Final answer:
To balance the given unbalanced equation and determine the moles of Ba(OH)2 needed to neutralize HC2H3O2, you need to multiply the HC2H3O2 by 2 and use the mole ratio from the balanced equation.
Step-by-step explanation:
To balance the given unbalanced equation HC2H3O2 (aq) + Ba(OH)2 (aq) -> H2O (l) + Ba(C2H3O2)2 (aq), you need to ensure that the number of atoms on both sides of the equation is equal. In this case, there are 2 hydrogen atoms on the left side and 4 hydrogen atoms on the right side, so you need to multiply the HC2H3O2 on the left side by 2:
2 HC2H3O2 (aq) + Ba(OH)2 (aq) -> H2O (l) + Ba(C2H3O2)2 (aq)
To determine the moles of Ba(OH)2 required to neutralize 0.461 mole of HC2H3O2, we use the mole ratio from the balanced equation. The ratio is 1 mole of Ba(OH)2 to 2 moles of HC2H3O2. Therefore, to neutralize 0.461 mole of HC2H3O2, you would need:
0.461 mole HC2H3O2 x (1 mole Ba(OH)2 / 2 moles HC2H3O2) = 0.2305 mole Ba(OH)2