A compound has the empiical fomula CHCl. a 256-mL flask, at 373 K and 750. Torr, contains 0.800 g of the gaseous compound. Give the molecular formula.
To determine the molecular formula of the compound given the empirical formula and the experimental data, we need to calculate the molar mass of the empirical formula and compare it to the molar mass obtained from the experimental data.
The empirical formula CHCl gives us the ratio of carbon, hydrogen, and chlorine atoms in the compound as 1:1:1. To calculate the molar mass of the empirical formula, we need to know the atomic masses of carbon (C), hydrogen (H), and chlorine (Cl).
The atomic masses are as follows:
- Carbon (C) = 12.01 g/mol
- Hydrogen (H) = 1.01 g/mol
- Chlorine (Cl) = 35.45 g/mol
So, the molar mass of the empirical formula CHCl can be calculated as:
(1 * 12.01 g/mol) + (1 * 1.01 g/mol) + (1 * 35.45 g/mol) = 48.47 g/mol
Now, let's determine the number of moles of the compound using the given mass and the molar mass.
Given:
Mass of the compound = 0.800 g
Molar mass of the empirical formula CHCl = 48.47 g/mol
Moles of the compound = Mass / Molar mass
Moles of the compound = 0.800 g / 48.47 g/mol = 0.0165 mol
Next, we need to calculate the molar volume of the gas at the given temperature and pressure. The ideal gas equation can be used for this:
PV = nRT
Where:
P = Pressure in atmospheres (750 Torr / 760 Torr = 0.987 atm)
V = Volume in liters (256 mL / 1000 mL/L = 0.256 L)
n = Moles of the gas (0.0165 mol)
R = Ideal gas constant (0.0821 L·atm/mol·K)
T = Temperature in Kelvin (373 K)
Plugging in the values, we can rearrange the equation to solve for V:
V = (nRT) / P
V = (0.0165 mol * 0.0821 L·atm/mol·K * 373 K) / 0.987 atm
V ≈ 0.508 L
Now, we have the molar volume of the gas at the given temperature and pressure.
Finally, we can calculate the molar mass of the compound using the formula:
Molar mass = Mass / Volume
Molar mass = 0.800 g / 0.508 L = 1.575 g/L
Comparing the molar mass of the empirical formula (48.47 g/mol) to the molar mass obtained from the experimental data (1.575 g/L), we can see that the latter is significantly lower. This indicates that the empirical formula does not represent the actual molecular formula.
To determine the molecular formula, we need to find the ratio between the molar mass of the empirical formula and the molar mass obtained from the experimental data:
Molar mass ratio = Experimental molar mass / Empirical molar mass
Molar mass ratio = 1.575 g/L / 48.47 g/mol ≈ 0.0324
Now, we have the molar mass ratio. To find the molecular formula, we need to multiply the subscripts in the empirical formula by this ratio. Since the empirical formula has equal subscripts for each element (CHCl), the molecular formula will be the same as the empirical formula.
Therefore, the molecular formula of the compound is CHCl.