Metal-halide lamps are a type of gas discharge lamp that contain tungsten electrodes doped with a metal M and an additional halide material (usually sodium iodide). The working temperature of the lamp varies between 1000-3000°C. At the working temperature of the lamp, sodium iodide dissociates to produce sodium and iodine atoms in gaseous form.
NaI(s) → Na(g) + I(g)
The iodine atoms react with the metal M to produce gaseous MI4.
M(s) + 4 I(g) ⇌ MI4(g)
The equilibrium pressure of I(g) at 1200°C within the lamp is 0.0240 atm. Show quantitatively that the pressure of MI4 at 1200°C will cause the reaction to go in the reverse direction at 2500°C (the pressure of I(g) is the same). Assume that for the theoretical metal M, the equilibrium constant (Kp) for the reaction is 210 at 1200°C and 15 at 2500°C.