A gas consists of 85.7 % carbon and 14.3% hydrogen, by weight. A sample of this gas weighing 0.673 g occupies 729 mL at a pressure of 720.0 mmHg and a temperature of 77$\degree$C. Calculate its empirical and molecular formulas.

Question

Quizplus · Accepted Answer

To find the empirical formula, we first need to convert the percentages to grams. Assuming a total mass of 100 g, we have 85.7 g of carbon and 14.3 g of hydrogen.

Next, we need to find the moles of each element. To do this, we divide the mass of each element by its respective atomic weight:

Moles of carbon = 85.7 g / 12.01 g/mol = 7.13 mol
Moles of hydrogen = 14.3 g / 1.01 g/mol = 14.2 mol

Next, we need to find the mole ratio of carbon to hydrogen by dividing each by the smallest number of moles:

Moles of carbon / smallest mole value = 7.13 mol / 7.13 mol = 1
Moles of hydrogen / smallest mole value = 14.2 mol / 7.13 mol = 1.99 or ~2

So the empirical formula is CH2.

To find the molecular formula, we need to know the molar mass of the compound. We can use the ideal gas law, PV = nRT, to find the number of moles of the gas:

n = PV / RT = (720.0 mmHg * 0.729 L) / (62.36 L·mmHg·K-1·mol-1 * 298.15 K) = 0.0295 mol

Next, we need to find the molar mass of the compound by dividing the mass of the sample by the number of moles:

Molar mass = 0.673 g / 0.0295 mol = 22.8 g/mol

Finally, we can use the molar mass and the empirical formula to determine the molecular formula. The molar mass of the empirical formula (CH2) is 14.03 g/mol, so we divide the molar mass by the empirical formula mass:

22.8 g/mol / 14.03 g/mol = 1.63

Rounding to the nearest whole number, this gives us a molecular formula of C2H4, which matches option B.

A Gas Consists of 85 °\degree° C Calculate Its Empirical and Molecular Formulas

A Gas Consists of 85 $\degree$ C Calculate Its Empirical and Molecular Formulas