CaCO3 + heat = CaO + CO2

Need a little help with this one because there's ''heat''.

Wow, it's been forever since I've done this, but it looks fun! So can I assume that the 3 and the 2 are subscripts, right? Like... small numbers hanging down at the bottom of the element?  As far as I recall, heat doesn't do anything to the actual process of balancing. It's been 11 or 12 years since I took chemistry, so we might want to make sure from someone else more freshly in the subject.  Or we could just google what effect heat has.  

Would you know how to balance it if the heat wasn't involved? (Trying to get a feel for how much you know about the process and where one would need to start in an explanation for you)

Well I'm really not sure about this one, but here's another one I attempted on my homework.

mso-bidi-theme-font:minor-bidi">Al (s) + HNO₃ (aq) àmso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:minor-bidi"> Al(NO₃)₃
(aq) + H₂ (g)

2 A₁
(s) + 6 HNO₃ (aq) = 2 A₁(NO₃)₃
(aq) + 3 H₂ (g)

And yes, those are subscripts.

xxeliza321xx : What you want to do is add Coefficients to the front of the compound. Coefficients multiply each element by that number. So lets say you have 2O2 you would then have 4 Oxygen atoms. 

Now for your first problem:
CaCO3 + heat = CaO + CO2

First count each element in the reactant and each element in the products.
In the reactants you have
1 Calcium
1 Carbon
3 Oxygen

Now in the Products you have
1 Calcium
3 Oxygen
1 Carbon

The elements in your reactants are equal to the elements in your products therefore your equation should already be balanced.

Now moving onto your second problem: 
Al (s) + HNO3 (aq) --> Al(NO3)3(aq) + H2 (g)

First off the terms (s) (Aq) and (G) means the element is in a solid aqueous and gaseous state respectively so you don't have to worry about those. What you want to do is worry about wants in the reactants (left of the arrow) and what's in the products (right of the arrow) 

So for your reactants you have:
1 Aluminum (Al)
1 Hydrogen (H)
1 Nitrogen (N)
3 Oxygen (O)

Now your products will be a little tricky
In your products you have
1 Aluminum (Al)
3 Nitrogen (Take the three outside the parenthesis and multiply it by 1 since there's no subscript that means that its an understood 1)
9 Oxygen
2 Hydrogen

Now your next step is to start balancing your equation. As you may have noticed you have the same amount of Aluminum on both sides. Now moving on you have different mounts of Nitrogen in your products so go to the left and add a 3 in front of HNO3

Al (s) +3 HNO3 (aq) --> Al(NO3)3(aq) + H2 (g)
Now you will notice that your equation still isn't balanced correctly and that you have 3 Hydrogen in your reactant and 2 Hydrogen in your product. So change the 3 you just added to a 6 and place a 3 in front of H3

Al (s) +6 HNO3 (aq) --> Al(NO3)3(aq) + 3H2 (g)
Now you're still not done! This is actually quite normal in chemistry so don't worry if you don't get it right the first couple of times. Now you'll notice that you have 6 Nitrogen and 18 Oxygen in your reactant while you have 3 Nitrogen and 9 Oxygen in your Product. So what do you do? Add a two in front of Al(NO3)3 

Al (s) +6 HNO3 (aq) -->2 Al(NO3)3(aq) +3 H2 (g)

Now since you added the 2 in front of Al(NO3)3 your aluminums are not even. So add a 2 in front of Al on your reactant side (left side)

2Al (s) +6 HNO3 (aq) -->2 Al(NO3)3(aq) +3 H2 (g)

After you do that recount each element to make sure that each element is even to the other side. You will notice that both sides are even therefore:
2Al (s) +6 HNO3 (aq) -->2 Al(NO3)3(aq) +3 H2 (g)
Is your final answer.

Now using that logic do you think you can handle the next one? If not Ill happily help you!

I got it. Thanks.