Answer:
(A) ![\Delta H^{\circ }_{r}= -144 kJ](https://tex.z-dn.net/?f=%5CDelta%20H%5E%7B%5Ccirc%20%7D_%7Br%7D%3D%20-144%20kJ)
(B) ![\Delta H^{\circ }_{r}= - 2552kJ](https://tex.z-dn.net/?f=%5CDelta%20H%5E%7B%5Ccirc%20%7D_%7Br%7D%3D%20-%202552kJ)
Explanation:
(A) 2NO(g) + O₂(g) → 2NO₂(g)
![1/2 N_{2}(g)+O_{2}(g)\rightarrow NO_{2}(g), \Delta H^{\circ }_{a}=33.2 kJ....equation (a)](https://tex.z-dn.net/?f=1%2F2%20N_%7B2%7D%28g%29%2BO_%7B2%7D%28g%29%5Crightarrow%20NO_%7B2%7D%28g%29%2C%20%5CDelta%20H%5E%7B%5Ccirc%20%7D_%7Ba%7D%3D33.2%20kJ....equation%20%28a%29)
Now, multiplying equation (a) with 2:
⇒ ![N_{2}(g)+2 O_{2}(g)\rightarrow 2 NO_{2}(g)....equation (a)](https://tex.z-dn.net/?f=N_%7B2%7D%28g%29%2B2%20O_%7B2%7D%28g%29%5Crightarrow%202%20NO_%7B2%7D%28g%29....equation%20%28a%29)
Then equation b is reversed and multiplied with 2:
![2 NO(g)\rightarrow N_{2}(g)+ O_{2}(g)....equation (b)](https://tex.z-dn.net/?f=2%20NO%28g%29%5Crightarrow%20N_%7B2%7D%28g%29%2B%20O_%7B2%7D%28g%29....equation%20%28b%29)
Now by adding the equation (a) and equation (b), we get:
⇒ ![2 NO(g)+ \bcancel N_{2}(g)+\bcancel 2 O_{2}(g)\rightarrow 2 NO_{2}(g) +\bcancel N_{2}(g)+ \bcancel O_{2}(g)](https://tex.z-dn.net/?f=2%20NO%28g%29%2B%20%5Cbcancel%20N_%7B2%7D%28g%29%2B%5Cbcancel%202%20O_%7B2%7D%28g%29%5Crightarrow%202%20NO_%7B2%7D%28g%29%20%2B%5Cbcancel%20N_%7B2%7D%28g%29%2B%20%5Cbcancel%20O_%7B2%7D%28g%29)
⇒ 2NO(g) + O₂(g) → 2NO₂(g)
<u>Therefore, the enthalpy of the reaction:</u>
![\Delta H^{\circ }_{r}= 2\times \Delta H^{\circ }_{a} - 2\times \Delta H^{\circ }_{b}](https://tex.z-dn.net/?f=%5CDelta%20H%5E%7B%5Ccirc%20%7D_%7Br%7D%3D%202%5Ctimes%20%5CDelta%20H%5E%7B%5Ccirc%20%7D_%7Ba%7D%20-%202%5Ctimes%20%5CDelta%20H%5E%7B%5Ccirc%20%7D_%7Bb%7D)
![= (2\times33.2)- (2\times90.2)=66.4 - 180.4= -144 kJ](https://tex.z-dn.net/?f=%3D%20%282%5Ctimes33.2%29-%20%282%5Ctimes90.2%29%3D66.4%20-%20180.4%3D%20-144%20kJ)
(B) 4B(s)+3O₂(g) → 2B₂O₃(s)
![B_{2}O_{3}(s)+3H_{2}O(g)\rightarrow 3O_{2}(g)+B_{2}H_{6}(g), \Delta H_{a }^{\circ }=+2035 kJ...equation (a)](https://tex.z-dn.net/?f=B_%7B2%7DO_%7B3%7D%28s%29%2B3H_%7B2%7DO%28g%29%5Crightarrow%203O_%7B2%7D%28g%29%2BB_%7B2%7DH_%7B6%7D%28g%29%2C%20%5CDelta%20H_%7Ba%20%7D%5E%7B%5Ccirc%20%7D%3D%2B2035%20kJ...equation%20%28a%29)
