# 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?

Jun 13, 2017

$9.0$ $\text{L}$

#### Explanation:

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

${P}_{1} {V}_{1} = {P}_{2} {V}_{2}$ (with constant temperature)

Since we need to find the final volume, let's rearrange this equation to solve for ${V}_{2}$:

${V}_{2} = \frac{{P}_{1} {V}_{1}}{{P}_{2}}$

Our known variables are

• ${P}_{1}$ - $12$ $\text{atm}$

• ${V}_{1}$ - $1.5$ $\text{L}$

• ${P}_{2}$ - $2.0$ $\text{atm}$

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.