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Chemistry help

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In some fireworks there is a reaction between powdered aluminium and powdered barium nitrate in which heat is evolved and an unreactive gas is produced.
What is the equation of the reaction
A 2Al +Ba(NO3)2 ---> Al2O3 + BaO + 2NO
B 4Al + 4Ba(NO3)2 ---> 2Al2O3 + 4Ba(NO2)2 + O2
C 2Al + 3Ba(NO3)2 ---> 5Al2O3 + 3BaO + 3N2
D 2Al + 18Ba(NO3)2 ---> 10Al(NO3)3 + 18BaO + 3N2
 
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In some fireworks there is a reaction between powdered aluminium and powdered barium nitrate in which heat is evolved and an unreactive gas is produced.
What is the equation of the reaction
A 2Al +Ba(NO3)2 ---> Al2O3 + BaO + 2NO
B 4Al + 4Ba(NO3)2 ---> 2Al2O3 + 4Ba(NO2)2 + O2
C 2Al + 3Ba(NO3)2 ---> 5Al2O3 + 3BaO + 3N2
D 2Al + 18Ba(NO3)2 ---> 10Al(NO3)3 + 18BaO + 3N2

As an unreactive gas produced so option A is eliminated as there's NO gas which is reactive .......
option B and D are not possible bcz the reaction is highly exothermic so 4Ba(NO2)2 and 10Al(NO3)3 shouldnt be in the products as they will be decomposed by the heat given off from the reaction .....
the option left is C so the ans is C.
 
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