# Question #dd886

Dec 7, 2014

In order to solve this problem, you need to use the ideal gas law: $\text{PV}$ = $\text{nRT}$, solving for n. Once you know n, you can convert the moles of ${\text{CH}}_{4}$ 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:
$\text{V = 2.00L}$
$\text{T = 50.0"^"o""C" + 273.15 = 323.15"K}$
$\text{P = 697 torr = 0.91711 atm}$ http://www.theunitconverter.com
$\text{R = 0.0821 L atm/mole K}$
${\text{molar mass CH}}_{4}$ = $\text{16.04g/mol}$ http://en.wikipedia.org/wiki/Methane

Unknowns:
number of moles, n
mass in grams of methane, $\text{CH"_4}$

Equation :
$\text{PV}$ = $\text{nRT}$

Solution:

Divide both sides of the equation by RT to isolate n. Solve for n.

$\text{n}$ = $\text{PV"/"RT}$ = $\text{(0.91711 atm)(2.00L)"/"(0.0821 L atm/mole K)(323.15K)}$= ${\text{0.0691 mol CH}}_{4}$

Multiply mol $\text{CH"_4}$ times its molar mass.

${\text{0.0691 mol CH}}_{4}$ x $\text{16.04g CH4"/"1 mol CH4}$ = $\text{1.11g CH"_4}$