Methane is formed in landfills by the action of certain bacteria on buried organic matter. If a sample of methane collected from a landfill has a volume of 500. mL at 744. torr and 22. °C, how many grams of methane are in the sample?
First, get the number of moles (n) by using the ideal gas law
n = PV/(RT)
R = 82.06 cm^3*atm/(mole*K)
V = 500 cm^3
P = 744/760 = 0.9789 atm
T = 295 K
n = 0.0202 moles
Then multipy n by the molecular weight(16 g/mole)
To determine the number of grams of methane in the sample, we can use the ideal gas law equation:
PV = nRT
Where:
P is the pressure of the gas in atm (converted from torr),
V is the volume of the gas in liters (converted from mL),
n is the number of moles of the gas,
R is the ideal gas constant (0.0821 L·atm/K·mol), and
T is the temperature of the gas in Kelvin (converted from °C).
First, let's convert the given values to the appropriate units:
Volume (V) = 500 mL = 500/1000 L = 0.5 L
Temperature (T) = 22 °C + 273.15 = 295.15 K
Pressure (P) = 744 torr = 744/760 atm (since 1 atm = 760 torr) ≈ 0.979 atm
Now, we can rearrange the ideal gas law equation to solve for moles:
n = PV / RT
Substituting the values:
n = (0.979 atm) * (0.5 L) / (0.0821 L·atm/K·mol) * (295.15 K)
After performing the calculation, we find that n ≈ 0.0183 moles of methane.
Finally, to convert moles to grams, we need to know the molar mass of methane, which is 16.04 g/mol.
Mass of methane = n * molar mass
Mass of methane = 0.0183 moles * 16.04 g/mol ≈ 0.294 grams
Therefore, there are approximately 0.294 grams of methane in the sample.