A 21-liter cylinder contains 1.5 moles of an ideal gas at 311 K. What is the pressure of the gas?

1 Answer
Jan 23, 2016

Answer:

#P = "1.8 atm"#

Explanation:

This is a pretty straightforward ideal gas law equation practice problem.

As you know, the ideal gas law equation looks like this

#color(blue)(PV = nRT)" "#, where

#P# - the pressure of the gas
#V# - the volume it occupies
#n# - the number of moles of gas
#R# - the universal gas constant, usually given as #0.0821 ("atm" * "L")/("mol" * "K")#
#T# - the temperature of the gas, always expressed in Kelvin

So, the problem provides you with

  • the volume of the gas, #V = "21 L"#
  • the number of moles of gas, #n = 1.5#
  • the absolute temperature of the gas, #T = "311 K"#

Since you know the value of #R#, you can use this information to find the pressure #P#. First, rearrange the ideal gas law equation to isolate #P# on one side

#PV = nRT implies P = (nRT)/V#

Next, make sure that the units given to you match those used in the expression of the universal gas constant.

# {:(color(red)("Need"), color(white)(aaaaa), color(blue)("Have")), (color(white)(aaaa), color(white)(aaaa), color(white)(aaaa)), (color(white)(aa)"L", color(white)(aaaa), color(white)(aa)"L"color(white)(aaaaaa)color(green)(sqrt())), ("moles", color(white)(aaaa), "moles"color(white)(aaaaa)color(green)(sqrt())), (color(white)(aa)"K", color(white)(aaaa), color(white)(aa)"K"color(white)(aaaaaa)color(green)(sqrt())) :}#

The units given to you match those used for #R#, so you're good to go. Plug in your values to get

#P = (1.5 color(red)(cancel(color(black)("moles"))) * 0.0821("atm" * color(red)(cancel(color(black)("L"))))/(color(red)(cancel(color(black)("mol"))) * color(red)(cancel(color(black)("K")))) * 311color(red)(cancel(color(black)("K"))))/(21color(red)(cancel(color(black)("L"))))#

#P = "1.824 atm"#

Rounded to two sig figs, the number of sig figs you have for the volume and number of moles of gas, the answer will be

#P = color(green)("1.8 atm")#