To determine the molecular formula of a hydrocarbon with a carbon-to-hydrogen atom ratio of 1:2 and a molecular mass of 56, we can follow these steps: ### Step 1: Understand the Ratio The ratio of carbon (C) to hydrogen (H) in the hydrocarbon is given as 1:2. This means that for every 1 carbon atom, there are 2 hydrogen atoms. We can express this as: - C = 1 - H = 2 ### Step 2: Determine the Empirical Formula From the ratio, we can derive the empirical formula. The simplest whole number ratio of carbon to hydrogen is: - C₁H₂ ### Step 3: Calculate the Molar Mass of the Empirical Formula Next, we need to calculate the molar mass of the empirical formula (C₁H₂): - The molar mass of carbon (C) = 12 g/mol - The molar mass of hydrogen (H) = 1 g/mol Calculating the molar mass of C₁H₂: \[ \text{Molar mass of C₁H₂} = (1 \times 12) + (2 \times 1) = 12 + 2 = 14 \text{ g/mol} \] ### Step 4: Determine the Molecular Formula Now, we know the molecular mass of the hydrocarbon is 56 g/mol. To find the molecular formula, we need to determine how many times the empirical formula fits into the molecular mass: \[ \text{Number of empirical units} = \frac{\text{Molecular mass}}{\text{Empirical formula mass}} = \frac{56}{14} = 4 \] This means the molecular formula consists of 4 times the number of each atom in the empirical formula: - C: \(1 \times 4 = 4\) - H: \(2 \times 4 = 8\) Thus, the molecular formula is C₄H₈. ### Step 5: Identify the Correct Option Now, we can compare our result with the provided options: - A. C₃H₆ - B. C₄H₈ - C. C₂H₄ - D. CH₂ The correct answer is **B. C₄H₈**. ### Step 6: Explain Why Other Options Are Incorrect - **A. C₃H₆**: The molar mass of C₃H₆ is calculated as follows: \[ (3 \times 12) + (6 \times 1) = 36 + 6 = 42 \text{ g/mol} \] This is not equal to 56 g/mol. - **C. C₂H₄**: The molar mass of C₂H₄ is: \[ (2 \times 12) + (4 \times 1) = 24 + 4 = 28 \text{ g/mol} \] This is also not equal to 56 g/mol. - **D. CH₂**: The molar mass of CH₂ is: \[ (1 \times 12) + (2 \times 1) = 12 + 2 = 14 \text{ g/mol} \] This is not equal to 56 g/mol. ### Summary - The hydrocarbon has a carbon-to-hydrogen ratio of 1:2, leading to an empirical formula of C₁H₂. - The empirical formula's molar mass is 14 g/mol, and the molecular mass is given as 56 g/mol. - The molecular formula is determined to be C₄H₈, which corresponds to option B. - Other options do not match the required molecular mass of 56 g/mol. ### Revision Summary - The ratio of carbon to hydrogen in the hydrocarbon is 1:2. - The empirical formula is C₁H₂ with a molar mass of 14 g/mol. - The molecular formula is C₄H₈, derived from multiplying the empirical formula by 4. - The correct answer is option B, as it matches the molecular mass of 56 g/mol.