A compound has the empirical formula CHCL .A flask with volume 253 cm3 at temperature of 373K and pressure of 1.0 atm contains 0.8 g of the gaseous compound. Find the molecular formula of the compound.
Use PV = nRT and solve for n = number of mols.
Then n = grams/molar mass. You know n and grams, solve for molar mass.
To determine the molecular formula of the compound, we need to find its molar mass first. We can do this by finding the molar mass of the empirical formula and then multiplying it by a whole number, which represents the ratio of the molecular formula to the empirical formula.
The empirical formula provides the simplest ratio of atoms in a compound. In this case, the empirical formula is CHCL.
To find the molar mass of the empirical formula, we need to determine the molar masses of each element in the formula and then sum them up. The molar mass of carbon (C) is 12.01 g/mol, the molar mass of hydrogen (H) is 1.008 g/mol, and the molar mass of chlorine (Cl) is 35.45 g/mol.
Molar mass of CHCL = (1 * molar mass of C) + (1 * molar mass of H) + (1 * molar mass of Cl)
= (1 * 12.01 g/mol) + (1 * 1.008 g/mol) + (1 * 35.45 g/mol)
= 48.463 g/mol
Now, to find the molecular formula, we need to calculate the molar mass of the molecular formula. We can do this by dividing the given mass (0.8g) of the compound by its molar mass (48.463 g/mol):
Number of moles = Mass / Molar mass of empirical formula
= 0.8 g / 48.463 g/mol
= 0.0165 mol
Since the volume, temperature, and pressure of the compound are given, we can use the ideal gas law to determine the number of moles of the compound:
PV = nRT
Where:
P = pressure (1.0 atm)
V = volume in liters (253 cm^3 = 253 / 1000 = 0.253 L)
n = number of moles of the compound
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature in Kelvin (373K)
Rearranging the formula to solve for n, we get:
n = PV / RT
n = (1.0 atm * 0.253 L) / (0.0821 L·atm/(mol·K) * 373 K)
n = 0.00991 mol
The number of moles calculated from the ideal gas law (0.00991 mol) is almost the same as the number of moles calculated from the mass-to-molar mass ratio (0.0165 mol). Since the molar mass based on the empirical formula is slightly below the actual molar mass, we can conclude that the empirical formula does not represent the true molecular formula.
To find the ratio between the molecular formula and the empirical formula, divide the actual number of moles (0.0165 mol) by the number of moles calculated from the ideal gas law (0.00991 mol):
Ratio = Actual mole value / Ideal mole value
= 0.0165 mol / 0.00991 mol
= 1.664
The ratio is approximately 1.664. Since the ratio should be a whole number, round it to the nearest whole number, which is 2.
Finally, multiply the subscripts in the empirical formula by the ratio to find the molecular formula:
Molecular formula = Empirical formula * Ratio
= (CHCL)2
= C2H2CL2
Therefore, the molecular formula of the compound is C2H2CL2.