What is the molecular formula of a compound with percent composition 26% aluminum, 27% silicon,46% oxygen and 2% hydrogen and a molar mass of 205 g/mol?
A) Al53si55O94H4
B) Al2Si206H4
C) Alsi203h4
D) ALSiO3H2
2% H = 4.1/1 = H4
46%O = 94.3/16 = O6
Looks like B to me
@oobleck. This procedure I've never seen before. Time wise it sure speeds up the calculated answer. It works because of two approximations plus a luxury we allow ourselves.
1. We assume the molar mass of 205 is correct. It is not 205 but it's close.
2. Since the molar mass is just close, then we don't get EXACT whole number so we fudge a little, call that some word(s) that excuses us (experimental error comes to mind), and
3. Use the luxury of rounding up or down to make a whole number which often stretches the boundary of what we can call experimental error.
We can't get away with the excuse for high accuracy. Only a few of those atomic masses in the periodic table come from a chemist anyway. Mass spectrometry beats chemical every day of the week for those values in the periodic table.
To determine the molecular formula of a compound given its percent composition and molar mass, we need to first convert the percent composition to moles.
1. Start by assuming we have 100 grams of the compound.
- Based on the percent composition, we would have:
26 grams of aluminum (Al)
27 grams of silicon (Si)
46 grams of oxygen (O)
2 grams of hydrogen (H)
2. Next, calculate the number of moles of each element:
- Divide each mass by the molar mass of the respective element:
- Aluminum (Al): 26 g / 27 g/mol ≈ 0.963 moles
- Silicon (Si): 27 g / 28 g/mol ≈ 0.964 moles
- Oxygen (O): 46 g / 16 g/mol ≈ 2.875 moles
- Hydrogen (H): 2 g / 1 g/mol ≈ 2 moles
3. Determine the simplest whole number ratio of moles.
- Divide each number of moles by the smallest number of moles (in this case, 0.963 moles):
- Aluminum (Al): 0.963 moles / 0.963 moles ≈ 1 mole
- Silicon (Si): 0.964 moles / 0.963 moles ≈ 1 mole
- Oxygen (O): 2.875 moles / 0.963 moles ≈ 2.988 moles ≈ 3 moles
- Hydrogen (H): 2 moles / 0.963 moles ≈ 2.075 moles ≈ 2 moles
4. Write the empirical formula using the whole number ratios:
- Empirical formula: AlSiO3H2
5. Finally, determine the molecular formula by considering the molar mass.
- Calculate the molar mass of the empirical formula:
- Al: 1 * atomic mass of Al = 1 * 27 g/mol = 27 g/mol
- Si: 1 * atomic mass of Si = 1 * 28 g/mol = 28 g/mol
- O: 3 * atomic mass of O = 3 * 16 g/mol = 48 g/mol
- H: 2 * atomic mass of H = 2 * 1 g/mol = 2 g/mol
- Total molar mass of the empirical formula: 27 g/mol + 28 g/mol + 48 g/mol + 2 g/mol = 105 g/mol
- Divide the molar mass of the compound by the molar mass of the empirical formula:
- 205 g/mol / 105 g/mol = 1.952 ≈ 2
- Multiply each atom's subscript in the empirical formula by the whole number ratio obtained (2):
- Al2Si2O6H4
Given the options provided, the correct molecular formula of the compound would be B) Al2Si2O6H4.