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 100. mL at 754 torr and 21.2 °C, how many grams of methane are in the sample?
Use PV = nRT and solve for n = nuumber of mols, then n = grams/molar mass. You know molar mass and n, solve for grams.
To determine the number of grams of methane in the sample, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure of the gas (in atm)
V = volume of the gas (in liters)
n = number of moles of the gas
R = ideal gas constant (0.0821 L.atm/mol.K)
T = temperature of the gas (in Kelvin)
First, we need to convert the given values to the appropriate units.
1 atm = 760 torr
So, the pressure can be converted to atm by dividing 754 torr by 760 torr/atm:
P = 754 torr / 760 torr/atm = 0.992 atm
The volume is given as 100 mL. To convert it to liters, divide by 1000:
V = 100 mL / 1000 mL/L = 0.1 L
The temperature is given as 21.2 °C. To convert it to Kelvin, we can use the formula:
T(K) = T(°C) + 273.15
T(K) = 21.2 °C + 273.15 = 294.35 K
Now, we can substitute the values into the ideal gas law equation:
(0.992 atm) * (0.1 L) = n * (0.0821 L.atm/mol.K) * (294.35 K)
Simplifying the equation:
0.0992 = n * 24.2081535
Divide both sides of the equation by 24.2081535 to solve for n:
n = 0.0992 / 24.2081535
n ≈ 0.004094 moles
Finally, we can convert moles to grams using the molar mass of methane. The molar mass of methane (CH4) is calculated by adding the atomic masses of its components: 12.01 g/mol (carbon) + 4(1.01 g/mol) (hydrogen).
Molar mass of methane = 12.01 g/mol + 4(1.01 g/mol) = 16.05 g/mol
To calculate the mass of methane in the sample, multiply the number of moles by the molar mass:
mass = n * molar mass
mass = 0.004094 moles * 16.05 g/mol
mass ≈ 0.0659 g
Therefore, there are approximately 0.0659 grams of methane in the sample.