Question #a9717

1 Answer
Jun 5, 2017

Answer:

#1.29 xx 10^7# #"L"#

Explanation:

Any time you're given three of the four primary characteristics of gases (pressure, volume, quantity, and temperature), you'll be using the ideal-gas equation to find the fourth quantity:

#PV = nRT#

When using the ideal-gas equation,

  • the pressure #P# must be in atmospheres (#"atm"#)

  • the volume #L# must be in liters (#"L"#)

  • the quantity #n# must be in moles (#"mol"#)

  • the temperature #T# must be the absolute temperature; i.e. in Kelvin (#"K"#)

And #R# is the universal gas constant, #0.08206("L" · "atm")/("mol" · "K")#.

(I'll assume the given quantity #0.600# #"million"# is the number of moles. This is equal to #600,000# #"mol"#)

We need to calculate the Kelvin temperature, which we can do using the equation

#"K" = ""^"o""C" + 273 = 15.0^"o""C" + 273 = color(red)(288# #color(red)("K"#

Now that we have all our necessary variables, we can plug them in to the ideal-gas equation, and rearrange the equation to solve for the volume, #V#:

#V = (nRT)/P = ((600000cancel("mol"))(0.08206("L" · cancel("atm"))/(cancel("mol") · cancel("K")))(288cancel("K")))/(1.10cancel("atm"))#

#= color(blue)(1.29 xx 10^7# #color(blue)("L"#