First of all, the equation is actually Na + H20 -> NaOH + H2 since hydrogen gas will also be made when sodium reacts with water.
So this is a trick I learned. First put coefficients in front of each element/compound/molecule as A, B, C, and D, so then the equation would look like:
A Na+ B H2O -> C NaOH + D H2
To have a balanced equation means that there is the same amount of each element on each side of the arrow. Therefore you can set up equations like this:
Na: A = C
H: 2B (since there are two hydrogen atoms) = C + 2D
O: B = C
Because B = C and A = C, then B = A as well. We can just replace B and C with just A. This then makes the equation look like:
A Na + A H2O -> A NaOH + D H2
Since A = B, then also the hydrogen coefficient equation changes from 2B = C + 2D to 2A = A + 2D. Therefore, A = 2D, making the equation:
2D Na + 2D H2O -> 2D NaOH + D H2
What's the smallest number D can be in order for every coefficient to be a positive integer? D can be one, so now we can replace all the Ds in the equation with the number one. This will then look like
2 Na + 2 H2O -> 2 NaOH + H2
You can check by making sure that there are equal amounts of Na, H, and O on each side of the arrow. And when you do, you'll see that there are.
