A sample of a gas occupies a volume of 27.8 L at 29 ºC and 720 . torr. What will be the new volume if the temperature increases to 64 ºC and the pressure decreases to 465 torr?

Answer 1

We will first look at which variables of the gas law are present. Then, we will choose which equation contains only the variables that we have.

Here are the possible gas law equations we could use:

PV = nRT

P1V1 = P2V2

P1/T1 = P2/T2

V1/T1 = V2/T2

P1V1/T1 = P2V2/T2

First, we are given “volume of 27.8 L at 29 deg C and 720. torr.” From this, we can identify V1, T1, and P1.

V1 = 27.8 L

T1 = 29 deg C

P1 = 720 torr

Next, we are asked “what will be the new volume,” which tells us that our unknown is V2

V2 = ?

Finally, we are told the new temperature is 64 deg C and the new pressure is 465 torr. These will be T2 and P2

T2 = 64 deg C

P2 = 465 torr

****Something super important to note****

Temperature must be in Kelvin!!!! For all of these equations - no matter what. We must convert Celsius to kelvin.

P1 and P2 can be any unit they want, as long as they match.

V1 and V2 can be any unit they want, as long as they match.

n must be in moles.

So before we can choose an equation, we need temperature to be in kelvin:

Celsius + 273 = Kelvin

T1: 29C + 273 = 302K

T2: 64C + 273 = 337K

P1 is torr and P2 is torr so they match

V1 is Liters so that means V2 will come out in Liters

Now for calculation, we have

P1 = 720 torr P2 = 465 torr

V1 = 27.8 L V2 = ?

T1 = 302 K T2 = 337 K

We can only use an equation that has P V T in it and no other letters. It looks like the last equation is the correct one!

P1V1/T1 = P2V2/T2

We are looking for V2. Let’s plug in what we have:

(720)*(27.8) / 302 = (465)*V2 / 337

It is your preference on how you get V2 by itself, but one method that works for all gas laws is to start with cross multiplying —> the bottom of the left side will multiply with the top of the right side, and the bottom of the right side will multiply with the top of the left side. That way, there will be no more fractions.

720 * 27.8 * 337 = 465 * V2 * 302 multiply it out

6745392 = 140430 * V2 divide 140430 to the other side

6745392 / 140430 = V2

48.033838 = V2

Lastly, we will decide significant digits and units.

For units, we must match V1 —> the units are Liters (L)

For sig figs, we look to the original numbers given:

27.8 29 720. 64 465

The smallest number of sig figs here is 2, so we can only keep 2 significant digits in our answer:

V2 = 48. L