If 2.0 moles of nitroglycerin explodes, what is the total number of moles of gaseous products produced?
4 C3H5N3O9(l) --> 12 CO9g) + 10 H2O(g) + 6 N2(g) + O2(g)

How many moles of Al(l) are produced if 4.5 moles of Al2O3(s) reacts?

How many moles of C(s) are necessary to produce 3.2 moles of Al(l)?

What is the formula, how do you manipulate it and how to solve these questions?

I really need your help, please, thank you so much in advance.

Easy, the moles are in the equation (are you sure that the equation is correct?):
4 moles nitro give 12 moles CO, 10 moles water, 6 moles nitrogen, one mole oxygen, all together 29 moles of gas. (note that the oxygen would probably burn part of the CO, but that is another story).
So, 2 moles nitro will give 14.5 moles of gas.
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If one were able to extract aluminum from its oxide, the equation would be:
Al2O3 + something -> 2Al + something else containing oxygen
- or, one mole Al2O3 gives 2 moles Al, so 4.5 moles Al2O3 will give 9 moles Al.