(8.8400x10^-1) mol of an ideal gas has a pressure of (1.50x10^2) kPa and temperature of (2.5700x10^2) K. What is the volume of the gas?

1 Answer
May 2, 2017

Answer:

The volume of the gas is #1.26 × 10^1 color(white)(l)"L"#.

Explanation:

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

#color(blue)(bar(ul(|color(white)(a/a)pV = nRTcolor(white)(a/a)|)))" "#

where

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

We can rearrange the Ideal Gas Law to get

#V = (nRT)/p#

In this problem,

#n = 8.8400 × 10^"-1"color(white)(l) "mol"#
#R = "8.314 kPa·L·K"^"-1""mol"^"-1"#
#T = 2.5700 × 10^2 color(white)(l)"K"#
#p = 1.50 ×10^2 color(white)(l)"kPa"#

#V = (8.8400 ×10^"-1" color(red)(cancel(color(black)("mol"))) × 8.314 color(red)(cancel(color(black)("kPa")))·"L"·color(red)(cancel(color(black)("K"^"-1"·"mol"^"-1"))) × 2.5700× 10^2color(red)(cancel(color(black)("K"))))/(1.50 × 10^2 color(red)(cancel(color(black)("kPa")))) = 1.26 × 10^1 color(white)(l)"L"#