A 3.6 mole sample of methane gas is kept in a 1.50 liter container at a temperature of 100°C. What is the pressure of the gas?

1 Answer
Mar 25, 2018

Answer:

I get #7442.7 \ "kPa"#.

Explanation:

We use the ideal gas law, which states that,

#PV=nRT#

  • #P# is the pressure

  • #V# is the volume in liters (for this case)

  • #n# is the number of moles of the substance

  • #R# is the ideal gas constant, which varies

  • #T# is the temperature in Kelvin

Since we need to find pressure, we can rearrange the equation into:

#P=(nRT)/V#

Now, we need to convert the temperature into Kelvin. We know that #"K"=""^@"C"+273.15#, and so #100^@"C"=100+273.15=373 \ "K"#.

Since our temperature is in #"K"# and volume in liters, let's use #R=8.314 \ "L" \ "kPa" \ "K"^-1 \ "mol"^-1#. Taken from: https://en.wikipedia.org/wiki/Gas_constant

And so, we find that the pressure is:

#P=(3.6 \ "mol"*8.314 \ "L" \ "kPa" \ "K"^-1 \ "mol"^-1*373 \ "K")/(1.5 \ "L")#

#=(11164.0392color(red)cancelcolor(black)"mol"color(red)cancelcolor(black)"L" \ "kPa"color(red)cancelcolor(black)"K"^-1color(red)cancelcolor(black)"mol"^-1color(red)cancelcolor(black)"K")/(1.5color(red)cancelcolor(black)"L")#

#=7442.6928 \ "kPa"#

#~~7442.7 \ "kPa"#