The volume is #1.42 × 10^15color(white)(l) "km"^3#.
We can convert the mass to moles of methane and then use the Ideal Gas Law to calculate the volume at STP.
Moles of #"CH"_4#
#"Moles of CH"_4 = 1.00 × 10^24 color(red)(cancel(color(black)("g CH"_4))) × ("1 mol CH"_4)/(16.04 color(red)(cancel(color(black)("g CH"_4)))) = 6.234 × 10^22 color(white)(l)"mol CH"_4#
Volume at STP
The Ideal Gas Law is:
#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
#V = (nRT)/P#
STP is 1 bar and 0 °C.
#n = 6.234 × 10^22color(white)(l) "mol"#
#R = "0.083 14 bar·L·K"^"-1""mol"^"-1"#
#T = "273.15 K"#
#P = "1 bar"#
#V = (nRT)/P = (6.234 × 10^22 color(red)(cancel(color(black)("mol"))) × "0.083 14" color(red)(cancel(color(black)("bar")))·"L"· color(red)(cancel(color(black)("K"^"-1""mol"^"-1"))) × 273.15 color(red)(cancel(color(black)("K"))))/(1 color(red)(cancel(color(black)("bar")))) = 1.42 × 10^24 color(white)(l)"L" = 1.42 × 10^21color(white)(l) "m"^3 = 1.42 × 10^15color(white)(l) "km"^3#
This is almost exactly the volume of Jupiter.
