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.
