Fluorination of acetone, C3H6O (substitution of fluorine for H) produces a gaseous compound with the formula C3H6?xFxO. To identify this compound its molar mass was determined by measuring the gas density. The following data were obtained: Mass of gas, 1.53 g; volume of flask = 264 mL; pressure exerted by gas, 722 mm Hg; temperature, 22 °C. Calculate the molar mass from this information, then identify the molecular formula.
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To calculate the molar mass of a gas using the given information, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure in atmospheres (convert mm Hg to atm by dividing by 760)
V = volume in liters (convert mL to L by dividing by 1000)
n = number of moles
R = ideal gas constant (0.0821 L•atm/mol•K)
T = temperature in Kelvin (convert Celsius to Kelvin by adding 273.15)
Let's calculate the molar mass step by step:
1. Convert the given pressure from mm Hg to atm:
Pressure = 722 mm Hg / 760 mm Hg/atm = 0.949 atm
2. Convert the given volume from mL to L:
Volume = 264 mL / 1000 mL/L = 0.264 L
3. Convert the given temperature from Celsius to Kelvin:
Temperature = 22 °C + 273.15 = 295.15 K
4. Rearrange the ideal gas law equation to solve for n (moles):
n = PV / RT
n = (0.949 atm) * (0.264 L) / (0.0821 L•atm/mol•K) * (295.15 K)
n = 0.00877 mol
5. Now that we have the number of moles (n), we can calculate the molar mass (M) using the formula:
Molar Mass = Mass / Moles
Given mass = 1.53 g and moles = 0.00877 mol,
Molar Mass = 1.53 g / 0.00877 mol
Molar Mass ≈ 174.9 g/mol
Now, to identify the molecular formula, we need to determine the ratio of atoms of each element in the compound.
Given that the original compound is acetone (C₃H₆O), and fluorination of acetone replaces a hydrogen with a fluorine atom, we have:
C₃H₅FO
Therefore, the molecular formula of the compound is C₃H₅FO.