Question

potassium + water gives rise to potassium Hydroxide + hydrogen gas balance the equation

Answer 1

Given, potassium + water gives rise to potassium hydroxide + hydrogen gas
Let's first write the equation unbalanced and then balance it.
                                    K + H₂O → KOH + H₂↑
Now, we cannot alter the compounds, and we should see that the number of atoms of a particular element are equal on the reactants side as well as on the products side.
Let's, first compare the number of atoms of Hydrogen ( you can select any                                                                  other atom if you wish to)
           Reactants side = 2
            Products side = 3
Now let's balance only hydrogens, 
                                K + 2 H₂O → 2 KOH + 2 H₂↑
Now, the hydrogens on
           Reactants side = 4
           Products side = 4
In this partly balanced equation, hydrogens are balanced.
Now let's compare potassium atoms on both the sides.
           Reactants side = 1
           Products side = 2
Now, let's balance potassium atoms,
                            2 K + 2 H₂O → 2 KOH + H₂↑
In this partly balanced equation, the potassium atoms on
           Reactants side = 2
           Products side = 2
Now, we have to check for hydrogen atoms also,
            Reactants side = 4
            Products side = 4
Now, in this equation both hydrogen atoms and potassium atoms are balanced.
Now, let's check for oxygen atoms,
           Reactants side = 2
           Products side = 2
∴ The balanced equation is
                         2 K + 2 H₂O → 2 KOH + H₂ ↑

Hope my answer helps you..