#"SATP"# is standard ambient temperature and pressure, which is #"25"^@"C"# or #"298 K"#, and #"1 bar"#.
Balanced equation
#"CH"_4("g") + "2O"_2("g")"##rarr##"CO"_2("g") + "2H"_2"O(g)"#
Determine moles methane #("CH"_4")# using the equation for the ideal gas law.
#PV=nRT#
Known
#P="1 bar"#
#V="1.00 L"#
#R="0.0831447 L bar K"^(-1) "mol"^(-1)"#
#T="298 K"#
Unknown
#n#
Calculate moles #"CH"_4#
Rearrange the equation to isolate #n#. Plug in the known values and solve.
#n=(PV)/(RT)#
#n=((1color(red)cancel(color(black)("bar")))xx(1.00color(red)cancel(color(black)("L"))))/((0.0831447color(red)cancel(color(black)("L"))color(red)cancel(color(black)("bar")) color(red)cancel(color(black)("K"))^(-1) "mol"^(-1))xx(298color(red)cancel(color(black)("K"))))="0.040360 mol"#
I am keeping some extra digits to reduce rounding errors. The final answer will be rounded to two significant figures.
Moles #"O"_2#
To determine moles #"O"_2#, multiply mol #"CH"_4# by the mol ratio between #"O"_2# and #"CH"_4# in the balanced equation, with mol #"O"_2# in the numerator.
#0.040360color(red)cancel(color(black)("mol CH"_4))xx(2"mol O"_2)/(1color(red)cancel(color(black)("mol CH"_4)))="0.08072 mol O"_2"#
Mass #"O"_2#
To determine the mass of the oxygen, multiply mol #"O"_2# by its molar mass.
#0.08072color(red)cancel(color(black)("mol O"_2))xx(31.998"g O"_2)/(1color(red)cancel(color(black)("mol O"_2)))="2.6 g O"_2"# (rounded to two significant figures)
