An unknown compound has a percent composition of 75.95% C, 17.72% N, and 6.33% H by mass with a molar mass of about 240 g/mol. Determine the molecular formula of the dye. (Atomic mass of C-12.011 g/mol; N =14.007 g/mol; H- 1.008 g/mol).
To determine the molecular formula, we first need to determine the empirical formula.
1. Assume we have 100 g of the compound, which means we have 75.95 g C, 17.72 g N, and 6.33 g H.
2. Convert the mass of each element to moles using its molar mass:
- Moles of C = 75.95 g / 12.011 g/mol = 6.316 mol
- Moles of N = 17.72 g / 14.007 g/mol = 1.264 mol
- Moles of H = 6.33 g / 1.008 g/mol = 6.286 mol
3. Divide each mole value by the smallest mole value to get the mole ratio:
- C:N:H = 6.316 mol / 1.264 mol / 6.286 mol = 5 : 1 : 5
4. The empirical formula is C5H5N.
5. To determine the molecular formula, we need to know the molecular mass. The molar mass of the compound is given as 240 g/mol, which is approximately 10 times the molar mass of the empirical formula (5[C5H5N] = 225 g/mol).
6. Divide the molar mass of the compound by the molar mass of the empirical formula to get the scaling factor:
- Scaling factor = 240 g/mol / 225 g/mol ≈ 1.07
7. Multiply the subscripts in the empirical formula by the scaling factor to get the molecular formula:
- C5H5N becomes C5.36H5.36N, which we round to C5.4H5.4N.
Therefore, the molecular formula of the dye is likely C5.4H5.4N.
To determine the molecular formula of the dye, we need to find the empirical formula first. The empirical formula gives the simplest ratio of elements in a compound.
1. Convert the percentage composition to grams:
- 75.95% C: (75.95 / 100) * 240 g/mol = 182.28 g C
- 17.72% N: (17.72 / 100) * 240 g/mol = 42.53 g N
- 6.33% H: (6.33 / 100) * 240 g/mol = 15.19 g H
2. Determine the number of moles for each element:
- Moles of C: 182.28 g / 12.011 g/mol = 15.18 moles
- Moles of N: 42.53 g / 14.007 g/mol = 3.04 moles
- Moles of H: 15.19 g / 1.008 g/mol = 15.08 moles
3. Divide each mole value by the smallest mole value to obtain a simple ratio:
- Divide by 3.04:
- C: 15.18 moles / 3.04 moles ≈ 5
- N: 3.04 moles / 3.04 moles = 1
- H: 15.08 moles / 3.04 moles ≈ 5
- The simple ratio is C5N1H5.
4. Determine the empirical formula mass:
- Empirical formula mass = (5 * molar mass of C) + (1 * molar mass of N) + (5 * molar mass of H)
- Empirical formula mass = (5 * 12.011 g/mol) + (1 * 14.007 g/mol) + (5 * 1.008 g/mol) ≈ 71.11 g/mol
5. Calculate the ratio of the molar mass to the empirical formula mass:
- Ratio = molar mass / empirical formula mass
- Ratio = 240 g/mol / 71.11 g/mol ≈ 3.38
6. Multiply the subscripts in the empirical formula by the ratio obtained:
- Molecular formula = (5 * 3.38) C + (1 * 3.38) N + (5 * 3.38) H
- Molecular formula = C16.9N3.38H16.9
However, we need to find the simplest whole number ratio for the molecular formula:
- Divide the subscripts by the smallest value (approximately 3.38)
- Dividing by 3.38:
- C: 16.9 / 3.38 ≈ 5
- N: 3.38 / 3.38 = 1
- H: 16.9 / 3.38 ≈ 5
Therefore, the molecular formula of the dye is C5N1H5, which simplifies to C5NH5.