# How to find Volume at STP?

I’m so confused. I’m being asked to find the volume of “a gas” (not specified) at STP if 317 mL of the gas was collected at 29.7 C and 96 kPa. I know there’s something to do here since my peers got answers of something above 200 but I don’t know what I need to do to find the answer. I’d appreciate a push in the right direction, but not necessarily the answer bc just the answer isn’t helpful next time I need to do it. Thanks

### 5 Answers

- Dr WLv 72 months agoFavourite answer
from the ideal gas law

.. PV = nRT

for 2 gases... since R is a constant..

.. P1V1 / (n1T1) = R = P2V2 / (n2T2)

ie

.. P1V1 / (n1T1) = P2V2 / (n2T2)

here's how you use that 1 equation

.. (1) write it down

.. (2) rearrange for your desired unknown

.. (3) identify and cancel anything held constant

.. (4) plug in your values and chug out the result

.. .. ..remember... T must be absolute.. K or R.. never °C, nor °F

**********

this problem

step (1) start with

.. P1V1 / (n1T1) = P2V2 / (n2T2)

step (2) rearrange for V2

.. V2 = V1 * (P1 / P2) * (T2 / T1) * (n2 / n1)... <---- note the grouping!

step (3) n is constant.. why? (1) the problem states "a gas" implying no gas is added nor removed, (2) the problem doesn't mention adding or removing gas, (3) we couldn't solve this if n was not constant. So that n2 = n1 and that term drops out. leaving

.. V2 = V1 * (P1 / P2) * (T2 / T1)

step (4).. STP = 101.325 kPa and 273.15K.. verify this!

.. V2 = 317 mL * (96 kPa / 101.325 kPa) * (273.15 K / 302.85K)

.. V2 = ___ mL

you get to finish

************

one thing.. IF the gas was collected "over water", you'll need to subtract the vapor pressure of water at that 29.7°C (302.85K) from 96 kPa to get the starting pressure of the gas/

- Roger the MoleLv 72 months ago
(317 mL) x (273.15 K) / (29.7 + 273.15) K x (96 kPa / 100 kPa) = 274 mL

[billrussell42: There is nothing misleading or requiring guessing. A volume is given at 29.7°C and 96 kPa, then the question asks what would be is the new volume at STP.]

- JimLv 72 months ago
STP is defined as exactly 100 kPa of pressure (0.986 atm) and 273 K (0°C), any gas at STP has a volume of 22.4 L per mole of gas.

PV = nRT

since nR is constant (in this case), PV/T₁ = PV/T₂

Solve for V₂

V₂ = (PV/T₁) (T/P₂)

Convert your temps to absolute (+273.15°C), insert your values, and plug into your calculator.

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- billrussell42Lv 72 months ago
first of all your question is misleading. STP, standard temperature and pressure, is 0ºC & 1 ATM, which is NOT 29.7ºC and 96 kPa.

making some guesses, the gas starts at 317 mL, 29.7ºC, 96 kPa. and you want the volume at STP ?? also which STP, there are two. I'll use the old one.

1 atm = 101.325 kPa

V₂ = P₁V₁T₂/T₁P₂ = (96)(317)(273.16) / (273.16+29.7)(101.325)

V₂ = 271 mL

Combined Gas law

P₁V₁/T₁ = P₂V₂/T₂

V₂ = P₁V₁T₂/T₁P₂

pressure and temperature are absolute

STP = 0ºC & 1 ATM (new 100 kPa)