Question

Which of these gases, if any, is behaving ideally?

Gas I. A 0.357-mol sample takes up 10.2 L at STP.
Gas II. Under 85.5 mmHg of pressure and at 258 K, a full 23.0 L container holds 0.140 moles of gas.
Gas III. At 50.0 °C, a 75.0 L container holds 6.70 moles of gas under 240. kPa of pressure.

Gas I only

Gas II only

Gas III only

None of these gases are behaving ideally.

Answer 1

gas 1) Using ideal gas equation ,PV=nRT

n/V=P/RT

n=mol of gas=0.357 mol

Volume=V=10.2L

R=universal gas constant=0.0821L atm/Kmol

standard T=273K

std P=1atm

So for ideal gas( P/RT)ideal=1atm/(0.0821Latm/K.mol)*273K=0.0446 mol/L

for given gas ,n/V=0.357mol/10.2L=0.035 mol/L=P/RT is not equal to (P/RT)ideal.So it is not ideal

gas ll

P1=85.5 mmhg=85.5mmhg/760mmhg/atm=0.112 atm

V1=23.0L

T1=258K

at STP,

P2=1 atm

T2=273K

V2=22.4L

P1V1/T1=0.112 atm*23L/258K=0.01 atmL/K=nR

for ideal gas,p2V2/T2=1atm*22.4L/273K=0.0821 atm/LK

As P1V1/T1 is not equal to P2V2/T2 ,gas 2 is not ideal

gas lll) At 50.0 °C, a 75.0 L container holds 6.70 moles of gas under 240. kPa of pressure.

T1=50+273=323K

P1=240KPa*(1 atm/101.325 kpa)=2.369 atm

V1=75L

n=6.7mol

R=PV/nT=2.369atm*75L/6.7mol*323K=0.0821 Latm/K.mol

R(ideal)=1atm*22.4L/1mol*273K=0.0821Latm/K.mol

Rgas=R(ideal) so this gas is behaving ideally

Answer:gas lll is behaving ideally