Question

Question #5d932

Answer 1

`V_1 = 318` `"mL"`

Explanation:

We're asked to find the original volume of `"F"_2` using gas equations.

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

`P_1V_1 = P_2V_2`

where

• `P_1` is the original pressure, given as `900.` `"torr"`

• `V_1` is the original volume (what we're trying to find)

• `P_2` is the final pressure, given as `1.5` `"atm"`

• `V_2` is the final volume, given as `250.` `"mL"`

We need the units for pressure to be consistent, so let's convert the `900` `"torr"` quantity to `"atm"`:

`900cancel("torr")((1color(white)(l)"atm")/(760cancel("torr"))) = 1.18` `"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.