Gas law question?

Question

An ideal gas occupies a volume of 3.2 L at 31oC and 303.0 mm Hg. What volume in L will it occupy at STP?

Answer 1

pv/t=PV/T
3.2*303/273+31=760*V/273
V=3.2*303*273/304*760
V=1.1456 L

Answer 2

The relevant equation is PV = nRT,
P = pressure
V = volume
n = no.of moles
R = the Gas Constant (8.314 JK-1mol-1)
T = temperature.

First of all, for the equation to work, you must have the right units.
Pressure needs to be in NEWTONS PER SQUARE METRE, also known as PASCALS (Pa).
1 mm Hg = 133.322 Pa.
Therefore, 303 mm Hg = 40396.6 Pa

Volume needs to be in CUBIC METRES (because pressure is in metre units as well).
1 cubic metre = 1000 litres.
Therefore, 3.2L = 0.0032 m3

Temperature needs to be in KELVINS.
0 K = 273 oC.
Therefore, 31 oC = 31 + 273 = 304 K

Now, if we rearrange PV = nRT, we get n = PV/RT
'n' is the amount of gas we are dealing with.
So, to begin with,
P(1) = 40396.6 Pa
V(1) = 0.0032 m3
R = 8.314 JK-1mol-1
T(1) = 304 K

Now, 'n' is always the same, because you are dealing with the same amount of gas throughout. In the second case, you have standard conditions, which are:
P(2) = 100000 Pa
T(2) = 298 K

Now, rearranging the equation PV = nRT gives n = PV/RT. Since n is always the same, n = P(1)V(1)/RT(1) in the intial case, and n = P(2)V(2)/RT(2) in the second case.

Therefore,

P(1)V(1)/RT(1) = P(2)V(2)/RT(2)

'R' is on both sides of the equation and can be cancelled out to simplify.
So,
P(1)V(1)/T(1) = P(2)V(2)/T(2)

Substituting in the numbers above works out as :

0.425 = 335.6V(2)

Rearrange:
V(2) = 0.425/335.6 = 0.0013 m3 = 1.27 L.

Answer 3

Lancenigo di Villorba (TV), Italy

Since you wrote me about "Ideal Gas", I refer to "Ideal Gas law" at 303 mmHg = 0.4 atm as follows

n = P * V / (R * T) = (0.399 * 3.2) / (0.0821 * 304.16) =
= 0.051 mol

so I know the mole's number like 0.050.
This amount may occupy a particular volume when I refer to Standard Conditions (0°C = 273.16 K and 1 atm)

Vstd = n * R * Tstd / Pstd = 0.051 * 0.0821 * 273.16 / 1 =
= 1.14 L

I hope this helps you.

Answer 4

now as we know that,

(P * V) / T =constt.

P1= 303 , T1= 304K, V1= 3.2L, P2=760mm of Hg , T2= 273k

( 303* 3.2)/304 = (760* V2)/273

V2= (303*3.2*273)/(304* 760) = 1.145L