a flask with a volume of 267.5 mL contains a few milliliters of a volatile hydrocarbon. after vaporizing the gas at 100 degrees C, the flask is weighed and found to contain 0.728 grams of hydrocarbon vapor at 755 mmHg. a separate combustion analysis experiment revealed that the empirical formula osf the hydrocarbon was CH2. What is the molecular formula?

Question

a flask with a volume of 267.5 mL contains a few milliliters of a volatile hydrocarbon. after vaporizing the gas at 100 degrees C, the flask is weighed and found to contain 0.728 grams of hydrocarbon vapor at 755 mmHg. a separate combustion analysis experiment revealed that the empirical formula osf the hydrocarbon was CH2. What is the molecular formula?

Answer 1

To determine the molecular formula of the hydrocarbon, you can use the ideal gas law and the molar mass of the empirical formula.

First, let's calculate the number of moles of the hydrocarbon vapor using the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.

Convert the pressure from mmHg to atm by dividing by 760 mmHg/atm:
Pressure (P) = 755 mmHg / 760 mmHg/atm = 0.9934 atm

Convert the volume from milliliters to liters by dividing by 1000 mL/L:
Volume (V) = 267.5 mL / 1000 mL/L = 0.2675 L

The temperature (T) is provided as 100 degrees Celsius, so convert it to Kelvin by adding 273.15:
Temperature (T) = 100°C + 273.15 = 373.15 K

The ideal gas constant (R) is 0.0821 L·atm/(mol·K).

Now, rearrange the ideal gas law equation to solve for the number of moles (n) of the hydrocarbon:
n = PV / RT

n = (0.9934 atm * 0.2675 L) / (0.0821 L·atm/(mol·K) * 373.15 K) ≈ 0.011 mol

Next, calculate the molar mass of the empirical formula, CH2:
Molar mass of C = 12.01 g/mol
Molar mass of H = 1.01 g/mol

Molar mass of CH2 = 12.01 g/mol (1 C atom) + 1.01 g/mol (2 H atoms) = 14.03 g/mol

Divide the molar mass of the hydrocarbon vapor (0.728 g) by the molar mass of CH2 (14.03 g/mol) to find the number of empirical formula units in the sample:
Number of empirical formula units = 0.728 g / 14.03 g/mol ≈ 0.052

Since the empirical formula is CH2 and there are approximately 0.052 empirical formula units per sample, the molecular formula can be determined by multiplying the empirical formula by the appropriate factor to obtain the whole number ratio.

In this case, CH2 multiplied by 19 gives us C19H38 as the molecular formula.

Therefore, the molecular formula of the hydrocarbon is C19H38.