![2B(s)+3H_{2}(g)\rightarrow B_{2}H_{6}(g), \Delta H_{b }^{\circ }= +36 kJ...equation (b)](https://tex.z-dn.net/?f=2B%28s%29%2B3H_%7B2%7D%28g%29%5Crightarrow%20B_%7B2%7DH_%7B6%7D%28g%29%2C%20%5CDelta%20H_%7Bb%20%7D%5E%7B%5Ccirc%20%7D%3D%20%2B36%20kJ...equation%20%28b%29)
![H_{2}(g)+1/2O_{2}(g)\rightarrow H_{2}O(l), \Delta H_{c }^{\circ }= -285 kJ...equation (c)](https://tex.z-dn.net/?f=H_%7B2%7D%28g%29%2B1%2F2O_%7B2%7D%28g%29%5Crightarrow%20H_%7B2%7DO%28l%29%2C%20%5CDelta%20H_%7Bc%20%7D%5E%7B%5Ccirc%20%7D%3D%20-285%20kJ...equation%20%28c%29)
![H_{2}O(l)\rightarrow H_{2}O(g), \Delta H_{d }^{\circ }=+44 kJ...equation (d)](https://tex.z-dn.net/?f=H_%7B2%7DO%28l%29%5Crightarrow%20H_%7B2%7DO%28g%29%2C%20%5CDelta%20H_%7Bd%20%7D%5E%7B%5Ccirc%20%7D%3D%2B44%20kJ...equation%20%28d%29)
Now multiplying equation (b) with 2, reversing equation (a) and multiplying with 2. Reversing equation (c) and (d) and multiplying both with 6.
![4B(s)+6H_{2}(g)\rightarrow 2B_{2}H_{6}(g)...equation (b)](https://tex.z-dn.net/?f=4B%28s%29%2B6H_%7B2%7D%28g%29%5Crightarrow%202B_%7B2%7DH_%7B6%7D%28g%29...equation%20%28b%29)
![6H_{2}O(l)\rightarrow 6H_{2}(g)+3O_{2}(g)...equation (c)](https://tex.z-dn.net/?f=6H_%7B2%7DO%28l%29%5Crightarrow%206H_%7B2%7D%28g%29%2B3O_%7B2%7D%28g%29...equation%20%28c%29)
![6H_{2}O(g)\rightarrow 6H_{2}O(l)...equation (d)](https://tex.z-dn.net/?f=6H_%7B2%7DO%28g%29%5Crightarrow%206H_%7B2%7DO%28l%29...equation%20%28d%29)
Now by adding the equations (a), (b), (c), (d); we get:
4B(s)+3O₂(g) → 2B₂O₃(s)
<u>Therefore, the enthalpy of the reaction: </u>
![\Delta H^{\circ }_{r}= -2\times \Delta H^{\circ }_{a} + 2\times \Delta H^{\circ }_{b} - 6 \times \Delta H_{c }^{\circ } - 6 \times \Delta H_{d }^{\circ }](https://tex.z-dn.net/?f=%5CDelta%20H%5E%7B%5Ccirc%20%7D_%7Br%7D%3D%20-2%5Ctimes%20%5CDelta%20H%5E%7B%5Ccirc%20%7D_%7Ba%7D%20%2B%202%5Ctimes%20%5CDelta%20H%5E%7B%5Ccirc%20%7D_%7Bb%7D%20-%206%20%5Ctimes%20%5CDelta%20H_%7Bc%20%7D%5E%7B%5Ccirc%20%7D%20-%206%20%5Ctimes%20%5CDelta%20H_%7Bd%20%7D%5E%7B%5Ccirc%20%7D%20)
![= -2\times (+2035 kJ)+ 2\times (+36 kJ) - 6 \times (-285 kJ)- 6 \times (+44 kJ) = -4070 + 72 + 1710 - 264 = - 2552kJ](https://tex.z-dn.net/?f=%3D%20-2%5Ctimes%20%28%2B2035%20kJ%29%2B%202%5Ctimes%20%28%2B36%20kJ%29%20-%206%20%5Ctimes%20%28-285%20kJ%29-%206%20%5Ctimes%20%28%2B44%20kJ%29%20%3D%20-4070%20%2B%2072%20%2B%201710%20-%20264%20%3D%20-%202552kJ)