Final answer:
To calculate the molecular formula of the gas, we first determine its empirical formula, which is CH₂. Given the molar mass, we calculate the number of empirical units in the molar mass to determine the molecular formula, which is C₂H₂. option C) C₂H₂
Step-by-step explanation:
To calculate the molecular formula for the gas, we first need to determine its empirical formula. Given that the gas is composed of 85.7% carbon and 14.3% hydrogen by mass, we can assume a 100 g sample and convert the percentages into grams. This gives us 85.7 g of carbon and 14.3 g of hydrogen.
Next, we calculate the number of moles of carbon and hydrogen by dividing their masses by their respective molar masses. Carbon has a molar mass of 12.01 g/mol, so 85.7 g of carbon is equivalent to approximately 7.136 moles. Hydrogen has a molar mass of 1.01 g/mol, so 14.3 g of hydrogen is equivalent to approximately 14.2 moles.
To determine the empirical formula, we divide the number of moles of carbon and hydrogen by the smallest number of moles (in this case, 7.136). This gives us a ratio of approximately 1:2, so the empirical formula is CH₂.
Since the molar mass of the gas is given as 1.56 g and the empirical mass of CH₂ is 14.03 g, we can calculate the molecular formula by dividing the molar mass by the empirical mass. This gives us approximately 0.111, which means the molecular formula is C₂H₂. Therefore, the correct answer is option C) C₂H₂.