use the experimental molar mass to determine the molecular formula for ocompounds having the following analysis.b) 54.53% carbon 9.15% hydrogen, and 36.32% oxygen; experimental molar mass 88
To determine the molecular formula of a compound using its analysis and experimental molar mass, you need to follow these steps:
Step 1: Convert the percentages of each element into grams.
- Suppose we have a 100g sample of the compound.
- 54.53% carbon in 100g = 54.53g carbon
- 9.15% hydrogen in 100g = 9.15g hydrogen
- 36.32% oxygen in 100g = 36.32g oxygen
Step 2: Calculate the number of moles for each element.
- To calculate the moles, divide the grams of each element by its respective molar mass.
- Molar mass of carbon (C) = 12.01 g/mol
- Molar mass of hydrogen (H) = 1.01 g/mol
- Molar mass of oxygen (O) = 16.00 g/mol
- Moles of carbon (C) = 54.53g / 12.01 g/mol = 4.54 mol
- Moles of hydrogen (H) = 9.15g / 1.01 g/mol = 9.06 mol
- Moles of oxygen (O) = 36.32g / 16.00 g/mol = 2.27 mol
Step 3: Divide each element's mole value by the smallest mole value.
- In this case, the smallest mole value is 2.27 mol (oxygen).
- Carbon mole ratio = 4.54 mol / 2.27 mol = 2
- Hydrogen mole ratio = 9.06 mol / 2.27 mol = 4
- Oxygen mole ratio = 2.27 mol / 2.27 mol = 1
Step 4: Determine the empirical formula using the mole ratios.
- The empirical formula shows the simplest ratio of atoms in a compound.
- Based on the mole ratios obtained: C2H4O
Step 5: Calculate the empirical formula mass.
- Add the molar masses for each element in the empirical formula.
- Empirical formula mass = (2 * molar mass of C) + (4 * molar mass of H) + (1 * molar mass of O)
- Empirical formula mass = (2 * 12.01 g/mol) + (4 * 1.01 g/mol) + (1 * 16.00 g/mol)
- Empirical formula mass = 24.02 g/mol + 4.04 g/mol + 16.00 g/mol
- Empirical formula mass = 44.06 g/mol
Step 6: Divide the experimental molar mass by the empirical formula mass to find the integer multiplier.
- Experimental molar mass / empirical formula mass = 88 g/mol / 44.06 g/mol = 2
Step 7: Multiply the subscripts in the empirical formula by the integer multiplier to obtain the molecular formula.
- Molecular formula = C2H4O * 2 = C4H8O
Therefore, the molecular formula for the compound with the given analysis is C4H8O.
To determine the molecular formula for a compound using experimental molar mass and elemental analysis, follow these steps:
1. Convert the given percentages of each element into grams.
- Carbon: 54.53% * 88g = 48.005g
- Hydrogen: 9.15% * 88g = 8.052g
- Oxygen: 36.32% * 88g = 32.006g
2. Calculate the number of moles for each element using their respective molar masses (atomic masses).
- Carbon: moles = grams/molar mass = 48.005g / 12.01g/mol = 3.996 moles
- Hydrogen: moles = grams/molar mass = 8.052g / 1.008g/mol = 7.996 moles
- Oxygen: moles = grams/molar mass = 32.006g / 16.00g/mol = 2.000 moles
3. Determine the simplest whole number ratio of the elements by dividing each mole value by the smallest mole value. In this case, the smallest mole value is 2.000 moles.
- Carbon: 3.996 moles / 2.000 moles = 1.998 ≈ 2
- Hydrogen: 7.996 moles / 2.000 moles = 3.998 ≈ 4
- Oxygen: 2.000 moles / 2.000 moles = 1
So, the empirical formula of the compound is C2H4O.
4. Finally, compare the empirical formula mass (sum of the atomic masses in empirical formula) to the experimental molar mass given (88g). If the empirical formula mass is less than the experimental molar mass, the compound's molecular formula is a multiple of the empirical formula.
- Empirical formula mass = (2 * 12.01g) + (4 * 1.008g) + (1 * 16.00g) = 44.056g
Since the empirical formula mass is less than the experimental molar mass (88g), we can double the empirical formula to obtain the molecular formula.
- Molecular formula = (C2H4O) * 2 = C4H8O2
Therefore, the molecular formula for the compound is C4H8O2, assuming the experimental molar mass is accurate.