What volume will be occupied if the gas is moved to a new area with 2.00 ATM and 88 degrees C?

Question

a gas at capital S capital T capital P occupies a volume of 100. ml. What volume will be occupied if the gas is moved to a new area with 2.00 ATM and 88 degrees C? Capital S capital T capital P equals standard temperature and pressure (25 degrees C and 1.00 ATM)

Answer 1

At STP 1 mole of gas occupies 22.4 L, so calculate moles occupied by 100 ml or 0.1 L.

0.1 L x 1 mol/22.4 L = 0.00446 moles of gas

From PV = nRT, calculate volume, V

V = nRT/P = (0.00446 mol)(0.0821 Latm/Kmol)(361K)/2.00 atm

V = 0.0661 liters

 

Done another way, you have 2 conditions:

P1 = 1.00 atm

V1 = 0.1 L

T1 = 298 K

P2 = 2.00 atm

V2 = ?

T2 = 361 K

P1V1/T1 = P2V2/T2 and solving for V2

V2 = P1V1T2/P2T1 = (1atm)(0.1L)(361K)/(2atm)(298K)

V2 = 0.061 liters

NOTE: the difference stems from the fact that STP is actually oºC and not 25ºC as stated in the problem.  If you substitute 273K for 298 K in the second calculation, you will get 0.0661 liters as determined in the first calculation.