You follow a systematic procedure to balance the equation.
The other product is calcium hydroxide.
Start by converting the words to a chemical equation.:
"CaC"_2 + "H"_2"O" → "C"_2"H"_2 + "Ca(OH)"_2
A method that often works is first to balance everything other than "O" and "H", then balance "O", and finally balance "H".
Another useful procedure is to start with what looks like the most complicated formula.
The most complicated formula looks like "Ca(OH)"_2. We put a 1 in front of it to remind ourselves that the number is now fixed.
"CaC"_2 + "H"_2"O" → "C"_2"H"_2 + color(red)(1)"Ca(OH)"_2
Balance "Ca":
We have "1 Ca" on the right, so we need "1 Ca" on the left. We put a 1 in front of the "CaC"_2.
color(orange)(1)"CaC"_2 + "H"_2"O" → "C"_2"H"_2 + color(red)(1)"Ca(OH)"_2
Balance "C":
We have fixed "2 C" on the left. We need "2 C" on the right. Put a 1 in front of "C"_2"H"_2.
color(orange)(1)"CaC"_2 + "H"_2"O" → color(blue)(1)"C"_2"H"_2 + color(red)(1)"Ca(OH)"_2
Balance "O":
We have fixed "2 O" on the right. We need "2 O" on the left. Put a 2 in front of "H"_2"O".
color(orange)(1)"CaC"_2 + color(purple)(2)"H"_2"O" → color(blue)(1)"C"_2"H"_2 + color(red)(1)"Ca(OH)"_2
Every formula now has a coefficient. We should have a balanced equation.
Let's check.
bb("Atom" color(white)(m)"lhs"color(white)(m)"rhs")
color(white)(m)"Ca"color(white)(mml)1color(white)(mml)1
color(white)(m)"C"color(white)(mmm)2color(white)(mml)2
color(white)(m)"H"color(white)(mmm)4color(white)(mml)4
color(white)(m)"O"color(white)(mmm)2color(white)(mml)2
All atoms balance. The balanced equation is
"CaC"_2 + "2H"_2"O" → "C"_2"H"_2 + "Ca(OH)"_2
