Since the metal forms the hydroxide "XOH", it must be an alkali metal.
That means the gas it creates is hydrogen, "H"_2.
The unbalanced equation is
"X" color(white)(l)+ "H"_2"O" → "XOH" + "H"_2
Step 1. Start by putting a 1 in front of the most complicated formula. Let's pick "H"_2"O".
"X" color(white)(l)+ color(red)(1)"H"_2"O" → "XOH" + "H"_2"O".
Step 2. Balance "O".
Put a 1 in front of "XOH".
"X"color(white)(l) + color(red)(1)"H"_2"O" → color(blue)(1)"XOH" + "H"_2
Step 3. Balance "H".
There is no way to balance "H" without using fractions.
We start over, multiplying all our old coefficients by 2.
"X"color(white)(l) + color(red)(2)"H"_2"O" → color(blue)(2)"XOH" + "H"_2
Now, we have fixed 4 "H" atoms on the left and 2 on the right.
We can get 4 "H" atoms on the right by putting a 1 in front of "H"_2.
"X"color(white)(l) + color(red)(2)"H"_2"O" → color(blue)(2)"XOH" + color(orange)(1)"H"_2
Step 4. Finally, balance "X".
Put a 2 in front of "X".
color(green)(2)"X" + color(red)(2)"H"_2"O" → color(blue)(2)"XOH" + color(orange)(1)"H"_2
The equation should now be balanced.
Step 5. Check that atoms balance.
"Atom"color(white)(m)"LHS"color(white)(m)"RHS"
stackrel(————————)(color(white)(m)"X"color(white)(mmm)2color(white)(mmll)2)
color(white)(m)"H"color(white)(mmm)4color(white)(mmll)4
color(white)(m)"O"color(white)(mmm)2color(white)(mmll)2
All atoms balance.
The balanced equation is
2"X" + 2"H"_2"O" → 2"XOH" + "H"_2
