This is an incomplete question, here is a complete question.
Manganese commonly occurs in nature as a mineral. The extraction of manganese from the carbonite mineral rhodochrosite, involves a two-step process. In the first step, manganese (II) carbonate and oxygen react to form manganese (IV) oxide and carbon dioxide:
![2MnCO_3(s)+O_2(g)\rightarrow 2MnO_2(s)+2CO_2(g)](https://tex.z-dn.net/?f=2MnCO_3%28s%29%2BO_2%28g%29%5Crightarrow%202MnO_2%28s%29%2B2CO_2%28g%29)
In the second step, manganese (IV) oxide and aluminum react to form manganese and aluminum oxide:
![3MnO_2(s)+4Al(s)\rightarrow 3Mn(s)+2Al_2O_3(s)](https://tex.z-dn.net/?f=3MnO_2%28s%29%2B4Al%28s%29%5Crightarrow%203Mn%28s%29%2B2Al_2O_3%28s%29)
Write the net chemical equation for the production of manganese from manganese (II) carbonate, oxygen and aluminum. Be sure your equation is balanced.
Answer : The net chemical equation for the production of manganese is:
![6MnCO_3(s)+3O_2(g)+8Al(s)\rightarrow 6CO_2(g)+6Mn(s)+4Al_2O_3(s)](https://tex.z-dn.net/?f=6MnCO_3%28s%29%2B3O_2%28g%29%2B8Al%28s%29%5Crightarrow%206CO_2%28g%29%2B6Mn%28s%29%2B4Al_2O_3%28s%29)
Explanation :
The given two chemical reactions are:
(1) ![2MnCO_3(s)+O_2(g)\rightarrow 2MnO_2(s)+2CO_2(g)](https://tex.z-dn.net/?f=2MnCO_3%28s%29%2BO_2%28g%29%5Crightarrow%202MnO_2%28s%29%2B2CO_2%28g%29)
(2) ![3MnO_2(s)+4Al(s)\rightarrow 3Mn(s)+2Al_2O_3(s)](https://tex.z-dn.net/?f=3MnO_2%28s%29%2B4Al%28s%29%5Crightarrow%203Mn%28s%29%2B2Al_2O_3%28s%29)
First we are multiplying reaction 1 by 3, and reaction 2 by 2, we get:
(1)
(2) ![6MnO_2(s)+8Al(s)\rightarrow 6Mn(s)+4Al_2O_3(s)](https://tex.z-dn.net/?f=6MnO_2%28s%29%2B8Al%28s%29%5Crightarrow%206Mn%28s%29%2B4Al_2O_3%28s%29)
Now we are adding both the reactions, we get the overall chemical reaction.
![6MnCO_3(s)+3O_2(g)+6MnO_2(s)+8Al(s)\rightarrow 6MnO_2(s)+6CO_2(g)+6Mn(s)+4Al_2O_3(s)](https://tex.z-dn.net/?f=6MnCO_3%28s%29%2B3O_2%28g%29%2B6MnO_2%28s%29%2B8Al%28s%29%5Crightarrow%206MnO_2%28s%29%2B6CO_2%28g%29%2B6Mn%28s%29%2B4Al_2O_3%28s%29)
The
is common on both side, by cancelling it, we get:
The net chemical equation for the production of manganese is:
![6MnCO_3(s)+3O_2(g)+8Al(s)\rightarrow 6CO_2(g)+6Mn(s)+4Al_2O_3(s)](https://tex.z-dn.net/?f=6MnCO_3%28s%29%2B3O_2%28g%29%2B8Al%28s%29%5Crightarrow%206CO_2%28g%29%2B6Mn%28s%29%2B4Al_2O_3%28s%29)