Question #def0e

1 Answer
Mar 11, 2017

Answer:

#"7.02 L"#

Explanation:

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)))#

Here

  • #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 of gas and had an unknown volume #V_1#. After you add #1.25# moles, the total number of moles of gas present in the balloon will be equal to

#"4.51 moles + 1.25 moles = 5.76 moles"#

The volume of the balloon went from #V_1# to #"8.97 L"#. Right from the start, you can say that the volume increased, i.e. that

#V_1 < "8.97 L"#

because the number of moles of gas increased.

Rearrange the equation to solve for #V_1#

#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.