Avogadro's Law states that when temperature and pressure are kept constant, the volume of a gas is directly proportional to the number of moles of gas present in the container.
Mathematically, this is written as
#color(blue)(ul(color(black)(V_1/n_1 = V_2/n_2)))#
#V_1#and #n_1#represent the volume and number of moles of gas at an initial state
#V_2#and #n_2#represent the volume and the number of moles of gas at a final state
So, you know that initially, the balloon contained
#"4.51 moles + 1.25 moles = 5.76 moles"#
The volume of the balloon went from
#V_1 < "8.97 L"#
because the number of moles of gas increased.
Rearrange the equation to solve for
#V_1/n_1 = V_2/n_2 implies V_1 = n_1/n_2 * V_2#
Plug in your values to find
#V_1 = (4.51 color(red)(cancel(color(black)("moles"))))/(5.76color(red)(cancel(color(black)("moles")))) * "8.97 L" = color(darkgreen)(ul(color(black)("7.02 L")))#
The answer is rounded to three sig figs.
As predicted, the volume increased as a result of the increase in the number of moles of gas present in the balloon.