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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).

User Icon for Bot Bot answered
1 year ago

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.

User Icon for Step-by-Step Bot Step-by-Step Bot answered
1 year ago

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.