Question

The heat of formation(ΔH_f^O) for AsCl₃(l) is -305.0 kJ/mol, and ΔH^O = -548.8 kJ for the following reaction:

2 As (s) + 3 Cl₂ (l) --> 2 AsCl₃ (l)

Find the heat of vaporization for Cl_2. (Vaporization is a phase change from liquid to gas, so the heat of vaporization would be ΔH^O for the process Cl₂(l) --> Cl₂(g).)

Answer 1

Given that 2 As (s) + 3 Cl2 (l) --> 2 AsCl3 (l)

  ΔH_f^o [AsCl3 (l) ]=-305.0 kJ/mol

   ΔH^o = -548.8 kJ

We know that  ΔH_f^o [As(s) ]= 0

ΔH^o = ΔH_f^o(products) - ΔH_f^o(reactants)

   ΔH^o =  2x ΔH_f^o [AsCl3 (l) ] - { 3xΔH_f^o [Cl2(l)]+ ΔH_f^o [As(s)] }

-548.8 kJ = 2x -305.0 kJ/mol - { 3xΔH_f^o [Cl2(l)]+ 0 }

-548.8 kJ = -610.0 kJ/mol - { 3xΔH_f^o [Cl2(l)] }

3xΔH_f^o [Cl2(l)] =  -610.0 kJ/mol + 548.8 kJ

ΔH_f^o [Cl2(l)] = -20.4 kJ

Heat of vaporization for Cl2

Cl2(l) --> Cl2(g)

From above, ΔH_f^o [Cl2(l)] = -20.4 kJ

We know that ΔH_f^o [Cl2(g)] = 0

Heat of vaporization  ΔH^o = ΔH_f^o [Cl2(g)] - ΔH_f^o [Cl2(l)]

= 0 - { -20.4 kJ }

= + 20.4 kJ

  ΔH^o = +20.4 kJ

Hence, heat of vaporization for Cl2 = +20.4 kJ