An unknown organic compound contains carbon, hydrogen, and bromine only. The mass percentage of
C is 12.81% C. Bromine from 1.88 g of this compound has been completely precipitated as 3.78 g of AgBr.
The molar mass of unknown organic compound is 188 u. Determine the molecular formula of the unknown
Assume our whole sample weighs 100 grams.
C = 12.77 % = 12.77/100 = 12.77 g C
H = 1.60 % = 1.60 g H
100 g - 12.77g - 1.60 g = 85.63g = our bromine
Now that we know the element components of the unknown compound we have to find out what they are in moles.
C : 12.77 g C ( 1 mol C / 12.01 g C) = 1.06 mol C
H: 1.60 g H ( 1 mol H / 1.008 g H) = 1.59 mol = 1.5 mol H
Br: 85.63 g Br ( 1 mol Br / 79.904 g Br) = 1.07 mol Br
C : 1.06 mol/ 1.06 = 1 * 2 = 2
H : 1.59 mol/1.06 = 1.5 * 2 = 3
Br : 1.07 mol/ 1.06 = ~1 * 2= 2
therefore we get C2H3Br2. To double check, we find the molar mass of one unit of this. We get ~186.8 which is pretty close.
(12.011 * 2) + (1.008 * 3) + (79.904 * 2) = 186.854 grams per mole of C2H3Br2
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.
To determine the molecular formula of the unknown organic compound, we need to first calculate the number of moles of bromine present in the compound.
1. Calculate the number of moles of AgBr precipitated:
- Mass of AgBr = 3.78 g
- Molar mass of AgBr = 187.77 g/mol (107.87 g/mol for Ag + 79.9 g/mol for Br)
- Moles of AgBr = Mass of AgBr / Molar mass of AgBr
2. Since AgBr is formed by one mole of bromine reacting with one mole of Ag, the number of moles of bromine is equal to the number of moles of AgBr.
3. Determine the mass of bromine from the number of moles and the molar mass of bromine:
- Moles of bromine = Moles of AgBr
- Molar mass of bromine = 79.9 g/mol
- Mass of bromine = Moles of bromine * Molar mass of bromine
4. Calculate the mass of carbon:
- Given mass percentage of carbon = 12.81%
- Mass of carbon = mass of unknown organic compound * mass percentage of carbon
5. Calculate the mass of hydrogen:
- Mass of hydrogen = mass of unknown organic compound - (mass of carbon + mass of bromine)
6. Calculate the number of moles of carbon, hydrogen, and bromine:
- Moles of carbon = Mass of carbon / Molar mass of unknown organic compound
- Moles of hydrogen = Mass of hydrogen / Molar mass of unknown organic compound
- Moles of bromine = Mass of bromine / Molar mass of bromine
7. Determine the empirical formula:
- Divide the number of moles of each element by the smallest number of moles to obtain a simple ratio
- If necessary, multiply the subscripts to obtain whole numbers
8. Determine the molecular formula:
- Calculate the molar mass of the empirical formula
- Determine the ratio of the molar mass of the molecular formula to the molar mass of the empirical formula
- Multiply the subscripts of the empirical formula by this ratio to obtain the molecular formula
By following these steps, you should be able to determine the molecular formula of the unknown organic compound.