A 1.5 gram sample of a gaseous hydrocarbon has a volume of 820 mL when measured at 227 oC and 2.50 atm. Which of the following is the formula for the gas?
No options.
Use PV = nRT and solve for n= number of moles. Then n = grams/molar mass. You know n and grams, solve for molar mass. Finally compare the molar mass in the answer above with the molar mass of each of the possibilities you have as answers and identify the gas that way. Post your work if you get stuck. Don't forget T must be in kelvin.
To determine the formula for the gas, we need to use the ideal gas law equation: PV = nRT.
First, let's convert the given temperature to Kelvin:
T = 227°C + 273.15 = 500.15 K
Next, we can calculate the number of moles using the ideal gas law equation:
n = PV / RT
n = (2.50 atm) * (820 mL / 1000 mL/L) / (0.0821 L·atm/mol·K) * (500.15 K)
n ≈ 0.0969 mol
Now that we have the number of moles, we can determine the molar mass of the gas:
Molar mass = mass / moles
Given the mass of the sample is 1.5 grams and the number of moles is 0.0969 mol, the molar mass is:
Molar mass ≈ 1.5 g / 0.0969 mol ≈ 15.44 g/mol
By comparing the molar mass (15.44 g/mol) to the molar masses of known hydrocarbons, we can identify the closest match. The closest match is C2H6 (ethane) with a molar mass of 30.07 g/mol.
Therefore, the formula for the gas is C2H6 (ethane).