[orgo814]

The dissociation vapor pressure of NH4Cl at 427 Celsius is 608 kPa but at 459 Celsius it has risen to 1115 kPa. Calculate a) the equilibrium constant  b) the standard reaction gibbs energy  c) the standard enthalpy  d) the standard entropy of dissociation, all at 427 Celsius. Assume vapor behaves ideally and that delta H and delta S are independent of temperature in the range given.

I understand how to find everything but the equilibrium constant (which is necessary to finding the other components). I know that the reaction is NH4Cl (s) = NH3 (g) + HCl (g). Hence, the equilibrium expression is K = (PNH3)(PHCl). Since the ratio is 1:1 PNH3 = PHCl, so P = P(NH3)^2. However, I'm confused after this. My solutions source doesn't explain the next step and simply says K = 1/4 (608 kPa/100 kPa)^2 = 9.24160 for 608 kPa (and same thing for 1115 kPa). I'm confused as to where the 1/4 and where the 100 kPa came from. Any insight would be great.

[magician4]

ref. " 1/100"

there are many ways to express K with gases, for example by expressing it concentration related ( i.e. K_c) or partial pressure related (K_p)  [those are the most common ways to do it]

however, you also could relate it to moles- (partial pressure-) fractions, i.e. [itex]\chi_n[/itex] or [itex]\chi_p[/itex]  (which is identical for ideal gas behaviour)

to do so, you'd have to devide by standard pressure (in case of pressures) , hence by 100 kPa

ref. "1/4"
the total pressure is composed of two (equal) single pressures: p(NH3) and p(HCl) = 0.5 p_total , each.
hence, p(NH₃) * p(HCl) = (0.5 p_total) * (0.5 p_total) = 0.25 p_total² = 1/4 p_total²


regards

Ingo

[Radu]

  you need to make sure that the constant is adimensional, given that its formula is derived from dG=VdP-SdT, and logharitmation and exponentials require adimensional units. hence,
      k=(p/p°)^{2. with p=p_total/2.}