Notice that the problem doesn't mention temperature or number of moles of gas, which means that they are being kept constant.
When that is the case, volume and pressure have an inverse relationship described by Boyle's Law.
Boyle's Law tells you that when pressure Increases, volume decreases, and when pressure decreases, volume increases.
Mathematically, this is expressed as
#color(blue)(|bar(ul(color(white)(a/a)P_1V_1 = P_2V_2color(white)(a/a)|)))" "#, where
In your case, the pressure decreases from
Rearrange the above equation and solve for
#P_1V_1 = P_2V_2 implies V_2 = P_1/P_2 * V_1#
Plug in your values to get
#V_2 = (4.4 color(red)(cancel(color(black)("atm"))))/(1.0color(red)(cancel(color(black)("atm")))) * "350 mL" = color(green)(|bar(ul(color(white)(a/a)"1540 mL"color(white)(a/a)|)))#
The answer is rounded to three sig figs.