A 1.5 liter flask is filled with nitrogen at a pressure of 12 atmospheres. What size flask would be required to hold this gas at a pressure of 2.0 atmospheres?

Question

Peyton Adams · Accepted Answer

#9.0# #"L"#

To solve this equation, we can use the pressure-volume relationship of gases, illustrated by Boyle's law:

#P_1V_1 = P_2V_2# (with constant temperature)

Since we need to find the final volume, let's rearrange this equation to solve for #V_2#:

#V_2 = (P_1V_1)/(P_2)#

Our known variables are

#P_1# - #12# #"atm"#

#V_1# - #1.5# #"L"#

#P_2# - #2.0# #"atm"#

Plugging these into the equation we have

#V_2 = ((12cancel("atm"))(1.5"L"))/(2.0cancel("atm")) = color(red)(9.0# #color(red)("L"#

Thus, when a #1.5#-liter flask containing gas with a pressure of #12# atmospheres is subjected to a decrease in pressure to #2.0# atmospheres, at constant temperature the volume will expand to #color(red)(9.0# liters.

Luna Chen · Answer

undefined To determine the size of the flask required to hold the nitrogen gas at a pressure of 2.0 atmospheres, we can use Boyle's Law, which states that the pressure of a gas is inversely proportional to its volume when temperature is constant.

Boyle's Law equation: P1V1 = P2V2

Where:
P1 = initial pressure (12 atmospheres)
V1 = initial volume (1.5 liters)
P2 = final pressure (2.0 atmospheres)
V2 = final volume (unknown)

Rearranging the equation to solve for V2:

V2 = (P1 * V1) / P2

Substituting the given values:

V2 = (12 atm * 1.5 L) / 2 atm
V2 = 9.0 L

So, a flask with a volume of 9.0 liters would be required to hold the nitrogen gas at a pressure of 2.0 atmospheres.