If 49.5 moles of an ideal gas occupies 37.5 liters at 479 K, what is the pressure of the gas?

1 Answer
Apr 17, 2016

Answer:

The pressure of the gas is 51.9 atm.

Explanation:

This looks like a good time to apply the Ideal Gas Law:

#color(blue)(|bar(ul(PV = nRT)|)#,

where

  • #P# is the pressure
  • #V# is the volume
  • #n# is the number of moles
  • #R# is the gas constant
  • #T# is the temperature

We can rearrange the Ideal Gas Law to get

#P = (nRT)/V#

#n = "49.5 mol"#
#R = "0.082 06 L·atm·K"^"-1""mol"^"-1"#
#T = "479 K"#
#V = "37.5 L"#

#P = (nRT)/V = (49.5 color(red)(cancel(color(black)("mol"))) × "0.082 06" color(red)(cancel(color(black)("L")))"·atm·"color(red)(cancel(color(black)("K"^"-1""mol"^"-1"))) × 479 color(red)(cancel(color(black)("K"))))/(37.5 color(red)(cancel(color(black)("L")))) = "51.9 atm"#