I'd be happy to help you balance the equation for the half reaction.
The first step is to identify the changes in oxidation states for each element involved in the reaction. In this case, U goes from an oxidation state of +4 to +6, which means it has gained 2 electrons. To represent this change, we include the symbol "2e-" in the equation.
Now, let's balance the atoms other than oxygen and hydrogen. In this case, we have U on the left-hand side and UO2 on the right-hand side. To balance the uranium atoms, we simply need to include a coefficient of 1 in front of both "U" and "UO2":
U --> UO2
Next, let's balance the oxygen atoms. On the left-hand side, we have 0 oxygen atoms, while on the right-hand side, we have 2 oxygen atoms in UO2. To balance this, we can add 2 water molecules (H2O) to the left-hand side:
U + 2H2O --> UO2
Now, let's balance the hydrogen atoms. On the left-hand side, we have 4 hydrogen atoms from the water molecules, while on the right-hand side, we have 2 hydrogen atoms in UO2. To balance this, we can add 2H+ ions (from an acidic solution) on the left-hand side:
U + 2H2O + 2H+ --> UO2
Finally, let's balance the charges. On the left-hand side, the total charge is +2 (from the two H+ ions), while on the right-hand side, the total charge is 0. To balance this, we need to add 2e- (two electrons) to the right-hand side:
U + 2H2O + 2H+ + 2e- --> UO2
And there you have it! The balanced equation for the half reaction is:
U + 2H2O + 2H+ + 2e- --> UO2
This equation represents the half reaction that occurs in an acidic solution when U^4+ is converted to UO2^+.