When `10g` of `AI` is used for reduction in each of the following alumino thermic reactions. Which reaction would generate more heat and by hwo much?
a. `2AI + Cr_(2)O_(3) rarr AI_(2)O_(3) +2Cr`
b. `2AI +Fe_(2)O_(3) rarr AI_(2)O_(3) +2Fe`
Standard heat of formation of `AI_(2)O_(3), Cr_(2)O_(3)`, and `Fe_(2)O_(3)` are `-1676 kJ, 1141 kJ`, and `-822.2 kJ`, respectively.

Explanation

Given,
`{:(2AI+(3)/(2)O_(2)rarrAI_(2)O_(3),,,DeltaH_(1)=-1676kJ..(i)),(2Cr+(3)/(2)O_(2)rarrCr_(2)O_(3),,,DeltaH_(2)=-1141kJ..(ii)),(2Fe+(3)/(2)O_(2)rarrFe_(2)O_(3),,,DeltaH_(3)=-822.2 kJ..(iii)):}`
To calculate ltbr. `DeltaH_(a) = ?`
For `2AI+ Cr_(2)O_(3)rarr AI_(2)O_(3) +2Cr ...(iv)`
Operate:
`DeltaH_(a) = DeltaH_(1)-DeltaH_(2)`
`=- 1676 -(-1141) =- 535 kJ`
`DeltaH_(b) = ?`
For `2AI +Fe_(2)O_(3) rarr AI_(2)O_(3) +2Fe ......(v)`
Operate:
`DeltaH_(b) = DeltaH_(1) -DeltaH_(3)`
`=- 1676 -(-822.2) =- 853.8 kJ`
For reaction (iv)
`2 xx 27 g` of AI produces` = 535 kJ` of heat
`10g` of AI produces `=(535xx10)/(2xx27) = 99.07 kJ`
For reaction (v)
`2 xx 27g` of AI produces `= 853.8 kJ` of heat
`10g` of AI produces `= (853.8xx10)/(54) = 158.11kJ`
Reaction (ii) produces more heat `= 158.11 -99.07`
`= 59.04 kJ`