Question

Given that $AB$ , ${A_2}$ and ${B_2}$ ​ are diatomic molecules. If the bond enthalpies of $AB$ , ${A_2}$ and ${B_2}$ ​ are in the ratio $1:1:0.5$ and enthalpy of formation of $AB$ from ${A_2}$ and ${B_2}$ ​ is $ - 100kJmo{l^{ - 1}}$. What is the bond energy of ${A_2}$ ​?
A. $200KJmo{l^{ - 1}}$
B. $100KJmo{l^{ - 1}}$
C. $300KJmo{l^{ - 1}}$
D. $400KJmo{l^{ - 1}}$

Answer 1

Hint: As we know that write the common balanced equation of the reaction and make sure to make it for 1 mole of $AB$ . You are given the enthalpy of reaction and a ratio of bond enthalpies, derive an equation from the reaction and put the values to get the value of bond enthalpy of ${A_2}$ ..

Complete step by step answer:
Let’s write the initial equation which will be required to solve this question. The equation is given down below:
${{\text{A}}_2}{\text{ + }}{{\text{B}}_2} \to {\text{2AB}}$
We are given that the bond enthalpies are in the ratio of $1:1:0.5$ for ${A_2}:AB:{B_2}$ , also the enthalpy of formation for AB is -100KJ/mol. So the formation of AB will take place if half of $A_2 $ and half of $B_2 $ reacts which means
$\dfrac{1}{2}{{\text{A}}_2}{\text{ + }}\dfrac{1}{2}{{\text{B}}_2} \to {\text{AB}}$
Hence the enthalpy of this reaction is -100 KJ/mol. Now taking the bond enthalpy of $A_2 $ as x we get the equation
$\dfrac{1}{2}x{\text{ + }}\dfrac{1}{2}(\dfrac{x}{2}) - {\text{ }}x{\text{ = }} - 100{\text{ KJmo}}{{\text{l}}^{ - 1}}$
Solving this we will get the equation
$\dfrac{x}{4} = 100{\text{ KJmo}}{{\text{l}}^{ - 1}}$
Solving this we are getting $x = 400KJmo{l^{ - 1}}$

So, the correct answer is Option D.

Note: In many reactions it is necessary that we calculate the heat of the reaction and at this point the enthalpy of the reaction comes into the picture. Not only theoretically but practically also enthalpy values come handy. In calculating the refrigeration effect and the efficiency of the engine, enthalpy plays a huge role in calculating all these. As we know that the extensive properties like energy, volume and enthalpy depend on the mass of the system. For example, if the mass of the system gets doubled, the enthalpy of the system may also get doubled.