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).
C10H15N3
C15H10N3
C15H15N3
C15H12N3
The first step is to find the empirical formula by dividing the percent composition by the respective atomic/molecular masses and finding the smallest whole-number ratio of the elements. The molar ratios will give the subscripts of the empirical formula.
For carbon:
75.95 g C / 12.011 g/mol C = 6.324 mol C
For nitrogen:
17.72 g N / 14.007 g/mol N = 1.262 mol N
For hydrogen:
6.33 g H / 1.008 g/mol H = 6.286 mol H
The smallest whole-number ratio of these molar ratios is approximately 1:1:1. Therefore, the empirical formula is C1H1N1, which can be simplified to just "CHN".
Next, we need to find the molecular formula by determining how many empirical formula units are in the molecule. To do this, we divide the molar mass of the compound by the empirical formula mass.
Empirical formula mass = 12.011 + 1.008 + 14.007 = 27.026 g/mol
Molecule formula units = 240 g/mol / 27.026 g/mol = 8.88
The molecular formula is then obtained by multiplying the subscripts in the empirical formula by 8.88:
C8.88H8.88N8.88
Simplifying (dividing by 8.88 and rounding to the nearest whole number), we get:
C1H1N1
Therefore, the molecular formula is the same as the empirical formula: CHN.
To determine the molecular formula of the dye, we need to calculate the empirical formula and then determine the molecular formula using the molar mass.
1. Start by assuming a 100g sample of the compound, which allows us to convert the percentages into grams.
Percent composition:
C: 75.95g
N: 17.72g
H: 6.33g
2. Convert the grams of each element into moles by dividing by their molar masses.
Molar mass:
C: 12.011 g/mol
N: 14.007 g/mol
H: 1.008 g/mol
Moles:
Moles of C = 75.95 g / 12.011 g/mol = 6.321 mol
Moles of N = 17.72 g / 14.007 g/mol = 1.265 mol
Moles of H = 6.33 g / 1.008 g/mol = 6.286 mol
3. Divide each number of moles by the smallest number of moles (in this case, 1.265 mol) to get the simplest possible whole-number ratio.
C: 6.321 mol / 1.265 mol = 4.993 ≈ 5
N: 1.265 mol / 1.265 mol = 1
H: 6.286 mol / 1.265 mol = 4.964 ≈ 5
The empirical formula is C5H5N.
4. Now, calculate the molar mass of the empirical formula by adding up the molar masses of each element.
Molar mass:
C (12.011 g/mol) × 5 = 60.055 g/mol
H (1.008 g/mol) × 5 = 5.04 g/mol
N (14.007 g/mol) × 1 = 14.007 g/mol
Molar mass of empirical formula: 60.055 g/mol + 5.04 g/mol + 14.007 g/mol = 79.102 g/mol
5. Finally, compare the molar mass of the empirical formula (79.102 g/mol) with the given molar mass (240 g/mol).
240 g/mol / 79.102 g/mol = 3
The ratio of the molar mass to the empirical formula mass is approximately 3, which means the molecular formula is three times the empirical formula.
C5H5N × 3 = C15H15N3
So, the molecular formula of the dye is C15H15N3.