To determine the molecular formula of the unknown organic compound, we need to find the empirical formula first. The empirical formula gives the simplest whole number ratio of atoms in a compound.
1. Calculate the moles of AgBr precipitated:
- The molar mass of AgBr = 107.87 g/mol (from the periodic table)
- Moles of AgBr = mass of AgBr / molar mass of AgBr = 3.78 g / 107.87 g/mol = 0.035 mol
2. Calculate the moles of bromine in AgBr:
- AgBr contains one mole of bromine per mole of AgBr
- Moles of Br = 0.035 mol
3. Calculate the moles of bromine in the unknown compound:
- Since 1.88 g of the unknown compound yielded 0.035 mol of bromine, the molar mass of bromine in the unknown compound is:
- Molar mass of Br = mass of Br / moles of Br = 1.88 g / 0.035 mol = 53.71 g/mol
4. Calculate the mass of carbon in the unknown compound:
- Mass of C = mass percentage of C / 100 * molar mass of unknown compound
- Mass of C = 12.81% * 188 g/mol = 24.1 g
5. Calculate the moles of carbon in the unknown compound:
- Moles of C = mass of C / molar mass of C = 24.1 g / 12.01 g/mol = 2.005 mol
6. Calculate the moles of hydrogen in the unknown compound:
- Since the unknown compound contains only carbon, hydrogen, and bromine, we can assume that the remaining mass percentage is hydrogen.
- Mass percentage of H = 100% - mass percentage of C - mass percentage of Br = 100% - 12.81% - (3.78 g / 1.88 g/mol * 100%) = 83.41%
- Mass of H = mass percentage of H / 100 * molar mass of unknown compound = 83.41% * 188 g/mol = 156.91 g
7. Calculate the moles of hydrogen in the unknown compound:
- Moles of H = mass of H / molar mass of H = 156.91 g / 1.01 g/mol = 155.35 mol
8. Divide the moles of each element by the smallest mole value calculated above (in this case, H):
- Moles of C / Moles of H = 2.005 mol / 155.35 mol ≈ 0.0129
- Moles of Br / Moles of H = 0.035 mol / 155.35 mol ≈ 0.00023
9. Multiply each of the moles obtained above by the smallest whole number that gives whole number ratios:
- Moles of C / Moles of H = 0.0129 * 100 ≈ 1.29 ≈ 1
- Moles of Br / Moles of H = 0.00023 * 1000 ≈ 0.23 ≈ 1 (rounded to the nearest whole number)
10. The empirical formula of the compound is CHBr.
To determine the molecular formula, we need to find the molecular mass of this empirical formula and compare it to the given molar mass (188 g/mol).
11. Calculate the molecular mass of the empirical formula:
- C: 1 atom * 12.01 g/mol = 12.01 g/mol
- H: 1 atom * 1.01 g/mol = 1.01 g/mol
- Br: 1 atom * 79.90 g/mol = 79.90 g/mol
- Molecular mass = 12.01 g/mol + 1.01 g/mol + 79.90 g/mol = 93.92 g/mol.
12. Calculate the factor by which the empirical formula needs to be multiplied to give the molar mass:
- Factor = molar mass / molecular mass = 188 g/mol / 93.92 g/mol ≈ 2
13. Multiply the subscripts in the empirical formula by the factor calculated above:
- Molecular formula = (CHBr) * 2 = C2H2Br2
Therefore, the molecular formula of the unknown organic compound is C2H2Br2.