A hydrocarbon found in fuel is analyzed and found to contain 84.2% C and 15.8% H. What is its empirical formula?
The correct answer and explanation is:
Let’s solve this step-by-step:
Given:
- Carbon (C) = 84.2%
- Hydrogen (H) = 15.8%
We need to find the empirical formula of the hydrocarbon, which means the simplest whole number ratio of atoms of carbon and hydrogen.
Step 1: Assume 100 g sample
- Carbon: 84.2 g
- Hydrogen: 15.8 g
Step 2: Convert grams to moles
- Molar mass of C = 12.01 g/mol
- Molar mass of H = 1.008 g/mol
Moles of C=84.2 g12.01 g/mol=7.01 moles\text{Moles of C} = \frac{84.2 \text{ g}}{12.01 \text{ g/mol}} = 7.01 \text{ moles} Moles of H=15.8 g1.008 g/mol=15.67 moles\text{Moles of H} = \frac{15.8 \text{ g}}{1.008 \text{ g/mol}} = 15.67 \text{ moles}
Step 3: Determine mole ratio
Divide both mole values by the smallest number of moles: 7.017.01=1\frac{7.01}{7.01} = 1 15.677.01=2.24\frac{15.67}{7.01} = 2.24
Step 4: Find the nearest whole number ratio
The ratio for H is approximately 2.24, which is close to 2.25 (a quarter more than 2). Since 2.25 is a fraction (9/4), we multiply both numbers by 4 to get whole numbers: 1×4=41 \times 4 = 4 2.24×4=8.96≈92.24 \times 4 = 8.96 \approx 9
Step 5: Write empirical formula
The ratio of C:H is approximately 4:9, so the empirical formula is: C4H9\boxed{C_4H_9}
Explanation (about 300 words):
The empirical formula of a compound expresses the simplest whole-number ratio of atoms in the compound. Given the percentages of carbon and hydrogen in the hydrocarbon, we first convert these percentages to grams assuming a 100-gram sample. This assumption simplifies calculations because the percentage directly translates to grams.
Next, we convert the grams of each element to moles by dividing by their respective molar masses (12.01 g/mol for carbon and 1.008 g/mol for hydrogen). Moles represent the number of atoms or molecules, so this conversion is necessary to find the ratio of atoms present.
After calculating moles for carbon and hydrogen, we divide each by the smallest mole value to find the simplest ratio. This step normalizes the quantities and reveals the relative number of atoms of each element.
In this problem, the ratio was approximately 1 carbon atom to 2.24 hydrogen atoms. Since 2.24 is not a whole number, we multiply both ratios by 4 (because 2.24 is close to 2.25, which is 9/4) to get whole numbers. This results in a ratio of 4 carbons to 9 hydrogens.
Thus, the empirical formula for the hydrocarbon with 84.2% carbon and 15.8% hydrogen is C4H9C_4H_9, representing the simplest whole-number ratio of carbon and hydrogen atoms in the compound.