state'? If so, the pressure is ambient or ~1 atm (100 kPa, or 1 bar).
https://en.wikipedia.org/wiki/Standard_state#Conventional_standard_states

Given the standard state, one should be able to determine the density of the gases. What does one's textbook indicate about STP, standard state and Gibbs free energy?

The problem statement one provides indicates gases.

 

[tbn032]

my confusion is arising from the fact that in my book it is written that
Δ G = -RT ln K_eq
K_eq=K_porK_c as the standard state is referred in terms of partial pressure or concentration
Δ G = -RT ln K_p
Δ G = -RT ln K_k
if calculate the value of K_eq from the equation Δ G = -RT ln K_eq using R=8.3144598J⋅K^-1⋅mol^-1.the value of K_eq is dimensionless
so I am not able to conclude if Keq=Kp or Keq=Kc
kp≠kc because Kp = Kc(RT)^Δn and Δn=-1/2(for this reaction).

 

[Chestermiller]

The standard state for gases is 1 bar. So, in this example, the Keq is Kp. It is in terms of the partial pressures of the components in bars.

Incidentally, you omitted the superscript 0 in $\Delta G^0$

 

[Terrakron]

Homework Statement:: for the reaction
SO2(g)+(1/2)O2(g)⇌SO3(g);ΔH=-98.32KJ/mole,ΔS=-95J/(mole-K).
find Kp at 298 Kelvin?
Relevant Equations:: SO2(g)+(1/2)O2(g)⇌SO3(g);ΔH=-98.32KJ/mole,ΔS=-95J/(mole-K).

SO₂(g)+1/2O₂(g)⇌SO₃(g);ΔH^o=-98.32KJ/mole,ΔS^o=-95J/(mole-K).
find K_p at 298 Kelvin?
In given question at first Δ G will be calculated using formula ΔG = Δ H – T x ΔS, by putting the given values in formula we get ΔG = -70.01 kJ/mol.
Then K_eq will be calculated using equation = Δ G = -RT ln K_eq ,ln K_eq = -70010J/-8.314 x 298 = 28.25 .or K_eq = e^28.25 = 1.86x10¹².
Now my confusion is K_eq=K_por K_eq=K_c(depending on if we measure the equilibrium constant in terms of pressure or molarity, gases can be measured in both).and
K_p = K_c(RT)^Δn and Δn=-1/2(for this reaction).
No information about the pressure or concentration is given so how do I conclude that K_eq=K_p or K_eq=K_c and thus calculate the correct value of K_p

The equation is giving it up as you have SO2(g) you are dealing with gases