# Question 5d932

Jul 16, 2017

${V}_{1} = 318$ $\text{mL}$

#### Explanation:

We're asked to find the original volume of ${\text{F}}_{2}$ using gas equations.

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

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

where

• ${P}_{1}$ is the original pressure, given as $900.$ $\text{torr}$

• ${V}_{1}$ is the original volume (what we're trying to find)

• ${P}_{2}$ is the final pressure, given as $1.5$ $\text{atm}$

• ${V}_{2}$ is the final volume, given as $250.$ $\text{mL}$

We need the units for pressure to be consistent, so let's convert the $900$ $\text{torr}$ quantity to $\text{atm}$:

900cancel("torr")((1color(white)(l)"atm")/(760cancel("torr"))) = 1.18 $\text{atm}$

Plugging in known values, and solving for the original volume, ${V}_{1}$, we have

V_1 = (P_2V_2)/(P_1) = ((1.5cancel("atm"))(250color(white)(l)"mL"))/(1.18cancel("atm")) = color(red)(318 color(red)("mL"#

which I'll round to $3$ significant figures, the amount given for the other volume measurement.