Question

# What is the enthalpy of the disproportion of MgCl if the enthalpy of formation of hypothetical MgCl is -125 $KJmol^{ -1 }$ and the $MgCl_{ 2 }$ is -642?A 767 $KJmol^{ -1 }$B 767 $KJmol^{ -1 }$C 392 $KJmol^{ -1 }$D 392 $KJmol^{ -1 }$

Hint: Try to figure out what is a disproportionate reaction. Try to find out oxidation states of magnesium in both compounds and then balance the reaction. The formation of a native form of an element involves no change in heat of reaction.

We know that some elements form a different type of compounds with the same element by exhibiting different valencies. Let us write the reaction of the formation of MgCl from its elements.
Formation of MgCl reaction:
$Mg+\frac { 1 }{ 2 } Cl_{ 2 }\rightarrow MgCl\quad \quad \triangle H=-125KJmol^{ -1 }$
Let this reaction be 1.
Formation of $MgCl_{ 2 }$ reaction:
$Mg+Cl_{ 2 }\rightarrow MgCl_{ 2 }\quad \quad \triangle H=-642KJmol^{ -1 }$
Let this reaction be 2.
In a disproportionate reaction, the same element will oxidize and reduce. Some atoms of the element will gain electrons and some other atoms will lose electrons. So, the same element will undergo oxidation and reduction. Magnesium exhibits a +2 oxidation state most of the time. In MgCl magnesium has a +1 oxidation state so the compound is unstable and it disproportionates.
Disproportion reaction is:
$2MgCl\rightarrow MgCl_2+Mg$
If the direction of the reaction is reversed the heat of the formation will change its sign.
The heat of formation of the above reaction will be
$\triangle H=2\times -\left( -125 \right) KJmol^{ -1 }+\left( -642 \right) KJmol^{ -1 }+0=250-642\quad KJmol^{ -1 }$
$\triangle H=-392KJmol^{ -1 }$

Therefore, option C is correct.

Note: Chlorine general oxidation state will be -1 in presence of lesser electronegative elements. Generally, we do not observe the formation of MgCl because Mg is stable in its +2 state. We need to multiply the coefficient of the compound with its heat of formation for obtaining heat of reaction.