A compound has the empirical formula CHCl. A 256 mL flask, at 373 K and 750. torr, contains 0.800 g of the gaseous compound. Give the molecular formula.
Use PV = nRT and solve for n.
Then n = grams/molar mass
Solve for molar mass.
Divide molar mass/empirical mass and round to a whole number which I will call x. Then (CHCl)x will be the molecular formula.
To determine the molecular formula of the compound, we first need to find the molar mass of the empirical formula CHCl.
The molar mass of carbon (C) is 12.01 g/mol, hydrogen (H) is 1.01 g/mol, and chlorine (Cl) is 35.45 g/mol.
The empirical formula CHCl has a total molar mass of (1 × 12.01) + (1 × 1.01) + (1 × 35.45) = 48.47 g/mol.
Next, we can calculate the number of moles of the compound using the ideal gas law equation:
PV = nRT,
Where P is the pressure (750. torr), V is the volume (256 mL = 0.256 L), n is the number of moles, R is the ideal gas constant (0.0821 L·atm/(mol·K)), and T is the temperature in Kelvin (373 K).
Rewriting the equation to solve for n:
n = PV / RT.
Substituting the values:
n = (750. torr × 0.256 L) / (0.0821 L·atm/(mol·K) × 373 K) = 8.007 mol.
Now we can determine the molar mass of the compound using the mass and moles:
molar mass = mass / moles = 0.800 g / 8.007 mol = 0.0999 g/mol.
Finally, we can find the ratio between the molar mass of the empirical formula (48.47 g/mol) and the molar mass calculated in the previous step (0.0999 g/mol):
ratio = molar mass empirical formula / molar mass calculated = 48.47 g/mol / 0.0999 g/mol ≈ 484.
The ratio of approximately 484 indicates that the molecular formula is approximately 484 times the size of the empirical formula.
Therefore, the molecular formula of the compound is approximately (CHCl)486, which can be simplified to C486H486Cl486.
To determine the molecular formula of the compound, we need to compare the molar mass of the empirical formula with the molar mass obtained from the given experimental data.
Let's start by finding the molar mass of the empirical formula (CHCl).
Molar mass of carbon (C) = 12.01 g/mol
Molar mass of hydrogen (H) = 1.01 g/mol
Molar mass of chlorine (Cl) = 35.45 g/mol
Adding them up, we get:
(1 x Molar mass of C) + (1 x Molar mass of H) + (1 x Molar mass of Cl) = (1 x 12.01 g/mol) + (1 x 1.01 g/mol) + (1 x 35.45 g/mol) = 48.47 g/mol
Now let's calculate the molar mass using the experimental data given:
First, convert the given volume (256 mL) to moles using the ideal gas law equation:
PV = nRT
P = pressure (750. torr)
V = volume (256 mL = 0.256 L)
n = moles of gas
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature in Kelvin (373 K)
Rearranging the equation to solve for n:
n = (PV) / (RT) = (750. torr * 0.256 L) / (0.0821 L·atm/mol·K * 373 K)
Now, we can calculate the moles of the compound:
moles = (750. torr * 0.256 L) / (0.0821 L·atm/mol·K * 373 K) = 0.0227 mol
Next, calculate the molar mass of the compound using the given mass and moles:
molar mass = mass / moles = 0.800 g / 0.0227 mol = 35.19 g/mol
Now we can compare the molar mass of the empirical formula (48.47 g/mol) with the molar mass obtained from the experimental data (35.19 g/mol).
We divide the experimental molar mass by the empirical molar mass to find the ratio:
35.19 g/mol / 48.47 g/mol = 0.725
The molecular formula is obtained by multiplying the empirical formula by this ratio.
Molecular formula = empirical formula x ratio = CHCl x 0.725 = C0.725H0.725Cl0.725
Since it is not possible to have fractions of atoms in a molecular formula, we need to round the subscripts to the nearest whole number.
The molecular formula of the compound is CH2Cl2.