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 200. mL at 741 torr and 27.2 °C, how many grams of methane are in the sample?
I get the PV=nRT
p is 741/760= .975
V to L 200mL =.200L
T to K 27.2+273.15= 300.4
.975atm x .200L = n x .08205 x 300.4
.195=n x 24.6164
= .0079
.0079 x mm CH4
So 1.267? Does that sound right?
almost.
n = 0.0079? Why did you throw away the 1 on 0.00791. You have three places in yur other numbers; you should keep three for the answers. Then if I multiply 0.00791 x 16 I get 0.1265678 which rounded to 3 s.f. is 0.127grams CH4.
Your calculations are close, but there is a small mistake in the conversion of liters to moles. Let's go through the calculation step by step to find the correct answer:
1. Convert the volume from mL to L:
200 mL = 0.200 L
2. Convert the pressure from torr to atm:
741 torr ÷ 760 torr/atm = 0.974 atm
3. Convert the temperature from °C to K:
27.2 °C + 273.15 = 300.35 K (use 300.35 K for accuracy)
4. Plug the values into the ideal gas law equation (PV = nRT):
(0.974 atm) × (0.200 L) = n × (0.08205 L·atm/mol·K) × (300.35 K)
Simplify the equation:
0.1948 L·atm = n × 24.6947 L·atm/mol
n = 0.1948 L·atm / 24.6947 L·atm/mol
n ≈ 0.00789 mol
5. Convert moles of methane to grams:
The molar mass of methane (CH4) is approximately 16.04 g/mol.
Mass = n × molar mass
Mass = 0.00789 mol × 16.04 g/mol
Mass ≈ 0.1264 g
Therefore, the sample of methane collected from the landfill contains approximately 0.1264 grams of methane.
To find the number of moles of methane in the sample, you correctly used the ideal gas law equation, PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature.
First, convert the given pressure from torr to atm:
741 torr ÷ 760 torr/atm = 0.975 atm.
Next, convert the given volume from milliliters to liters:
200 mL ÷ 1000 mL/L = 0.200 L.
Also, convert the given temperature from Celsius to Kelvin:
27.2 °C + 273.15 = 300.35 K.
Now, substitute these values into the equation:
(0.975 atm) × (0.200 L) = n × (0.08205 L·atm/(mol·K)) × (300.35 K).
Simplifying the equation gives:
0.195 = 24.6164n.
Isolating the variable n gives:
n = 0.195 / 24.6164.
Calculating this gives:
n ≈ 0.00792 mol.
To find the mass of methane in grams, we need to multiply the number of moles by the molar mass of methane (CH4), which is 16.04 g/mol.
So, the mass of methane in the sample is:
0.00792 mol × 16.04 g/mol ≈ 0.127 grams.
Therefore, the correct answer is approximately 0.127 grams of methane in the sample.