In order to solve this problem, you need to use the ideal gas law: #"PV"# = #"nRT"#, solving for n. Once you know n, you can convert the moles of #"CH"_4# by multiplying n times its molar mass Temperature must be in Kelvins. K = Celsius + 273.15. If R = 0.0821 L atm/mol K, given pressure needs to be converted from torr to atm.
Given/Known:
#"V = 2.00L"#
#"T = 50.0"^"o""C" + 273.15 = 323.15"K"#
#"P = 697 torr = 0.91711 atm"# http://www.theunitconverter.com
#"R = 0.0821 L atm/mole K"#
#"molar mass CH"_4# = #"16.04g/mol"# http://en.wikipedia.org/wiki/Methane
Unknowns:
number of moles, n
mass in grams of methane, #"CH"_4"#
Equation :
#"PV"# = #"nRT"#
Solution:
Divide both sides of the equation by RT to isolate n. Solve for n.
#"n"# = #"PV"/"RT"# = #"(0.91711 atm)(2.00L)"/"(0.0821 L atm/mole K)(323.15K)"#= #"0.0691 mol CH"_4#
Multiply mol #"CH"_4"# times its molar mass.
#"0.0691 mol CH"_4# x #"16.04g CH4"/"1 mol CH4"# = #"1.11g CH"_4"#
Answer :
The mass of methane gas that occupies 2.00L, at 50.0 C, and 697 torr, is 1.11g.
