The standard enthalpy of formation of a solid alkali metal halide MX is -400 ~kJ ~mol ⁻¹ . The ionization enthalpy of M ( g ) is 520 ~kJ ~mol ⁻¹ , the bond dissociation enthalpy of X ₂( g ) is 160 ~kJ ~mol ⁻¹ , and the electron gain enthalpy of X ( g ) is -300 ~kJ ~mol ⁻¹ . If the lattice formation enthalpy of MX ( s ) is -780 ~kJ ~mol ⁻¹ , the standard enthalpy of sublimation of M ( s ) is kJ mol ⁻¹ .

Step-by-step solution

According to Hess's Law and the Born-Haber cycle for the formation of an ionic solid MX ( s ) : H _ f = H _ sub + IE + 1 2 H _ diss + H _ eg + H _ lattice Substituting the given values into the equation: -400 = H _ sub + 520 + 1 2 (160) + (-300) + (-780) -400 = H _ sub + 520 + 80 - 300 - 780 -400 = H _ sub + 600 - 1080 -400 = H _ sub - 480 H _ sub = -400 + 480 = 80 ~kJ ~mol ⁻¹ Answer: 80